%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET246-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 : Sun May  5 09:12:59 EDT 2024

% Result   : Unsatisfiable 25.83s 4.09s
% Output   : Refutation 26.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      : 1471
% Syntax   : Number of formulae    : 4703 ( 136 unt;   0 def)
%            Number of atoms       : 17339 (1629 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives : 22520 (9884   ~;11269   |;   0   &)
%                                         (1367 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :   28 (   3 avg)
%            Number of predicates  : 1379 (1377 usr;1368 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;  14 con; 0-3 aty)
%            Number of variables   : 6280 (6280   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f33292,plain,
    $false,
    inference(avatar_sat_refutation,[],[f208,f213,f218,f222,f227,f231,f235,f239,f243,f248,f253,f257,f261,f266,f270,f274,f278,f282,f286,f290,f294,f298,f302,f307,f312,f317,f322,f326,f330,f334,f338,f342,f346,f350,f354,f358,f362,f375,f379,f383,f388,f392,f397,f427,f431,f435,f442,f447,f451,f455,f459,f463,f467,f471,f480,f503,f507,f511,f516,f521,f529,f533,f537,f542,f546,f555,f559,f563,f567,f571,f577,f586,f590,f594,f598,f613,f617,f628,f632,f641,f645,f650,f654,f664,f669,f673,f677,f682,f686,f691,f700,f704,f710,f726,f731,f735,f739,f743,f749,f754,f761,f766,f770,f788,f798,f813,f820,f824,f828,f832,f893,f897,f901,f924,f928,f937,f947,f956,f960,f964,f968,f972,f977,f1013,f1017,f1021,f1025,f1029,f1033,f1092,f1096,f1105,f1109,f1113,f1117,f1164,f1168,f1172,f1176,f1180,f1230,f1239,f1248,f1252,f1256,f1287,f1291,f1295,f1299,f1303,f1307,f1325,f1329,f1360,f1370,f1374,f1378,f1382,f1386,f1453,f1457,f1461,f1465,f1474,f1482,f1486,f1524,f1532,f1539,f1552,f1558,f1565,f1587,f1593,f1606,f1611,f1623,f1629,f1648,f1665,f1669,f1714,f1720,f1754,f1782,f1802,f1807,f1817,f1821,f1877,f1915,f1922,f1932,f1944,f1954,f2003,f2007,f2035,f2065,f2076,f2089,f2102,f2106,f2119,f2129,f2133,f2146,f2148,f2232,f2236,f2266,f2270,f2274,f2286,f2296,f2312,f2321,f2327,f2352,f2360,f2366,f2371,f2375,f2379,f2383,f2391,f2396,f2401,f2405,f2413,f2421,f2429,f2433,f2443,f2453,f2464,f2468,f2473,f2477,f2481,f2499,f2506,f2515,f2519,f2523,f2539,f2545,f2549,f2558,f2578,f2618,f2710,f2714,f2722,f2728,f2732,f2734,f2747,f2751,f2755,f2759,f2767,f2830,f2834,f2838,f2842,f2846,f2851,f2856,f2879,f2933,f2944,f2951,f2958,f2963,f2968,f2972,f2976,f3065,f3076,f3084,f3089,f3094,f3099,f3120,f3141,f3160,f3164,f3168,f3172,f3176,f3180,f3184,f3190,f3194,f3199,f3206,f3210,f3216,f3224,f3233,f3237,f3241,f3245,f3263,f3332,f3346,f3350,f3354,f3359,f3483,f3491,f3497,f3503,f3512,f3519,f3523,f3527,f3531,f3535,f3539,f3544,f3549,f3553,f3557,f3561,f3565,f3570,f3574,f3653,f3657,f3790,f3794,f3798,f3802,f3806,f3811,f3815,f3819,f3823,f3827,f3831,f3835,f3839,f3843,f3847,f3851,f3855,f3859,f3863,f3867,f3871,f4239,f4243,f4247,f4251,f4255,f4259,f4267,f4271,f4275,f4279,f4283,f4288,f4292,f4301,f4306,f4310,f4634,f4681,f4799,f4803,f4809,f4814,f4841,f4845,f4849,f4853,f4857,f4862,f4867,f4871,f4875,f4879,f4887,f4891,f4904,f4908,f5198,f5202,f5206,f5518,f5527,f5534,f5539,f5549,f5555,f5560,f5564,f5572,f5578,f5586,f5590,f5595,f5599,f5603,f5607,f5611,f5616,f5627,f5692,f5863,f5867,f5928,f5935,f5939,f5944,f5948,f5952,f5957,f5962,f5966,f5970,f5974,f5987,f6067,f6071,f6229,f6234,f6238,f6243,f6255,f6259,f6263,f6271,f6277,f6281,f6285,f6289,f6448,f6453,f6457,f6461,f6465,f6470,f6475,f6479,f6483,f6487,f6491,f6495,f6499,f6503,f6511,f6643,f6647,f6740,f6858,f6863,f6867,f6871,f6875,f6879,f6883,f6887,f6891,f6895,f6923,f7047,f7051,f7055,f7059,f7063,f7067,f7076,f7080,f7085,f7089,f7093,f7299,f7371,f7375,f7379,f7383,f7396,f7404,f7409,f7414,f7430,f7439,f7444,f7448,f7452,f7456,f7460,f7464,f7468,f7472,f8136,f8144,f8148,f8152,f8156,f8160,f8186,f8197,f8204,f8215,f8219,f8223,f8227,f8231,f8235,f8239,f8246,f8251,f8255,f8265,f8279,f8283,f8287,f8291,f8295,f8644,f8656,f8660,f8664,f8668,f8672,f8798,f8802,f8810,f8814,f8818,f8827,f8834,f8968,f8972,f8976,f8981,f8985,f9052,f9075,f9079,f9086,f9093,f9106,f9111,f9116,f9122,f9171,f9175,f9179,f9184,f9189,f9193,f9197,f9201,f9313,f9319,f9323,f9330,f9337,f9342,f9347,f9354,f9359,f9367,f9379,f9383,f9497,f9501,f9509,f9628,f9707,f9714,f9721,f9725,f9732,f9736,f9740,f9744,f9757,f9798,f9802,f9806,f9810,f9814,f9818,f9822,f9934,f9948,f9954,f9962,f9968,f9976,f9981,f9985,f9989,f9993,f9997,f10001,f10005,f10009,f10013,f10017,f10021,f10048,f10360,f10367,f10371,f10375,f10379,f10479,f10484,f10488,f10492,f10500,f10533,f10537,f10541,f10628,f10718,f10888,f10889,f11011,f11016,f11242,f11246,f11251,f11255,f11259,f11263,f11267,f11647,f11651,f11655,f11660,f11664,f11682,f11686,f11748,f11786,f11790,f11824,f11831,f11836,f11842,f11851,f11857,f11863,f11874,f11878,f11896,f11900,f11904,f11932,f11936,f11940,f11969,f11973,f11977,f12065,f12069,f12073,f12085,f12123,f12128,f12133,f12137,f12145,f12151,f12155,f12159,f12163,f12507,f12512,f12570,f12576,f12580,f12584,f12588,f12950,f12954,f12958,f12962,f12966,f12970,f12974,f13049,f13053,f13346,f13370,f13437,f13441,f13472,f13476,f13480,f13498,f13502,f13637,f13641,f13645,f13660,f13664,f13752,f13756,f13760,f13775,f13779,f13783,f13787,f14089,f14152,f14156,f14160,f14164,f14406,f14410,f14414,f14418,f14496,f14646,f14694,f14702,f14709,f14717,f14811,f14844,f14848,f14852,f14857,f15117,f15121,f15301,f15323,f15331,f15336,f15345,f15350,f15368,f15377,f15383,f15387,f15391,f15399,f15404,f15408,f15610,f15614,f15618,f15644,f15648,f15653,f15658,f15662,f15666,f15670,f15681,f15685,f15769,f15773,f15832,f15839,f15873,f15950,f15964,f16027,f16035,f16040,f16048,f16053,f16205,f16209,f16213,f16309,f16313,f16324,f16334,f16355,f16363,f16453,f16457,f16479,f16519,f16523,f16586,f16590,f16598,f16604,f16676,f16681,f16685,f16873,f16878,f16883,f16887,f16892,f16897,f16901,f16905,f16930,f16982,f17100,f17104,f17108,f17112,f17121,f17125,f17173,f17218,f17259,f17263,f17267,f17286,f17290,f17343,f17351,f17359,f17363,f17367,f17509,f17513,f17517,f17640,f17671,f17700,f17722,f17726,f17742,f17746,f17750,f17754,f17800,f17804,f17808,f17812,f17816,f17820,f17824,f18130,f18134,f18138,f18220,f18224,f18228,f18416,f18420,f18466,f18498,f18502,f18637,f18641,f18673,f18705,f18709,f18754,f18758,f18762,f18766,f18770,f18774,f18819,f18909,f18983,f18987,f18991,f18995,f18999,f19003,f19007,f19114,f19118,f19361,f19365,f19369,f19391,f19436,f19440,f19444,f19469,f19473,f19477,f19481,f19485,f19780,f19784,f19830,f19880,f19885,f19889,f19893,f19934,f19983,f20003,f20008,f20012,f20016,f20038,f20072,f20077,f20081,f20119,f20263,f20288,f20292,f20346,f20382,f20386,f20420,f20425,f20456,f20460,f20464,f20468,f20472,f20476,f20480,f20484,f20488,f20681,f20698,f20708,f20713,f20730,f20760,f20790,f20809,f20850,f20891,f20924,f20963,f20967,f21002,f21008,f21014,f21019,f21023,f21028,f21033,f21038,f21042,f21047,f21052,f21056,f21060,f21064,f21069,f21073,f21077,f21082,f21087,f21091,f21096,f21100,f21104,f21108,f21112,f21116,f21120,f21124,f21128,f21132,f21136,f21181,f21185,f21189,f21193,f21197,f21202,f21207,f21212,f21217,f21222,f21227,f21343,f21952,f22043,f22049,f22075,f22076,f22077,f22078,f22079,f22429,f22455,f22461,f22470,f22474,f22478,f22483,f22496,f22500,f22504,f22508,f22512,f22517,f22521,f22525,f22529,f22533,f22537,f22541,f22546,f22550,f22555,f22559,f22573,f22577,f22581,f22844,f23574,f23578,f23582,f23587,f23591,f23596,f23600,f23604,f23618,f23622,f23626,f23631,f23636,f23640,f23644,f23649,f23654,f23658,f23920,f23924,f23929,f23933,f23938,f23942,f23946,f23950,f23954,f23958,f23963,f23968,f23972,f23976,f23980,f23984,f23988,f23992,f23996,f24000,f24004,f24013,f24018,f24023,f25284,f25366,f25370,f25374,f25379,f25386,f25395,f25402,f25407,f25420,f25429,f25445,f25449,f25453,f25457,f25461,f25465,f25469,f25473,f25477,f25481,f25497,f25501,f25505,f25510,f25514,f25518,f25523,f25527,f25531,f25535,f25541,f25545,f25550,f25554,f25558,f25563,f25568,f25572,f25577,f25590,f25595,f25601,f25607,f25611,f25615,f25619,f25740,f26121,f26498,f26791,f26795,f26802,f27214,f27218,f27222,f27226,f27230,f27234,f27238,f27242,f27246,f27377,f27381,f27386,f27390,f27394,f27398,f27402,f27559,f27587,f27591,f27595,f27599,f27603,f27607,f27611,f27615,f27620,f27624,f27628,f27632,f27636,f27640,f27646,f27652,f27658,f27664,f27669,f27675,f27679,f27684,f27689,f27693,f27697,f27701,f27705,f27709,f27713,f27717,f27722,f27726,f27734,f27739,f27746,f27955,f27959,f27963,f27968,f27972,f27976,f27980,f27988,f29498,f29502,f29506,f29510,f29516,f29520,f29524,f29528,f29533,f29541,f29552,f29557,f29561,f29566,f29570,f29574,f29578,f29582,f29586,f29590,f29594,f29598,f29602,f29606,f29611,f29615,f29619,f29623,f29627,f29631,f29635,f29639,f29643,f29647,f29652,f29657,f29662,f29666,f29670,f29674,f29678,f29682,f29686,f29690,f29694,f29699,f29703,f29707,f29711,f29715,f29719,f29723,f29727,f29731,f29743,f29748,f29752,f29756,f29760,f29764,f29831,f30255,f30624,f31049,f31809,f31813,f31818,f31824,f31828,f31836,f31840,f31849,f31856,f31861,f31867,f31872,f31877,f31881,f31885,f31889,f31893,f31897,f31901,f31905,f31909,f31913,f31917,f32031,f32033,f32048,f32052,f32056,f32060,f32064,f32068,f32072,f32240,f32244,f32248,f32252,f32256,f32260,f32264,f32268,f32328,f32332,f32734,f33291]) ).

fof(f33291,plain,
    ( ~ spl0_952
    | spl0_1365 ),
    inference(avatar_contradiction_clause,[],[f33290]) ).

fof(f33290,plain,
    ( $false
    | ~ spl0_952
    | spl0_1365 ),
    inference(trivial_inequality_removal,[],[f33289]) ).

fof(f33289,plain,
    ( null_class != null_class
    | ~ spl0_952
    | spl0_1365 ),
    inference(superposition,[],[f32327,f18998]) ).

fof(f18998,plain,
    ( ! [X0] : null_class = intersection(X0,null_class)
    | ~ spl0_952 ),
    inference(avatar_component_clause,[],[f18997]) ).

fof(f18997,plain,
    ( spl0_952
  <=> ! [X0] : null_class = intersection(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f32327,plain,
    ( null_class != intersection(xr,null_class)
    | spl0_1365 ),
    inference(avatar_component_clause,[],[f32325]) ).

fof(f32325,plain,
    ( spl0_1365
  <=> null_class = intersection(xr,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).

fof(f32734,plain,
    ( ~ spl0_1367
    | spl0_1
    | ~ spl0_1337 ),
    inference(avatar_split_clause,[],[f32074,f31875,f205,f32731]) ).

fof(f32731,plain,
    ( spl0_1367
  <=> null_class = intersection(null_class,xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).

fof(f205,plain,
    ( spl0_1
  <=> null_class = intersection(cross_product(null_class,y),xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f31875,plain,
    ( spl0_1337
  <=> ! [X0] : null_class = cross_product(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).

fof(f32074,plain,
    ( null_class != intersection(null_class,xr)
    | spl0_1
    | ~ spl0_1337 ),
    inference(superposition,[],[f207,f31876]) ).

fof(f31876,plain,
    ( ! [X0] : null_class = cross_product(null_class,X0)
    | ~ spl0_1337 ),
    inference(avatar_component_clause,[],[f31875]) ).

fof(f207,plain,
    ( null_class != intersection(cross_product(null_class,y),xr)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f205]) ).

fof(f32332,plain,
    ( spl0_1366
    | ~ spl0_237
    | ~ spl0_1336 ),
    inference(avatar_split_clause,[],[f31873,f31870,f2324,f32330]) ).

fof(f32330,plain,
    ( spl0_1366
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).

fof(f2324,plain,
    ( spl0_237
  <=> identity_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f31870,plain,
    ( spl0_1336
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).

fof(f31873,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_237
    | ~ spl0_1336 ),
    inference(forward_demodulation,[],[f31871,f2326]) ).

fof(f2326,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_237 ),
    inference(avatar_component_clause,[],[f2324]) ).

fof(f31871,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_1336 ),
    inference(avatar_component_clause,[],[f31870]) ).

fof(f32328,plain,
    ( ~ spl0_1365
    | spl0_59
    | ~ spl0_1337 ),
    inference(avatar_split_clause,[],[f32073,f31875,f513,f32325]) ).

fof(f513,plain,
    ( spl0_59
  <=> null_class = intersection(xr,cross_product(null_class,y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f32073,plain,
    ( null_class != intersection(xr,null_class)
    | spl0_59
    | ~ spl0_1337 ),
    inference(superposition,[],[f515,f31876]) ).

fof(f515,plain,
    ( null_class != intersection(xr,cross_product(null_class,y))
    | spl0_59 ),
    inference(avatar_component_clause,[],[f513]) ).

fof(f32268,plain,
    ( spl0_1364
    | ~ spl0_270
    | ~ spl0_744 ),
    inference(avatar_split_clause,[],[f12789,f12573,f2517,f32266]) ).

fof(f32266,plain,
    ( spl0_1364
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).

fof(f2517,plain,
    ( spl0_270
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f12573,plain,
    ( spl0_744
  <=> 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_744])]) ).

fof(f12789,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270
    | ~ spl0_744 ),
    inference(superposition,[],[f2518,f12575]) ).

fof(f12575,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_744 ),
    inference(avatar_component_clause,[],[f12573]) ).

fof(f2518,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270 ),
    inference(avatar_component_clause,[],[f2517]) ).

fof(f32264,plain,
    ( spl0_1363
    | ~ spl0_270
    | ~ spl0_742 ),
    inference(avatar_split_clause,[],[f12711,f12509,f2517,f32262]) ).

fof(f32262,plain,
    ( spl0_1363
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).

fof(f12509,plain,
    ( spl0_742
  <=> 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_742])]) ).

fof(f12711,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270
    | ~ spl0_742 ),
    inference(superposition,[],[f2518,f12511]) ).

fof(f12511,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_742 ),
    inference(avatar_component_clause,[],[f12509]) ).

fof(f32260,plain,
    ( spl0_1362
    | ~ spl0_68
    | ~ spl0_628 ),
    inference(avatar_split_clause,[],[f9634,f9623,f561,f32258]) ).

fof(f32258,plain,
    ( spl0_1362
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(first(unordered_pair(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).

fof(f561,plain,
    ( spl0_68
  <=> ! [X0,X3,X2,X1] :
        ( member(X2,X0)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f9623,plain,
    ( spl0_628
  <=> ! [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_628])]) ).

fof(f9634,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(first(unordered_pair(X0,X1)),X2) )
    | ~ spl0_68
    | ~ spl0_628 ),
    inference(superposition,[],[f562,f9624]) ).

fof(f9624,plain,
    ( ! [X2,X3] : unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3)))))
    | ~ spl0_628 ),
    inference(avatar_component_clause,[],[f9623]) ).

fof(f562,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f561]) ).

fof(f32256,plain,
    ( spl0_1361
    | ~ spl0_67
    | ~ spl0_628 ),
    inference(avatar_split_clause,[],[f9633,f9623,f557,f32254]) ).

fof(f32254,plain,
    ( spl0_1361
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(second(unordered_pair(X0,X1)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).

fof(f557,plain,
    ( spl0_67
  <=> ! [X0,X3,X2,X1] :
        ( member(X3,X1)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f9633,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(X0,X1),cross_product(X2,X3))
        | member(second(unordered_pair(X0,X1)),X3) )
    | ~ spl0_67
    | ~ spl0_628 ),
    inference(superposition,[],[f558,f9624]) ).

fof(f558,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | member(X3,X1) )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f557]) ).

fof(f32252,plain,
    ( spl0_1360
    | ~ spl0_330
    | ~ spl0_410 ),
    inference(avatar_split_clause,[],[f5125,f4847,f3231,f32250]) ).

fof(f32250,plain,
    ( spl0_1360
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).

fof(f3231,plain,
    ( spl0_330
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f4847,plain,
    ( spl0_410
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f5125,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2))))
    | ~ spl0_330
    | ~ spl0_410 ),
    inference(duplicate_literal_removal,[],[f5089]) ).

fof(f5089,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2))))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X0,intersection(X1,X2)))) )
    | ~ spl0_330
    | ~ spl0_410 ),
    inference(resolution,[],[f4848,f3232]) ).

fof(f3232,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_330 ),
    inference(avatar_component_clause,[],[f3231]) ).

fof(f4848,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1)
        | subclass(intersection(X0,intersection(X1,X2)),X3) )
    | ~ spl0_410 ),
    inference(avatar_component_clause,[],[f4847]) ).

fof(f32248,plain,
    ( spl0_1359
    | ~ spl0_330
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f5067,f4843,f3231,f32246]) ).

fof(f32246,plain,
    ( spl0_1359
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).

fof(f4843,plain,
    ( spl0_409
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f5067,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2))))
    | ~ spl0_330
    | ~ spl0_409 ),
    inference(duplicate_literal_removal,[],[f5031]) ).

fof(f5031,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2))))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X0,intersection(X1,X2)))) )
    | ~ spl0_330
    | ~ spl0_409 ),
    inference(resolution,[],[f4844,f3232]) ).

fof(f4844,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2)
        | subclass(intersection(X0,intersection(X1,X2)),X3) )
    | ~ spl0_409 ),
    inference(avatar_component_clause,[],[f4843]) ).

fof(f32244,plain,
    ( spl0_1358
    | ~ spl0_330
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f5008,f4839,f3231,f32242]) ).

fof(f32242,plain,
    ( spl0_1358
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).

fof(f4839,plain,
    ( spl0_408
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f5008,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2)))
    | ~ spl0_330
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f4972]) ).

fof(f4972,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(intersection(X0,X1),X2))) )
    | ~ spl0_330
    | ~ spl0_408 ),
    inference(resolution,[],[f4840,f3232]) ).

fof(f4840,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0)
        | subclass(intersection(intersection(X0,X1),X2),X3) )
    | ~ spl0_408 ),
    inference(avatar_component_clause,[],[f4839]) ).

fof(f32240,plain,
    ( spl0_1357
    | ~ spl0_330
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f4950,f4812,f3231,f32238]) ).

fof(f32238,plain,
    ( spl0_1357
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).

fof(f4812,plain,
    ( spl0_407
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f4950,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2)))
    | ~ spl0_330
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f4914]) ).

fof(f4914,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(intersection(X0,X1),X2))) )
    | ~ spl0_330
    | ~ spl0_407 ),
    inference(resolution,[],[f4813,f3232]) ).

fof(f4813,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1)
        | subclass(intersection(intersection(X0,X1),X2),X3) )
    | ~ spl0_407 ),
    inference(avatar_component_clause,[],[f4812]) ).

fof(f32072,plain,
    ( spl0_1356
    | ~ spl0_76
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4466,f4257,f610,f32070]) ).

fof(f32070,plain,
    ( spl0_1356
  <=> ! [X0] :
        ( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).

fof(f610,plain,
    ( spl0_76
  <=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f4257,plain,
    ( spl0_390
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f4466,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
        | null_class = intersection(X0,subset_relation) )
    | ~ spl0_76
    | ~ spl0_390 ),
    inference(superposition,[],[f4258,f612]) ).

fof(f612,plain,
    ( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f610]) ).

fof(f4258,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X1)
        | null_class = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f4257]) ).

fof(f32068,plain,
    ( spl0_1355
    | ~ spl0_76
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4383,f4249,f610,f32066]) ).

fof(f32066,plain,
    ( spl0_1355
  <=> ! [X0] :
        ( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).

fof(f4249,plain,
    ( spl0_388
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f4383,plain,
    ( ! [X0] :
        ( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
        | null_class = intersection(subset_relation,X0) )
    | ~ spl0_76
    | ~ spl0_388 ),
    inference(superposition,[],[f4250,f612]) ).

fof(f4250,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X0)
        | null_class = intersection(intersection(X0,X1),X2) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f4249]) ).

fof(f32064,plain,
    ( spl0_1354
    | ~ spl0_20
    | ~ spl0_383 ),
    inference(avatar_split_clause,[],[f4192,f3865,f288,f32062]) ).

fof(f32062,plain,
    ( spl0_1354
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | ~ member(X0,compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).

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

fof(f3865,plain,
    ( spl0_383
  <=> ! [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_383])]) ).

fof(f4192,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | ~ member(X0,compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))) )
    | ~ spl0_20
    | ~ spl0_383 ),
    inference(resolution,[],[f3866,f289]) ).

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

fof(f3866,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_383 ),
    inference(avatar_component_clause,[],[f3865]) ).

fof(f32060,plain,
    ( spl0_1353
    | ~ spl0_14
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f4058,f3829,f263,f32058]) ).

fof(f32058,plain,
    ( spl0_1353
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,domain_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).

fof(f263,plain,
    ( spl0_14
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f3829,plain,
    ( spl0_374
  <=> ! [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_374])]) ).

fof(f4058,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,domain_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_14
    | ~ spl0_374 ),
    inference(resolution,[],[f3830,f265]) ).

fof(f265,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f263]) ).

fof(f3830,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X1,X3)
        | subclass(X0,X2)
        | ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_374 ),
    inference(avatar_component_clause,[],[f3829]) ).

fof(f32056,plain,
    ( spl0_1352
    | ~ spl0_13
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f4052,f3829,f259,f32054]) ).

fof(f32054,plain,
    ( spl0_1352
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,omega)
        | member(not_subclass_element(X0,X1),X2)
        | ~ inductive(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).

fof(f259,plain,
    ( spl0_13
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f4052,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,omega)
        | member(not_subclass_element(X0,X1),X2)
        | ~ inductive(X2) )
    | ~ spl0_13
    | ~ spl0_374 ),
    inference(resolution,[],[f3830,f260]) ).

fof(f260,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f259]) ).

fof(f32052,plain,
    ( spl0_1351
    | ~ spl0_11
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f4051,f3829,f250,f32050]) ).

fof(f32050,plain,
    ( spl0_1351
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,successor_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).

fof(f250,plain,
    ( spl0_11
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f4051,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,successor_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_374 ),
    inference(resolution,[],[f3830,f252]) ).

fof(f252,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f32048,plain,
    ( spl0_1350
    | ~ spl0_10
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f4043,f3829,f245,f32046]) ).

fof(f32046,plain,
    ( spl0_1350
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,element_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).

fof(f245,plain,
    ( spl0_10
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f4043,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,element_relation)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_10
    | ~ spl0_374 ),
    inference(resolution,[],[f3830,f247]) ).

fof(f247,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f245]) ).

fof(f32033,plain,
    ( ~ spl0_4
    | spl0_1348 ),
    inference(avatar_contradiction_clause,[],[f32032]) ).

fof(f32032,plain,
    ( $false
    | ~ spl0_4
    | spl0_1348 ),
    inference(resolution,[],[f32026,f221]) ).

fof(f221,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f220]) ).

fof(f220,plain,
    ( spl0_4
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f32026,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),universal_class)
    | spl0_1348 ),
    inference(avatar_component_clause,[],[f32024]) ).

fof(f32024,plain,
    ( spl0_1348
  <=> subclass(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).

fof(f32031,plain,
    ( ~ spl0_1348
    | spl0_1349
    | ~ spl0_359
    | ~ spl0_367 ),
    inference(avatar_split_clause,[],[f3886,f3800,f3563,f32028,f32024]) ).

fof(f32028,plain,
    ( spl0_1349
  <=> subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).

fof(f3563,plain,
    ( spl0_359
  <=> ! [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_359])]) ).

fof(f3800,plain,
    ( spl0_367
  <=> ! [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_367])]) ).

fof(f3886,plain,
    ( subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation))
    | ~ subclass(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ spl0_359
    | ~ spl0_367 ),
    inference(duplicate_literal_removal,[],[f3883]) ).

fof(f3883,plain,
    ( subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation))
    | subclass(complement(cross_product(universal_class,universal_class)),complement(subset_relation))
    | ~ subclass(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ spl0_359
    | ~ spl0_367 ),
    inference(resolution,[],[f3801,f3564]) ).

fof(f3564,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_359 ),
    inference(avatar_component_clause,[],[f3563]) ).

fof(f3801,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation)
        | subclass(complement(cross_product(universal_class,universal_class)),X0) )
    | ~ spl0_367 ),
    inference(avatar_component_clause,[],[f3800]) ).

fof(f31917,plain,
    ( spl0_1347
    | ~ spl0_104
    | ~ spl0_237
    | ~ spl0_359 ),
    inference(avatar_split_clause,[],[f3780,f3563,f2324,f768,f31915]) ).

fof(f31915,plain,
    ( spl0_1347
  <=> ! [X0] :
        ( member(not_subclass_element(X0,complement(singleton_relation)),subset_relation)
        | subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).

fof(f768,plain,
    ( spl0_104
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f3780,plain,
    ( ! [X0] :
        ( member(not_subclass_element(X0,complement(singleton_relation)),subset_relation)
        | subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_104
    | ~ spl0_237
    | ~ spl0_359 ),
    inference(forward_demodulation,[],[f3779,f2326]) ).

fof(f3779,plain,
    ( ! [X0] :
        ( subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(identity_relation)),subset_relation) )
    | ~ spl0_104
    | ~ spl0_237
    | ~ spl0_359 ),
    inference(forward_demodulation,[],[f3769,f2326]) ).

fof(f3769,plain,
    ( ! [X0] :
        ( subclass(X0,complement(identity_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(identity_relation)),subset_relation) )
    | ~ spl0_104
    | ~ spl0_359 ),
    inference(resolution,[],[f3564,f769]) ).

fof(f769,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_104 ),
    inference(avatar_component_clause,[],[f768]) ).

fof(f31913,plain,
    ( spl0_1346
    | ~ spl0_103
    | ~ spl0_359 ),
    inference(avatar_split_clause,[],[f3771,f3563,f764,f31911]) ).

fof(f31911,plain,
    ( spl0_1346
  <=> ! [X0] :
        ( subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).

fof(f764,plain,
    ( spl0_103
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f3771,plain,
    ( ! [X0] :
        ( subclass(X0,complement(singleton_relation))
        | ~ subclass(X0,universal_class)
        | member(not_subclass_element(X0,complement(singleton_relation)),element_relation) )
    | ~ spl0_103
    | ~ spl0_359 ),
    inference(resolution,[],[f3564,f765]) ).

fof(f765,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f764]) ).

fof(f31909,plain,
    ( spl0_1345
    | ~ spl0_76
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f3745,f3559,f610,f31907]) ).

fof(f31907,plain,
    ( spl0_1345
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).

fof(f3559,plain,
    ( spl0_358
  <=> ! [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_358])]) ).

fof(f3745,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_76
    | ~ spl0_358 ),
    inference(superposition,[],[f3560,f612]) ).

fof(f3560,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_358 ),
    inference(avatar_component_clause,[],[f3559]) ).

fof(f31905,plain,
    ( spl0_1344
    | ~ spl0_18
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3592,f3517,f280,f31903]) ).

fof(f31903,plain,
    ( spl0_1344
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).

fof(f280,plain,
    ( spl0_18
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f3517,plain,
    ( spl0_348
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f3592,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,compose_class(X1))
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_18
    | ~ spl0_348 ),
    inference(resolution,[],[f3518,f281]) ).

fof(f281,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f280]) ).

fof(f3518,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X1,X2)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),X2) )
    | ~ spl0_348 ),
    inference(avatar_component_clause,[],[f3517]) ).

fof(f31901,plain,
    ( spl0_1343
    | ~ spl0_40
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3389,f3231,f381,f31899]) ).

fof(f31899,plain,
    ( spl0_1343
  <=> ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),null_class),X0)
        | subclass(regular(X0),null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).

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

fof(f3389,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(regular(X0),null_class),X0)
        | subclass(regular(X0),null_class)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_330 ),
    inference(superposition,[],[f3232,f382]) ).

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

fof(f31897,plain,
    ( spl0_1342
    | ~ spl0_112
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f2992,f2836,f830,f31895]) ).

fof(f31895,plain,
    ( spl0_1342
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).

fof(f830,plain,
    ( spl0_112
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f2836,plain,
    ( spl0_294
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f2992,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
        | ~ member(regular(X0),subset_relation) )
    | ~ spl0_112
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f831]) ).

fof(f831,plain,
    ( ! [X0] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,subset_relation) )
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f830]) ).

fof(f2837,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | null_class = X0
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_294 ),
    inference(avatar_component_clause,[],[f2836]) ).

fof(f31893,plain,
    ( spl0_1341
    | ~ spl0_144
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2906,f2324,f1170,f31891]) ).

fof(f31891,plain,
    ( spl0_1341
  <=> ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).

fof(f1170,plain,
    ( spl0_144
  <=> ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f2906,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_144
    | ~ spl0_237 ),
    inference(superposition,[],[f1171,f2326]) ).

fof(f1171,plain,
    ( ! [X0] :
        ( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation) )
    | ~ spl0_144 ),
    inference(avatar_component_clause,[],[f1170]) ).

fof(f31889,plain,
    ( spl0_1340
    | ~ spl0_38
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f2809,f2757,f373,f31887]) ).

fof(f31887,plain,
    ( spl0_1340
  <=> ! [X0,X1] :
        ( subclass(universal_class,complement(X0))
        | ~ subclass(X0,X1)
        | member(not_subclass_element(universal_class,complement(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).

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

fof(f2757,plain,
    ( spl0_289
  <=> ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f2809,plain,
    ( ! [X0,X1] :
        ( subclass(universal_class,complement(X0))
        | ~ subclass(X0,X1)
        | member(not_subclass_element(universal_class,complement(X0)),X1) )
    | ~ spl0_38
    | ~ spl0_289 ),
    inference(resolution,[],[f2758,f374]) ).

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

fof(f2758,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_289 ),
    inference(avatar_component_clause,[],[f2757]) ).

fof(f31885,plain,
    ( spl0_1339
    | ~ spl0_38
    | ~ spl0_288 ),
    inference(avatar_split_clause,[],[f2803,f2753,f373,f31883]) ).

fof(f31883,plain,
    ( spl0_1339
  <=> ! [X0,X1] :
        ( subclass(subset_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(not_subclass_element(subset_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).

fof(f2753,plain,
    ( spl0_288
  <=> ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f2803,plain,
    ( ! [X0,X1] :
        ( subclass(subset_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(not_subclass_element(subset_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_288 ),
    inference(resolution,[],[f2754,f374]) ).

fof(f2754,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_288 ),
    inference(avatar_component_clause,[],[f2753]) ).

fof(f31881,plain,
    ( spl0_1338
    | ~ spl0_38
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2792,f2749,f373,f31879]) ).

fof(f31879,plain,
    ( spl0_1338
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).

fof(f2749,plain,
    ( spl0_287
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f2792,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ subclass(element_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_38
    | ~ spl0_287 ),
    inference(resolution,[],[f2750,f374]) ).

fof(f2750,plain,
    ( ! [X0] :
        ( member(regular(X0),element_relation)
        | null_class = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_287 ),
    inference(avatar_component_clause,[],[f2749]) ).

fof(f31877,plain,
    ( spl0_1337
    | ~ spl0_998
    | ~ spl0_1316 ),
    inference(avatar_split_clause,[],[f31661,f29754,f20458,f31875]) ).

fof(f20458,plain,
    ( spl0_998
  <=> ! [X0] : ~ member(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f29754,plain,
    ( spl0_1316
  <=> ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).

fof(f31661,plain,
    ( ! [X0] : null_class = cross_product(null_class,X0)
    | ~ spl0_998
    | ~ spl0_1316 ),
    inference(resolution,[],[f29755,f20459]) ).

fof(f20459,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_998 ),
    inference(avatar_component_clause,[],[f20458]) ).

fof(f29755,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_1316 ),
    inference(avatar_component_clause,[],[f29754]) ).

fof(f31872,plain,
    ( spl0_1336
    | ~ spl0_38
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2783,f2745,f373,f31870]) ).

fof(f2745,plain,
    ( spl0_286
  <=> ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f2783,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ subclass(subset_relation,X1)
        | member(regular(X0),X1) )
    | ~ spl0_38
    | ~ spl0_286 ),
    inference(resolution,[],[f2746,f374]) ).

fof(f2746,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | null_class = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f2745]) ).

fof(f31867,plain,
    ( spl0_1335
    | ~ spl0_117
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2632,f2547,f926,f31865]) ).

fof(f31865,plain,
    ( spl0_1335
  <=> ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).

fof(f926,plain,
    ( spl0_117
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f2547,plain,
    ( spl0_275
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f2632,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),singleton_relation)
        | ~ subclass(X0,compose(element_relation,complement(identity_relation)))
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_275 ),
    inference(resolution,[],[f2548,f927]) ).

fof(f927,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),X1)
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f926]) ).

fof(f2548,plain,
    ( ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f2547]) ).

fof(f31861,plain,
    ( ~ spl0_1334
    | ~ spl0_237
    | spl0_1332 ),
    inference(avatar_split_clause,[],[f31850,f31846,f2324,f31858]) ).

fof(f31858,plain,
    ( spl0_1334
  <=> member(regular(compose(element_relation,complement(singleton_relation))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).

fof(f31846,plain,
    ( spl0_1332
  <=> member(regular(compose(element_relation,complement(identity_relation))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).

fof(f31850,plain,
    ( ~ member(regular(compose(element_relation,complement(singleton_relation))),singleton_relation)
    | ~ spl0_237
    | spl0_1332 ),
    inference(forward_demodulation,[],[f31848,f2326]) ).

fof(f31848,plain,
    ( ~ member(regular(compose(element_relation,complement(identity_relation))),singleton_relation)
    | spl0_1332 ),
    inference(avatar_component_clause,[],[f31846]) ).

fof(f31856,plain,
    ( ~ spl0_1333
    | ~ spl0_237
    | spl0_1331 ),
    inference(avatar_split_clause,[],[f31851,f31842,f2324,f31853]) ).

fof(f31853,plain,
    ( spl0_1333
  <=> null_class = compose(element_relation,complement(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).

fof(f31842,plain,
    ( spl0_1331
  <=> null_class = compose(element_relation,complement(identity_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).

fof(f31851,plain,
    ( null_class != compose(element_relation,complement(singleton_relation))
    | ~ spl0_237
    | spl0_1331 ),
    inference(forward_demodulation,[],[f31843,f2326]) ).

fof(f31843,plain,
    ( null_class != compose(element_relation,complement(identity_relation))
    | spl0_1331 ),
    inference(avatar_component_clause,[],[f31842]) ).

fof(f31849,plain,
    ( spl0_1331
    | ~ spl0_1332
    | ~ spl0_23
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2624,f2547,f300,f31846,f31842]) ).

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

fof(f2624,plain,
    ( ~ member(regular(compose(element_relation,complement(identity_relation))),singleton_relation)
    | null_class = compose(element_relation,complement(identity_relation))
    | ~ spl0_23
    | ~ spl0_275 ),
    inference(resolution,[],[f2548,f301]) ).

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

fof(f31840,plain,
    ( spl0_1330
    | ~ spl0_187
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2600,f2517,f1585,f31838]) ).

fof(f31838,plain,
    ( spl0_1330
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,complement(compose_class(X0)))
        | ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).

fof(f1585,plain,
    ( spl0_187
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f2600,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(compose_class(X0)))
        | ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class) )
    | ~ spl0_187
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f1586]) ).

fof(f1586,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f1585]) ).

fof(f31836,plain,
    ( spl0_1328
    | ~ spl0_1329
    | ~ spl0_126
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2595,f2517,f966,f31833,f31830]) ).

fof(f31830,plain,
    ( spl0_1328
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).

fof(f31833,plain,
    ( spl0_1329
  <=> subclass(universal_class,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).

fof(f966,plain,
    ( spl0_126
  <=> ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f2595,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(unordered_pair(X0,X1),identity_relation) )
    | ~ spl0_126
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f967]) ).

fof(f967,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,identity_relation) )
    | ~ spl0_126 ),
    inference(avatar_component_clause,[],[f966]) ).

fof(f31828,plain,
    ( spl0_1327
    | ~ spl0_998
    | ~ spl0_1315 ),
    inference(avatar_split_clause,[],[f31605,f29750,f20458,f31826]) ).

fof(f31826,plain,
    ( spl0_1327
  <=> ! [X0] : null_class = cross_product(X0,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).

fof(f29750,plain,
    ( spl0_1315
  <=> ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).

fof(f31605,plain,
    ( ! [X0] : null_class = cross_product(X0,null_class)
    | ~ spl0_998
    | ~ spl0_1315 ),
    inference(resolution,[],[f29751,f20459]) ).

fof(f29751,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_1315 ),
    inference(avatar_component_clause,[],[f29750]) ).

fof(f31824,plain,
    ( ~ spl0_1326
    | ~ spl0_237
    | spl0_1325 ),
    inference(avatar_split_clause,[],[f31819,f31815,f2324,f31821]) ).

fof(f31821,plain,
    ( spl0_1326
  <=> subclass(universal_class,complement(complement(compose(element_relation,complement(singleton_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).

fof(f31815,plain,
    ( spl0_1325
  <=> subclass(universal_class,complement(complement(compose(element_relation,complement(identity_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).

fof(f31819,plain,
    ( ~ subclass(universal_class,complement(complement(compose(element_relation,complement(singleton_relation)))))
    | ~ spl0_237
    | spl0_1325 ),
    inference(forward_demodulation,[],[f31817,f2326]) ).

fof(f31817,plain,
    ( ~ subclass(universal_class,complement(complement(compose(element_relation,complement(identity_relation)))))
    | spl0_1325 ),
    inference(avatar_component_clause,[],[f31815]) ).

fof(f31818,plain,
    ( spl0_1255
    | ~ spl0_1325
    | ~ spl0_125
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2592,f2517,f962,f31815,f27982]) ).

fof(f27982,plain,
    ( spl0_1255
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).

fof(f962,plain,
    ( spl0_125
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f2592,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(unordered_pair(X0,X1),singleton_relation) )
    | ~ spl0_125
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f963]) ).

fof(f963,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f962]) ).

fof(f31813,plain,
    ( spl0_1324
    | ~ spl0_30
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2585,f2517,f332,f31811]) ).

fof(f31811,plain,
    ( spl0_1324
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(X0,unordered_pair(X1,X2))))
        | ~ member(unordered_pair(X1,X2),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).

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

fof(f2585,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(X0,unordered_pair(X1,X2))))
        | ~ member(unordered_pair(X1,X2),universal_class) )
    | ~ spl0_30
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f333]) ).

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

fof(f31809,plain,
    ( spl0_1323
    | ~ spl0_29
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2584,f2517,f328,f31807]) ).

fof(f31807,plain,
    ( spl0_1323
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(unordered_pair(X0,X1),X2)))
        | ~ member(unordered_pair(X0,X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).

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

fof(f2584,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(unordered_pair(unordered_pair(X0,X1),X2)))
        | ~ member(unordered_pair(X0,X1),universal_class) )
    | ~ spl0_29
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f329]) ).

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

fof(f31049,plain,
    ( spl0_1322
    | ~ spl0_641
    | ~ spl0_1148 ),
    inference(avatar_split_clause,[],[f25410,f25404,f9800,f31046]) ).

fof(f31046,plain,
    ( spl0_1322
  <=> member(not_subclass_element(universal_class,complement(singleton_relation)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).

fof(f9800,plain,
    ( spl0_641
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f25404,plain,
    ( spl0_1148
  <=> member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).

fof(f25410,plain,
    ( member(not_subclass_element(universal_class,complement(singleton_relation)),universal_class)
    | ~ spl0_641
    | ~ spl0_1148 ),
    inference(resolution,[],[f25406,f9801]) ).

fof(f9801,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_641 ),
    inference(avatar_component_clause,[],[f9800]) ).

fof(f25406,plain,
    ( member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation)
    | ~ spl0_1148 ),
    inference(avatar_component_clause,[],[f25404]) ).

fof(f30624,plain,
    ( spl0_1321
    | ~ spl0_684
    | ~ spl0_1113 ),
    inference(avatar_split_clause,[],[f24578,f23656,f10885,f30621]) ).

fof(f30621,plain,
    ( spl0_1321
  <=> null_class = intersection(complement(element_relation),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).

fof(f10885,plain,
    ( spl0_684
  <=> subclass(successor_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).

fof(f23656,plain,
    ( spl0_1113
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).

fof(f24578,plain,
    ( null_class = intersection(complement(element_relation),successor_relation)
    | ~ spl0_684
    | ~ spl0_1113 ),
    inference(resolution,[],[f23657,f10887]) ).

fof(f10887,plain,
    ( subclass(successor_relation,element_relation)
    | ~ spl0_684 ),
    inference(avatar_component_clause,[],[f10885]) ).

fof(f23657,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0) )
    | ~ spl0_1113 ),
    inference(avatar_component_clause,[],[f23656]) ).

fof(f30255,plain,
    ( spl0_1320
    | ~ spl0_684
    | ~ spl0_1112 ),
    inference(avatar_split_clause,[],[f24488,f23652,f10885,f30252]) ).

fof(f30252,plain,
    ( spl0_1320
  <=> null_class = intersection(successor_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).

fof(f23652,plain,
    ( spl0_1112
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).

fof(f24488,plain,
    ( null_class = intersection(successor_relation,complement(element_relation))
    | ~ spl0_684
    | ~ spl0_1112 ),
    inference(resolution,[],[f23653,f10887]) ).

fof(f23653,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_1112 ),
    inference(avatar_component_clause,[],[f23652]) ).

fof(f29831,plain,
    ( spl0_1319
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_1088 ),
    inference(avatar_split_clause,[],[f23479,f22544,f2324,f394,f29829]) ).

fof(f29829,plain,
    ( spl0_1319
  <=> ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).

fof(f394,plain,
    ( spl0_43
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f22544,plain,
    ( spl0_1088
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).

fof(f23479,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(subset_relation,X0) )
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_1088 ),
    inference(forward_demodulation,[],[f23476,f2326]) ).

fof(f23476,plain,
    ( ! [X0] :
        ( subclass(identity_relation,X0)
        | ~ subclass(subset_relation,X0) )
    | ~ spl0_43
    | ~ spl0_1088 ),
    inference(superposition,[],[f22545,f396]) ).

fof(f396,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f394]) ).

fof(f22545,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X2,X0),X1)
        | ~ subclass(X0,X1) )
    | ~ spl0_1088 ),
    inference(avatar_component_clause,[],[f22544]) ).

fof(f29764,plain,
    ( spl0_1318
    | ~ spl0_109
    | ~ spl0_744 ),
    inference(avatar_split_clause,[],[f12782,f12573,f818,f29762]) ).

fof(f29762,plain,
    ( spl0_1318
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).

fof(f818,plain,
    ( spl0_109
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f12782,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_744 ),
    inference(superposition,[],[f819,f12575]) ).

fof(f819,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X1,X2),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f818]) ).

fof(f29760,plain,
    ( spl0_1317
    | ~ spl0_109
    | ~ spl0_742 ),
    inference(avatar_split_clause,[],[f12704,f12509,f818,f29758]) ).

fof(f29758,plain,
    ( spl0_1317
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).

fof(f12704,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_742 ),
    inference(superposition,[],[f819,f12511]) ).

fof(f29756,plain,
    ( spl0_1316
    | ~ spl0_23
    | ~ spl0_493 ),
    inference(avatar_split_clause,[],[f6837,f6501,f300,f29754]) ).

fof(f6501,plain,
    ( spl0_493
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f6837,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_493 ),
    inference(duplicate_literal_removal,[],[f6832]) ).

fof(f6832,plain,
    ( ! [X0,X1] :
        ( member(first(regular(cross_product(X0,X1))),X0)
        | cross_product(X0,X1) = null_class
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_493 ),
    inference(resolution,[],[f6502,f301]) ).

fof(f6502,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_493 ),
    inference(avatar_component_clause,[],[f6501]) ).

fof(f29752,plain,
    ( spl0_1315
    | ~ spl0_23
    | ~ spl0_491 ),
    inference(avatar_split_clause,[],[f6830,f6493,f300,f29750]) ).

fof(f6493,plain,
    ( spl0_491
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(second(regular(cross_product(X0,X1))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f6830,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_491 ),
    inference(duplicate_literal_removal,[],[f6825]) ).

fof(f6825,plain,
    ( ! [X0,X1] :
        ( member(second(regular(cross_product(X0,X1))),X1)
        | cross_product(X0,X1) = null_class
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_491 ),
    inference(resolution,[],[f6494,f301]) ).

fof(f6494,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(second(regular(cross_product(X0,X1))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_491 ),
    inference(avatar_component_clause,[],[f6493]) ).

fof(f29748,plain,
    ( spl0_1314
    | ~ spl0_32
    | ~ spl0_470 ),
    inference(avatar_split_clause,[],[f6247,f6240,f340,f29745]) ).

fof(f29745,plain,
    ( spl0_1314
  <=> 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_1314])]) ).

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

fof(f6240,plain,
    ( spl0_470
  <=> member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f6247,plain,
    ( member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
    | ~ spl0_32
    | ~ spl0_470 ),
    inference(resolution,[],[f6242,f341]) ).

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

fof(f6242,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_470 ),
    inference(avatar_component_clause,[],[f6240]) ).

fof(f29743,plain,
    ( ~ spl0_1311
    | spl0_1312
    | spl0_1313
    | ~ spl0_9
    | ~ spl0_435 ),
    inference(avatar_split_clause,[],[f5662,f5562,f241,f29741,f29737,f29733]) ).

fof(f29733,plain,
    ( spl0_1311
  <=> subclass(universal_class,regular(universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).

fof(f29737,plain,
    ( spl0_1312
  <=> universal_class = null_class ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).

fof(f29741,plain,
    ( spl0_1313
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).

fof(f241,plain,
    ( spl0_9
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f5562,plain,
    ( spl0_435
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | ~ member(unordered_pair(X0,X1),X2)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f5662,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | universal_class = null_class
        | ~ subclass(universal_class,regular(universal_class)) )
    | ~ spl0_9
    | ~ spl0_435 ),
    inference(resolution,[],[f5563,f242]) ).

fof(f242,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f241]) ).

fof(f5563,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(X0,X1),X2)
        | member(unordered_pair(X0,X1),null_class)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) )
    | ~ spl0_435 ),
    inference(avatar_component_clause,[],[f5562]) ).

fof(f29731,plain,
    ( spl0_1310
    | ~ spl0_393
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5412,f4906,f4273,f29729]) ).

fof(f29729,plain,
    ( spl0_1310
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X1,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).

fof(f4273,plain,
    ( spl0_393
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f4906,plain,
    ( spl0_421
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).

fof(f5412,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X1,singleton_relation) )
    | ~ spl0_393
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5409]) ).

fof(f5409,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X1,singleton_relation)
        | subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_393
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f4274]) ).

fof(f4274,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X3)
        | ~ subclass(X1,X3)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_393 ),
    inference(avatar_component_clause,[],[f4273]) ).

fof(f4907,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_421 ),
    inference(avatar_component_clause,[],[f4906]) ).

fof(f29727,plain,
    ( spl0_1309
    | ~ spl0_391
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5411,f4906,f4265,f29725]) ).

fof(f29725,plain,
    ( spl0_1309
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).

fof(f4265,plain,
    ( spl0_391
  <=> ! [X0,X3,X2,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f5411,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_391
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5410]) ).

fof(f5410,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_391
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f4266]) ).

fof(f4266,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X3)
        | ~ subclass(X0,X3)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_391 ),
    inference(avatar_component_clause,[],[f4265]) ).

fof(f29723,plain,
    ( spl0_1308
    | ~ spl0_393
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5388,f4902,f4273,f29721]) ).

fof(f29721,plain,
    ( spl0_1308
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X1,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).

fof(f4902,plain,
    ( spl0_420
  <=> ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f5388,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X1,singleton_relation) )
    | ~ spl0_393
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5385]) ).

fof(f5385,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X1,singleton_relation)
        | subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_393
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f4274]) ).

fof(f4903,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_420 ),
    inference(avatar_component_clause,[],[f4902]) ).

fof(f29719,plain,
    ( spl0_1307
    | ~ spl0_391
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5387,f4902,f4265,f29717]) ).

fof(f29717,plain,
    ( spl0_1307
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).

fof(f5387,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_391
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5386]) ).

fof(f5386,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | subclass(intersection(X0,X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_391
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f4266]) ).

fof(f29715,plain,
    ( spl0_1306
    | ~ spl0_131
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5355,f4889,f1019,f29713]) ).

fof(f29713,plain,
    ( spl0_1306
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).

fof(f1019,plain,
    ( spl0_131
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f4889,plain,
    ( spl0_419
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f5355,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_131
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5314]) ).

fof(f5314,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_131
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f1020]) ).

fof(f1020,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X2),X1)
        | ~ subclass(X0,X1)
        | subclass(X0,X2) )
    | ~ spl0_131 ),
    inference(avatar_component_clause,[],[f1019]) ).

fof(f4890,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_419 ),
    inference(avatar_component_clause,[],[f4889]) ).

fof(f29711,plain,
    ( spl0_1305
    | ~ spl0_305
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5349,f4889,f2966,f29709]) ).

fof(f29709,plain,
    ( spl0_1305
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).

fof(f2966,plain,
    ( spl0_305
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f5349,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5321]) ).

fof(f5321,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X0))
        | subclass(intersection(X0,X1),intersection(element_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f2967]) ).

fof(f2967,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),element_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_305 ),
    inference(avatar_component_clause,[],[f2966]) ).

fof(f29707,plain,
    ( spl0_1304
    | ~ spl0_313
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5346,f4889,f3118,f29705]) ).

fof(f29705,plain,
    ( spl0_1304
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).

fof(f3118,plain,
    ( spl0_313
  <=> ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f5346,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5333]) ).

fof(f5333,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | subclass(intersection(X0,X1),intersection(subset_relation,X0))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f3119]) ).

fof(f3119,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f3118]) ).

fof(f29703,plain,
    ( spl0_1303
    | ~ spl0_131
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5290,f4885,f1019,f29701]) ).

fof(f29701,plain,
    ( spl0_1303
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).

fof(f4885,plain,
    ( spl0_418
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f5290,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_131
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5249]) ).

fof(f5249,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_131
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f1020]) ).

fof(f4886,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_418 ),
    inference(avatar_component_clause,[],[f4885]) ).

fof(f29699,plain,
    ( spl0_1302
    | ~ spl0_305
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5284,f4885,f2966,f29697]) ).

fof(f29697,plain,
    ( spl0_1302
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).

fof(f5284,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5256]) ).

fof(f5256,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(element_relation,X1))
        | subclass(intersection(X0,X1),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f2967]) ).

fof(f29694,plain,
    ( spl0_1301
    | ~ spl0_313
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5281,f4885,f3118,f29692]) ).

fof(f29692,plain,
    ( spl0_1301
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).

fof(f5281,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5268]) ).

fof(f5268,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | subclass(intersection(X0,X1),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,X1),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f3119]) ).

fof(f29690,plain,
    ( spl0_1300
    | ~ spl0_135
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4762,f4308,f1090,f29688]) ).

fof(f29688,plain,
    ( spl0_1300
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X2))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).

fof(f1090,plain,
    ( spl0_135
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f4308,plain,
    ( spl0_401
  <=> ! [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_401])]) ).

fof(f4762,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X2))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_135
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4712]) ).

fof(f4712,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X2))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X0,X2)) )
    | ~ spl0_135
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f1091]) ).

fof(f1091,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1090]) ).

fof(f4309,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_401 ),
    inference(avatar_component_clause,[],[f4308]) ).

fof(f29686,plain,
    ( spl0_1299
    | ~ spl0_136
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4761,f4308,f1094,f29684]) ).

fof(f29684,plain,
    ( spl0_1299
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X2))
        | ~ subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).

fof(f1094,plain,
    ( spl0_136
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f4761,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X2))
        | ~ subclass(intersection(X0,X1),X2) )
    | ~ spl0_136
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4713]) ).

fof(f4713,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X2))
        | ~ subclass(intersection(X0,X1),X2)
        | subclass(intersection(X0,X1),intersection(X1,X2)) )
    | ~ spl0_136
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f1095]) ).

fof(f1095,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_136 ),
    inference(avatar_component_clause,[],[f1094]) ).

fof(f29682,plain,
    ( spl0_1298
    | ~ spl0_322
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4752,f4308,f3188,f29680]) ).

fof(f29680,plain,
    ( spl0_1298
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).

fof(f3188,plain,
    ( spl0_322
  <=> ! [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_322])]) ).

fof(f4752,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_322
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4723]) ).

fof(f4723,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,X1)) )
    | ~ spl0_322
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f3189]) ).

fof(f3189,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f3188]) ).

fof(f29678,plain,
    ( spl0_1297
    | ~ spl0_327
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4751,f4308,f3214,f29676]) ).

fof(f29676,plain,
    ( spl0_1297
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).

fof(f3214,plain,
    ( spl0_327
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f4751,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_327
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4724]) ).

fof(f4724,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,X1)) )
    | ~ spl0_327
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f3215]) ).

fof(f3215,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_327 ),
    inference(avatar_component_clause,[],[f3214]) ).

fof(f29674,plain,
    ( spl0_1296
    | ~ spl0_336
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4750,f4308,f3344,f29672]) ).

fof(f29672,plain,
    ( spl0_1296
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0))
        | ~ subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).

fof(f3344,plain,
    ( spl0_336
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f4750,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0))
        | ~ subclass(singleton_relation,X0) )
    | ~ spl0_336
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4727]) ).

fof(f4727,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0))
        | ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),X0)) )
    | ~ spl0_336
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f3345]) ).

fof(f3345,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_336 ),
    inference(avatar_component_clause,[],[f3344]) ).

fof(f29670,plain,
    ( spl0_1295
    | ~ spl0_337
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4749,f4308,f3348,f29668]) ).

fof(f29668,plain,
    ( spl0_1295
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0))
        | ~ subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).

fof(f3348,plain,
    ( spl0_337
  <=> ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f4749,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0))
        | ~ subclass(singleton_relation,X0) )
    | ~ spl0_337
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4732]) ).

fof(f4732,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0))
        | ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)) )
    | ~ spl0_337
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f3349]) ).

fof(f3349,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_337 ),
    inference(avatar_component_clause,[],[f3348]) ).

fof(f29666,plain,
    ( spl0_1294
    | ~ spl0_335
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4746,f4308,f3330,f29664]) ).

fof(f29664,plain,
    ( spl0_1294
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).

fof(f3330,plain,
    ( spl0_335
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f4746,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_335
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4737]) ).

fof(f4737,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1))
        | ~ subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,X1)) )
    | ~ spl0_335
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f3331]) ).

fof(f3331,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f3330]) ).

fof(f29662,plain,
    ( spl0_1293
    | ~ spl0_338
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4745,f4308,f3352,f29660]) ).

fof(f29660,plain,
    ( spl0_1293
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).

fof(f3352,plain,
    ( spl0_338
  <=> ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f4745,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_338
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4738]) ).

fof(f4738,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1))
        | ~ subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,X1)) )
    | ~ spl0_338
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f3353]) ).

fof(f3353,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_338 ),
    inference(avatar_component_clause,[],[f3352]) ).

fof(f29657,plain,
    ( spl0_1292
    | ~ spl0_330
    | ~ spl0_394 ),
    inference(avatar_split_clause,[],[f4668,f4277,f3231,f29655]) ).

fof(f29655,plain,
    ( spl0_1292
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class)))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).

fof(f4277,plain,
    ( spl0_394
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f4668,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class)))
        | null_class = X1 )
    | ~ spl0_330
    | ~ spl0_394 ),
    inference(duplicate_literal_removal,[],[f4640]) ).

fof(f4640,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class)))
        | null_class = X1
        | subclass(intersection(X0,null_class),intersection(X1,intersection(X0,null_class))) )
    | ~ spl0_330
    | ~ spl0_394 ),
    inference(resolution,[],[f4278,f3232]) ).

fof(f4278,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | subclass(intersection(X0,null_class),X1)
        | null_class = X2 )
    | ~ spl0_394 ),
    inference(avatar_component_clause,[],[f4277]) ).

fof(f29652,plain,
    ( spl0_1291
    | ~ spl0_330
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4619,f4273,f3231,f29650]) ).

fof(f29650,plain,
    ( spl0_1291
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).

fof(f4619,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0))) )
    | ~ spl0_330
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4586]) ).

fof(f4586,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0)))
        | subclass(intersection(X2,X0),intersection(X1,intersection(X2,X0))) )
    | ~ spl0_330
    | ~ spl0_393 ),
    inference(resolution,[],[f4274,f3232]) ).

fof(f29647,plain,
    ( spl0_1290
    | ~ spl0_330
    | ~ spl0_392 ),
    inference(avatar_split_clause,[],[f4570,f4269,f3231,f29645]) ).

fof(f29645,plain,
    ( spl0_1290
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0)))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).

fof(f4269,plain,
    ( spl0_392
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).

fof(f4570,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0)))
        | null_class = X1 )
    | ~ spl0_330
    | ~ spl0_392 ),
    inference(duplicate_literal_removal,[],[f4542]) ).

fof(f4542,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0)))
        | null_class = X1
        | subclass(intersection(null_class,X0),intersection(X1,intersection(null_class,X0))) )
    | ~ spl0_330
    | ~ spl0_392 ),
    inference(resolution,[],[f4270,f3232]) ).

fof(f4270,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | subclass(intersection(null_class,X0),X1)
        | null_class = X2 )
    | ~ spl0_392 ),
    inference(avatar_component_clause,[],[f4269]) ).

fof(f29643,plain,
    ( spl0_1289
    | ~ spl0_330
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4523,f4265,f3231,f29641]) ).

fof(f29641,plain,
    ( spl0_1289
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).

fof(f4523,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2))) )
    | ~ spl0_330
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4490]) ).

fof(f4490,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2)))
        | subclass(intersection(X0,X2),intersection(X1,intersection(X0,X2))) )
    | ~ spl0_330
    | ~ spl0_391 ),
    inference(resolution,[],[f4266,f3232]) ).

fof(f29639,plain,
    ( spl0_1288
    | ~ spl0_131
    | ~ spl0_377 ),
    inference(avatar_split_clause,[],[f4116,f3841,f1019,f29637]) ).

fof(f29637,plain,
    ( spl0_1288
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ subclass(intersection(X0,complement(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).

fof(f3841,plain,
    ( spl0_377
  <=> ! [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_377])]) ).

fof(f4116,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ subclass(intersection(X0,complement(X1)),X1) )
    | ~ spl0_131
    | ~ spl0_377 ),
    inference(duplicate_literal_removal,[],[f4098]) ).

fof(f4098,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ subclass(intersection(X0,complement(X1)),X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_131
    | ~ spl0_377 ),
    inference(resolution,[],[f3842,f1020]) ).

fof(f3842,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_377 ),
    inference(avatar_component_clause,[],[f3841]) ).

fof(f29635,plain,
    ( spl0_1287
    | ~ spl0_305
    | ~ spl0_377 ),
    inference(avatar_split_clause,[],[f4114,f3841,f2966,f29633]) ).

fof(f29633,plain,
    ( spl0_1287
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,complement(element_relation)),X1)
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).

fof(f4114,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(element_relation)),X1)
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_377 ),
    inference(duplicate_literal_removal,[],[f4101]) ).

fof(f4101,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(element_relation)),X1)
        | subclass(intersection(X0,complement(element_relation)),X1)
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_377 ),
    inference(resolution,[],[f3842,f2967]) ).

fof(f29631,plain,
    ( spl0_1286
    | ~ spl0_313
    | ~ spl0_377 ),
    inference(avatar_split_clause,[],[f4112,f3841,f3118,f29629]) ).

fof(f29629,plain,
    ( spl0_1286
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,complement(subset_relation)),X1)
        | ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).

fof(f4112,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(subset_relation)),X1)
        | ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_377 ),
    inference(duplicate_literal_removal,[],[f4110]) ).

fof(f4110,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,complement(subset_relation)),X1)
        | subclass(intersection(X0,complement(subset_relation)),X1)
        | ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_377 ),
    inference(resolution,[],[f3842,f3119]) ).

fof(f29627,plain,
    ( spl0_1285
    | ~ spl0_131
    | ~ spl0_376 ),
    inference(avatar_split_clause,[],[f4085,f3837,f1019,f29625]) ).

fof(f29625,plain,
    ( spl0_1285
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ subclass(intersection(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).

fof(f3837,plain,
    ( spl0_376
  <=> ! [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_376])]) ).

fof(f4085,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ subclass(intersection(complement(X0),X1),X0) )
    | ~ spl0_131
    | ~ spl0_376 ),
    inference(duplicate_literal_removal,[],[f4065]) ).

fof(f4065,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ subclass(intersection(complement(X0),X1),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_131
    | ~ spl0_376 ),
    inference(resolution,[],[f3838,f1020]) ).

fof(f3838,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_376 ),
    inference(avatar_component_clause,[],[f3837]) ).

fof(f29623,plain,
    ( spl0_1284
    | ~ spl0_305
    | ~ spl0_376 ),
    inference(avatar_split_clause,[],[f4083,f3837,f2966,f29621]) ).

fof(f29621,plain,
    ( spl0_1284
  <=> ! [X0,X1] :
        ( subclass(intersection(complement(element_relation),X0),X1)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).

fof(f4083,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(element_relation),X0),X1)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_376 ),
    inference(duplicate_literal_removal,[],[f4068]) ).

fof(f4068,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(element_relation),X0),X1)
        | subclass(intersection(complement(element_relation),X0),X1)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_305
    | ~ spl0_376 ),
    inference(resolution,[],[f3838,f2967]) ).

fof(f29619,plain,
    ( spl0_1283
    | ~ spl0_313
    | ~ spl0_376 ),
    inference(avatar_split_clause,[],[f4081,f3837,f3118,f29617]) ).

fof(f29617,plain,
    ( spl0_1283
  <=> ! [X0,X1] :
        ( subclass(intersection(complement(subset_relation),X0),X1)
        | ~ subclass(intersection(complement(subset_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).

fof(f4081,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(subset_relation),X0),X1)
        | ~ subclass(intersection(complement(subset_relation),X0),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_376 ),
    inference(duplicate_literal_removal,[],[f4077]) ).

fof(f4077,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(subset_relation),X0),X1)
        | subclass(intersection(complement(subset_relation),X0),X1)
        | ~ subclass(intersection(complement(subset_relation),X0),singleton_relation) )
    | ~ spl0_313
    | ~ spl0_376 ),
    inference(resolution,[],[f3838,f3119]) ).

fof(f29615,plain,
    ( spl0_1282
    | ~ spl0_13
    | ~ spl0_358 ),
    inference(avatar_split_clause,[],[f3741,f3559,f259,f29613]) ).

fof(f29613,plain,
    ( spl0_1282
  <=> ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).

fof(f3741,plain,
    ( ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X1,X2)) )
    | ~ spl0_13
    | ~ spl0_358 ),
    inference(resolution,[],[f3560,f260]) ).

fof(f29611,plain,
    ( ~ spl0_1281
    | ~ spl0_1158
    | spl0_1266 ),
    inference(avatar_split_clause,[],[f29542,f29538,f25471,f29608]) ).

fof(f29608,plain,
    ( spl0_1281
  <=> member(not_subclass_element(subset_relation,singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).

fof(f25471,plain,
    ( spl0_1158
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f29538,plain,
    ( spl0_1266
  <=> member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).

fof(f29542,plain,
    ( ~ member(not_subclass_element(subset_relation,singleton_relation),singleton_relation)
    | ~ spl0_1158
    | spl0_1266 ),
    inference(resolution,[],[f29540,f25472]) ).

fof(f25472,plain,
    ( ! [X0] :
        ( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_1158 ),
    inference(avatar_component_clause,[],[f25471]) ).

fof(f29540,plain,
    ( ~ member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | spl0_1266 ),
    inference(avatar_component_clause,[],[f29538]) ).

fof(f29606,plain,
    ( spl0_1280
    | ~ spl0_13
    | ~ spl0_357 ),
    inference(avatar_split_clause,[],[f3724,f3555,f259,f29604]) ).

fof(f29604,plain,
    ( spl0_1280
  <=> ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).

fof(f3555,plain,
    ( spl0_357
  <=> ! [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_357])]) ).

fof(f3724,plain,
    ( ! [X2,X0,X1] :
        ( subclass(omega,X0)
        | member(not_subclass_element(omega,X0),X1)
        | ~ inductive(intersection(X2,X1)) )
    | ~ spl0_13
    | ~ spl0_357 ),
    inference(resolution,[],[f3556,f260]) ).

fof(f3556,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_357 ),
    inference(avatar_component_clause,[],[f3555]) ).

fof(f29602,plain,
    ( spl0_1279
    | ~ spl0_237
    | ~ spl0_286
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f3717,f3551,f2745,f2324,f29600]) ).

fof(f29600,plain,
    ( spl0_1279
  <=> ! [X0] :
        ( ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation)
        | null_class = intersection(X0,complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).

fof(f3551,plain,
    ( spl0_356
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f3717,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(X0,complement(subset_relation)),singleton_relation)
        | null_class = intersection(X0,complement(subset_relation)) )
    | ~ spl0_237
    | ~ spl0_286
    | ~ spl0_356 ),
    inference(forward_demodulation,[],[f3705,f2326]) ).

fof(f3705,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(subset_relation))
        | ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) )
    | ~ spl0_286
    | ~ spl0_356 ),
    inference(duplicate_literal_removal,[],[f3703]) ).

fof(f3703,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(subset_relation))
        | null_class = intersection(X0,complement(subset_relation))
        | ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) )
    | ~ spl0_286
    | ~ spl0_356 ),
    inference(resolution,[],[f3552,f2746]) ).

fof(f3552,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(X0,complement(X1))),X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_356 ),
    inference(avatar_component_clause,[],[f3551]) ).

fof(f29598,plain,
    ( spl0_1278
    | ~ spl0_117
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f3709,f3551,f926,f29596]) ).

fof(f29596,plain,
    ( spl0_1278
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).

fof(f3709,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1) )
    | ~ spl0_117
    | ~ spl0_356 ),
    inference(duplicate_literal_removal,[],[f3691]) ).

fof(f3691,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ subclass(intersection(X0,complement(X1)),X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_117
    | ~ spl0_356 ),
    inference(resolution,[],[f3552,f927]) ).

fof(f29594,plain,
    ( spl0_1277
    | ~ spl0_287
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f3707,f3551,f2749,f29592]) ).

fof(f29592,plain,
    ( spl0_1277
  <=> ! [X0] :
        ( null_class = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).

fof(f3707,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_287
    | ~ spl0_356 ),
    inference(duplicate_literal_removal,[],[f3694]) ).

fof(f3694,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(element_relation))
        | null_class = intersection(X0,complement(element_relation))
        | ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
    | ~ spl0_287
    | ~ spl0_356 ),
    inference(resolution,[],[f3552,f2750]) ).

fof(f29590,plain,
    ( spl0_1276
    | ~ spl0_237
    | ~ spl0_286
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3687,f3547,f2745,f2324,f29588]) ).

fof(f29588,plain,
    ( spl0_1276
  <=> ! [X0] :
        ( ~ subclass(intersection(complement(subset_relation),X0),singleton_relation)
        | null_class = intersection(complement(subset_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).

fof(f3547,plain,
    ( spl0_355
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f3687,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(complement(subset_relation),X0),singleton_relation)
        | null_class = intersection(complement(subset_relation),X0) )
    | ~ spl0_237
    | ~ spl0_286
    | ~ spl0_355 ),
    inference(forward_demodulation,[],[f3676,f2326]) ).

fof(f3676,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(subset_relation),X0)
        | ~ subclass(intersection(complement(subset_relation),X0),identity_relation) )
    | ~ spl0_286
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3672]) ).

fof(f3672,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(subset_relation),X0)
        | null_class = intersection(complement(subset_relation),X0)
        | ~ subclass(intersection(complement(subset_relation),X0),identity_relation) )
    | ~ spl0_286
    | ~ spl0_355 ),
    inference(resolution,[],[f3548,f2746]) ).

fof(f3548,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(intersection(complement(X0),X1)),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_355 ),
    inference(avatar_component_clause,[],[f3547]) ).

fof(f29586,plain,
    ( spl0_1275
    | ~ spl0_117
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3680,f3547,f926,f29584]) ).

fof(f29584,plain,
    ( spl0_1275
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).

fof(f3680,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0) )
    | ~ spl0_117
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3660]) ).

fof(f3660,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ subclass(intersection(complement(X0),X1),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_117
    | ~ spl0_355 ),
    inference(resolution,[],[f3548,f927]) ).

fof(f29582,plain,
    ( spl0_1274
    | ~ spl0_287
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3678,f3547,f2749,f29580]) ).

fof(f29580,plain,
    ( spl0_1274
  <=> ! [X0] :
        ( null_class = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).

fof(f3678,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_287
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3663]) ).

fof(f3663,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(element_relation),X0)
        | null_class = intersection(complement(element_relation),X0)
        | ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
    | ~ spl0_287
    | ~ spl0_355 ),
    inference(resolution,[],[f3548,f2750]) ).

fof(f29578,plain,
    ( spl0_1273
    | ~ spl0_14
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3594,f3517,f263,f29576]) ).

fof(f29576,plain,
    ( spl0_1273
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).

fof(f3594,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_14
    | ~ spl0_348 ),
    inference(resolution,[],[f3518,f265]) ).

fof(f29574,plain,
    ( spl0_1272
    | ~ spl0_13
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3588,f3517,f259,f29572]) ).

fof(f29572,plain,
    ( spl0_1272
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).

fof(f3588,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,omega)
        | member(regular(X0),X1)
        | ~ inductive(X1) )
    | ~ spl0_13
    | ~ spl0_348 ),
    inference(resolution,[],[f3518,f260]) ).

fof(f29570,plain,
    ( spl0_1271
    | ~ spl0_11
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3587,f3517,f250,f29568]) ).

fof(f29568,plain,
    ( spl0_1271
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).

fof(f3587,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_11
    | ~ spl0_348 ),
    inference(resolution,[],[f3518,f252]) ).

fof(f29566,plain,
    ( ~ spl0_1270
    | ~ spl0_1150
    | spl0_1265 ),
    inference(avatar_split_clause,[],[f29534,f29530,f25427,f29563]) ).

fof(f29563,plain,
    ( spl0_1270
  <=> member(not_subclass_element(element_relation,singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).

fof(f25427,plain,
    ( spl0_1150
  <=> ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f29530,plain,
    ( spl0_1265
  <=> member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).

fof(f29534,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),singleton_relation)
    | ~ spl0_1150
    | spl0_1265 ),
    inference(resolution,[],[f29532,f25428]) ).

fof(f25428,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_1150 ),
    inference(avatar_component_clause,[],[f25427]) ).

fof(f29532,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | spl0_1265 ),
    inference(avatar_component_clause,[],[f29530]) ).

fof(f29561,plain,
    ( spl0_1269
    | ~ spl0_10
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3580,f3517,f245,f29559]) ).

fof(f29559,plain,
    ( spl0_1269
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).

fof(f3580,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,element_relation)
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_10
    | ~ spl0_348 ),
    inference(resolution,[],[f3518,f247]) ).

fof(f29557,plain,
    ( spl0_347
    | ~ spl0_1268
    | ~ spl0_237
    | ~ spl0_286
    | spl0_346 ),
    inference(avatar_split_clause,[],[f3515,f3505,f2745,f2324,f29554,f3509]) ).

fof(f3509,plain,
    ( spl0_347
  <=> null_class = complement(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f29554,plain,
    ( spl0_1268
  <=> subclass(complement(cross_product(universal_class,universal_class)),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).

fof(f3505,plain,
    ( spl0_346
  <=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).

fof(f3515,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),singleton_relation)
    | null_class = complement(cross_product(universal_class,universal_class))
    | ~ spl0_237
    | ~ spl0_286
    | spl0_346 ),
    inference(forward_demodulation,[],[f3513,f2326]) ).

fof(f3513,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ subclass(complement(cross_product(universal_class,universal_class)),identity_relation)
    | ~ spl0_286
    | spl0_346 ),
    inference(resolution,[],[f3507,f2746]) ).

fof(f3507,plain,
    ( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | spl0_346 ),
    inference(avatar_component_clause,[],[f3505]) ).

fof(f29552,plain,
    ( spl0_347
    | ~ spl0_1267
    | ~ spl0_117
    | spl0_346 ),
    inference(avatar_split_clause,[],[f3514,f3505,f926,f29549,f3509]) ).

fof(f29549,plain,
    ( spl0_1267
  <=> subclass(complement(cross_product(universal_class,universal_class)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).

fof(f3514,plain,
    ( ~ subclass(complement(cross_product(universal_class,universal_class)),subset_relation)
    | null_class = complement(cross_product(universal_class,universal_class))
    | ~ spl0_117
    | spl0_346 ),
    inference(resolution,[],[f3507,f927]) ).

fof(f29541,plain,
    ( ~ spl0_1266
    | spl0_910
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3414,f3231,f2324,f394,f17719,f29538]) ).

fof(f17719,plain,
    ( spl0_910
  <=> subclass(subset_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f3414,plain,
    ( subclass(subset_relation,singleton_relation)
    | ~ member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f3413,f2326]) ).

fof(f3413,plain,
    ( ~ member(not_subclass_element(subset_relation,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | subclass(subset_relation,identity_relation)
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f3394,f2326]) ).

fof(f3394,plain,
    ( ~ member(not_subclass_element(subset_relation,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | subclass(subset_relation,identity_relation)
    | ~ spl0_43
    | ~ spl0_330 ),
    inference(superposition,[],[f3232,f396]) ).

fof(f29533,plain,
    ( spl0_886
    | ~ spl0_1265
    | ~ spl0_41
    | ~ spl0_237
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3412,f3231,f2324,f385,f29530,f17118]) ).

fof(f17118,plain,
    ( spl0_886
  <=> subclass(element_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).

fof(f385,plain,
    ( spl0_41
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f3412,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | subclass(element_relation,singleton_relation)
    | ~ spl0_41
    | ~ spl0_237
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f3393,f2326]) ).

fof(f3393,plain,
    ( ~ member(not_subclass_element(element_relation,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | subclass(element_relation,singleton_relation)
    | ~ spl0_41
    | ~ spl0_330 ),
    inference(superposition,[],[f3232,f387]) ).

fof(f387,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f385]) ).

fof(f29528,plain,
    ( spl0_1264
    | ~ spl0_76
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f3288,f3166,f610,f29526]) ).

fof(f29526,plain,
    ( spl0_1264
  <=> ! [X0] :
        ( ~ subclass(X0,subset_relation)
        | null_class = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).

fof(f3166,plain,
    ( spl0_317
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f3288,plain,
    ( ! [X0] :
        ( ~ subclass(X0,subset_relation)
        | null_class = X0
        | member(regular(X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_76
    | ~ spl0_317 ),
    inference(superposition,[],[f3167,f612]) ).

fof(f3167,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_317 ),
    inference(avatar_component_clause,[],[f3166]) ).

fof(f29524,plain,
    ( spl0_1263
    | ~ spl0_41
    | ~ spl0_1088 ),
    inference(avatar_split_clause,[],[f23470,f22544,f385,f29522]) ).

fof(f29522,plain,
    ( spl0_1263
  <=> ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(element_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).

fof(f23470,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(element_relation,X0) )
    | ~ spl0_41
    | ~ spl0_1088 ),
    inference(superposition,[],[f22545,f387]) ).

fof(f29520,plain,
    ( spl0_1262
    | ~ spl0_20
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f2815,f2757,f288,f29518]) ).

fof(f29518,plain,
    ( spl0_1262
  <=> ! [X0] :
        ( subclass(universal_class,complement(complement(X0)))
        | ~ member(not_subclass_element(universal_class,complement(complement(X0))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).

fof(f2815,plain,
    ( ! [X0] :
        ( subclass(universal_class,complement(complement(X0)))
        | ~ member(not_subclass_element(universal_class,complement(complement(X0))),X0) )
    | ~ spl0_20
    | ~ spl0_289 ),
    inference(resolution,[],[f2758,f289]) ).

fof(f29516,plain,
    ( spl0_1261
    | ~ spl0_77
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2586,f2517,f615,f29514]) ).

fof(f29514,plain,
    ( spl0_1261
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,complement(cross_product(X0,X1)))
        | ~ member(X2,X1)
        | ~ member(X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).

fof(f615,plain,
    ( spl0_77
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,X0)
        | ~ member(X3,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f2586,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,complement(cross_product(X0,X1)))
        | ~ member(X2,X1)
        | ~ member(X3,X0) )
    | ~ spl0_77
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f616]) ).

fof(f616,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | ~ member(X3,X1)
        | ~ member(X2,X0) )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f615]) ).

fof(f29510,plain,
    ( spl0_1260
    | ~ spl0_165
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2492,f2381,f1372,f29508]) ).

fof(f29508,plain,
    ( spl0_1260
  <=> ! [X0] :
        ( subclass(identity_relation,intersection(X0,subset_relation))
        | ~ member(not_subclass_element(identity_relation,intersection(X0,subset_relation)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).

fof(f1372,plain,
    ( spl0_165
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f2381,plain,
    ( spl0_246
  <=> ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f2492,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(X0,subset_relation))
        | ~ member(not_subclass_element(identity_relation,intersection(X0,subset_relation)),X0) )
    | ~ spl0_165
    | ~ spl0_246 ),
    inference(duplicate_literal_removal,[],[f2489]) ).

fof(f2489,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(X0,subset_relation))
        | ~ member(not_subclass_element(identity_relation,intersection(X0,subset_relation)),X0)
        | subclass(identity_relation,intersection(X0,subset_relation)) )
    | ~ spl0_165
    | ~ spl0_246 ),
    inference(resolution,[],[f2382,f1373]) ).

fof(f1373,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1372]) ).

fof(f2382,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_246 ),
    inference(avatar_component_clause,[],[f2381]) ).

fof(f29506,plain,
    ( spl0_1259
    | ~ spl0_165
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2486,f2377,f1372,f29504]) ).

fof(f29504,plain,
    ( spl0_1259
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(X0,element_relation))
        | ~ member(not_subclass_element(singleton_relation,intersection(X0,element_relation)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).

fof(f2377,plain,
    ( spl0_245
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f2486,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(X0,element_relation))
        | ~ member(not_subclass_element(singleton_relation,intersection(X0,element_relation)),X0) )
    | ~ spl0_165
    | ~ spl0_245 ),
    inference(duplicate_literal_removal,[],[f2483]) ).

fof(f2483,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(X0,element_relation))
        | ~ member(not_subclass_element(singleton_relation,intersection(X0,element_relation)),X0)
        | subclass(singleton_relation,intersection(X0,element_relation)) )
    | ~ spl0_165
    | ~ spl0_245 ),
    inference(resolution,[],[f2378,f1373]) ).

fof(f2378,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f2377]) ).

fof(f29502,plain,
    ( spl0_1258
    | ~ spl0_115
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2251,f2234,f899,f29500]) ).

fof(f29500,plain,
    ( spl0_1258
  <=> ! [X0] :
        ( function(intersection(X0,cross_product(universal_class,universal_class)))
        | ~ single_valued_class(intersection(X0,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).

fof(f899,plain,
    ( spl0_115
  <=> ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

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

fof(f2251,plain,
    ( ! [X0] :
        ( function(intersection(X0,cross_product(universal_class,universal_class)))
        | ~ single_valued_class(intersection(X0,cross_product(universal_class,universal_class))) )
    | ~ spl0_115
    | ~ spl0_225 ),
    inference(resolution,[],[f2235,f900]) ).

fof(f900,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f899]) ).

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

fof(f29498,plain,
    ( spl0_1257
    | ~ spl0_115
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2240,f2230,f899,f29496]) ).

fof(f29496,plain,
    ( spl0_1257
  <=> ! [X0] :
        ( function(intersection(cross_product(universal_class,universal_class),X0))
        | ~ single_valued_class(intersection(cross_product(universal_class,universal_class),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).

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

fof(f2240,plain,
    ( ! [X0] :
        ( function(intersection(cross_product(universal_class,universal_class),X0))
        | ~ single_valued_class(intersection(cross_product(universal_class,universal_class),X0)) )
    | ~ spl0_115
    | ~ spl0_224 ),
    inference(resolution,[],[f2231,f900]) ).

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

fof(f27988,plain,
    ( spl0_1255
    | ~ spl0_1256
    | ~ spl0_109
    | ~ spl0_237
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f22083,f2547,f2324,f818,f27985,f27982]) ).

fof(f27985,plain,
    ( spl0_1256
  <=> subclass(universal_class,compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).

fof(f22083,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,compose(element_relation,complement(singleton_relation)))
        | ~ member(unordered_pair(X0,X1),singleton_relation) )
    | ~ spl0_109
    | ~ spl0_237
    | ~ spl0_275 ),
    inference(forward_demodulation,[],[f2634,f2326]) ).

fof(f2634,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),singleton_relation)
        | ~ subclass(universal_class,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_109
    | ~ spl0_275 ),
    inference(resolution,[],[f2548,f819]) ).

fof(f27980,plain,
    ( spl0_1254
    | ~ spl0_270
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f11208,f11013,f2517,f27978]) ).

fof(f27978,plain,
    ( spl0_1254
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).

fof(f11013,plain,
    ( spl0_686
  <=> not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).

fof(f11208,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270
    | ~ spl0_686 ),
    inference(superposition,[],[f2518,f11015]) ).

fof(f11015,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)))))
    | ~ spl0_686 ),
    inference(avatar_component_clause,[],[f11013]) ).

fof(f27976,plain,
    ( spl0_1253
    | ~ spl0_270
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11134,f11008,f2517,f27974]) ).

fof(f27974,plain,
    ( spl0_1253
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).

fof(f11008,plain,
    ( spl0_685
  <=> 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_685])]) ).

fof(f11134,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270
    | ~ spl0_685 ),
    inference(superposition,[],[f2518,f11010]) ).

fof(f11010,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_685 ),
    inference(avatar_component_clause,[],[f11008]) ).

fof(f27972,plain,
    ( spl0_1252
    | ~ spl0_270
    | ~ spl0_683 ),
    inference(avatar_split_clause,[],[f11060,f10715,f2517,f27970]) ).

fof(f27970,plain,
    ( spl0_1252
  <=> ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).

fof(f10715,plain,
    ( spl0_683
  <=> not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).

fof(f11060,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270
    | ~ spl0_683 ),
    inference(superposition,[],[f2518,f10717]) ).

fof(f10717,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
    | ~ spl0_683 ),
    inference(avatar_component_clause,[],[f10715]) ).

fof(f27968,plain,
    ( spl0_1251
    | ~ spl0_1051
    | ~ spl0_1189 ),
    inference(avatar_split_clause,[],[f27448,f26495,f21183,f27965]) ).

fof(f27965,plain,
    ( spl0_1251
  <=> subclass(singleton_relation,intersection(element_relation,subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).

fof(f21183,plain,
    ( spl0_1051
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).

fof(f26495,plain,
    ( spl0_1189
  <=> singleton_relation = intersection(subset_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).

fof(f27448,plain,
    ( subclass(singleton_relation,intersection(element_relation,subset_relation))
    | ~ spl0_1051
    | ~ spl0_1189 ),
    inference(superposition,[],[f21184,f26497]) ).

fof(f26497,plain,
    ( singleton_relation = intersection(subset_relation,singleton_relation)
    | ~ spl0_1189 ),
    inference(avatar_component_clause,[],[f26495]) ).

fof(f21184,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
    | ~ spl0_1051 ),
    inference(avatar_component_clause,[],[f21183]) ).

fof(f27963,plain,
    ( spl0_1250
    | ~ spl0_374
    | ~ spl0_684 ),
    inference(avatar_split_clause,[],[f10905,f10885,f3829,f27961]) ).

fof(f27961,plain,
    ( spl0_1250
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,successor_relation)
        | member(not_subclass_element(X0,X1),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).

fof(f10905,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,successor_relation)
        | member(not_subclass_element(X0,X1),element_relation) )
    | ~ spl0_374
    | ~ spl0_684 ),
    inference(resolution,[],[f10887,f3830]) ).

fof(f27959,plain,
    ( spl0_1249
    | ~ spl0_366
    | ~ spl0_628 ),
    inference(avatar_split_clause,[],[f9657,f9623,f3796,f27957]) ).

fof(f27957,plain,
    ( spl0_1249
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(second(unordered_pair(X0,X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).

fof(f3796,plain,
    ( spl0_366
  <=> ! [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_366])]) ).

fof(f9657,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(second(unordered_pair(X0,X1)),universal_class) )
    | ~ spl0_366
    | ~ spl0_628 ),
    inference(superposition,[],[f3797,f9624]) ).

fof(f3797,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_366 ),
    inference(avatar_component_clause,[],[f3796]) ).

fof(f27955,plain,
    ( spl0_1248
    | ~ spl0_365
    | ~ spl0_628 ),
    inference(avatar_split_clause,[],[f9656,f9623,f3792,f27953]) ).

fof(f27953,plain,
    ( spl0_1248
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(first(unordered_pair(X0,X1)),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).

fof(f3792,plain,
    ( spl0_365
  <=> ! [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_365])]) ).

fof(f9656,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(first(unordered_pair(X0,X1)),universal_class) )
    | ~ spl0_365
    | ~ spl0_628 ),
    inference(superposition,[],[f3793,f9624]) ).

fof(f3793,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_365 ),
    inference(avatar_component_clause,[],[f3792]) ).

fof(f27746,plain,
    ( spl0_1246
    | spl0_1247
    | ~ spl0_278
    | ~ spl0_589 ),
    inference(avatar_split_clause,[],[f8995,f8966,f2576,f27744,f27741]) ).

fof(f27741,plain,
    ( spl0_1246
  <=> ! [X2,X3] :
        ( ~ member(X2,X3)
        | member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).

fof(f27744,plain,
    ( spl0_1247
  <=> ! [X0,X1] : ~ subclass(universal_class,compose(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).

fof(f2576,plain,
    ( spl0_278
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f8966,plain,
    ( spl0_589
  <=> ! [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_589])]) ).

fof(f8995,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,compose(X0,X1))
        | ~ member(X2,X3)
        | member(X2,universal_class) )
    | ~ spl0_278
    | ~ spl0_589 ),
    inference(resolution,[],[f8967,f2577]) ).

fof(f2577,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,universal_class) )
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f2576]) ).

fof(f8967,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class)))))
        | ~ subclass(universal_class,compose(X0,X1)) )
    | ~ spl0_589 ),
    inference(avatar_component_clause,[],[f8966]) ).

fof(f27739,plain,
    ( ~ spl0_1245
    | spl0_1244
    | ~ spl0_489
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f8275,f8263,f6485,f27732,f27736]) ).

fof(f27736,plain,
    ( spl0_1245
  <=> subclass(domain_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).

fof(f27732,plain,
    ( spl0_1244
  <=> ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).

fof(f6485,plain,
    ( spl0_489
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f8263,plain,
    ( spl0_568
  <=> ! [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_568])]) ).

fof(f8275,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(element_relation)) )
    | ~ spl0_489
    | ~ spl0_568 ),
    inference(duplicate_literal_removal,[],[f8266]) ).

fof(f8266,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(element_relation)) )
    | ~ spl0_489
    | ~ spl0_568 ),
    inference(resolution,[],[f8264,f6486]) ).

fof(f6486,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | ~ member(X1,universal_class)
        | ~ subclass(domain_relation,complement(X0)) )
    | ~ spl0_489 ),
    inference(avatar_component_clause,[],[f6485]) ).

fof(f8264,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class) )
    | ~ spl0_568 ),
    inference(avatar_component_clause,[],[f8263]) ).

fof(f27734,plain,
    ( ~ spl0_1243
    | spl0_1244
    | ~ spl0_270
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f8271,f8263,f2517,f27732,f27728]) ).

fof(f27728,plain,
    ( spl0_1243
  <=> subclass(universal_class,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).

fof(f8271,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ subclass(universal_class,complement(element_relation)) )
    | ~ spl0_270
    | ~ spl0_568 ),
    inference(resolution,[],[f8264,f2518]) ).

fof(f27726,plain,
    ( spl0_1242
    | ~ spl0_23
    | ~ spl0_456 ),
    inference(avatar_split_clause,[],[f6053,f5946,f300,f27724]) ).

fof(f27724,plain,
    ( spl0_1242
  <=> ! [X0] :
        ( member(regular(X0),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).

fof(f5946,plain,
    ( spl0_456
  <=> ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f6053,plain,
    ( ! [X0] :
        ( member(regular(X0),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0)) )
    | ~ spl0_23
    | ~ spl0_456 ),
    inference(duplicate_literal_removal,[],[f5988]) ).

fof(f5988,plain,
    ( ! [X0] :
        ( member(regular(X0),null_class)
        | null_class = X0
        | ~ subclass(X0,regular(X0))
        | null_class = X0
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_456 ),
    inference(resolution,[],[f5947,f301]) ).

fof(f5947,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(X0),X1)
        | member(regular(X0),null_class)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_456 ),
    inference(avatar_component_clause,[],[f5946]) ).

fof(f27722,plain,
    ( spl0_1241
    | ~ spl0_1049
    | ~ spl0_1188 ),
    inference(avatar_split_clause,[],[f27265,f26118,f21134,f27719]) ).

fof(f27719,plain,
    ( spl0_1241
  <=> subclass(singleton_relation,intersection(subset_relation,element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).

fof(f21134,plain,
    ( spl0_1049
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).

fof(f26118,plain,
    ( spl0_1188
  <=> singleton_relation = intersection(element_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).

fof(f27265,plain,
    ( subclass(singleton_relation,intersection(subset_relation,element_relation))
    | ~ spl0_1049
    | ~ spl0_1188 ),
    inference(superposition,[],[f21135,f26120]) ).

fof(f26120,plain,
    ( singleton_relation = intersection(element_relation,singleton_relation)
    | ~ spl0_1188 ),
    inference(avatar_component_clause,[],[f26118]) ).

fof(f21135,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
    | ~ spl0_1049 ),
    inference(avatar_component_clause,[],[f21134]) ).

fof(f27717,plain,
    ( spl0_1240
    | ~ spl0_408
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5420,f4906,f4839,f27715]) ).

fof(f27715,plain,
    ( spl0_1240
  <=> ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).

fof(f5420,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_408
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5401]) ).

fof(f5401,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(intersection(singleton_relation,X0),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_408
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f4840]) ).

fof(f27713,plain,
    ( spl0_1239
    | ~ spl0_410
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5418,f4906,f4847,f27711]) ).

fof(f27711,plain,
    ( spl0_1239
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).

fof(f5418,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_410
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5403]) ).

fof(f5403,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(X0,intersection(singleton_relation,X1)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_410
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f4848]) ).

fof(f27709,plain,
    ( spl0_1238
    | ~ spl0_407
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5417,f4906,f4812,f27707]) ).

fof(f27707,plain,
    ( spl0_1238
  <=> ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).

fof(f5417,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_407
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5404]) ).

fof(f5404,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(intersection(X0,singleton_relation),X1),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_407
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f4813]) ).

fof(f27705,plain,
    ( spl0_1237
    | ~ spl0_409
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5413,f4906,f4843,f27703]) ).

fof(f27703,plain,
    ( spl0_1237
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).

fof(f5413,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_409
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5408]) ).

fof(f5408,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(X0,intersection(X1,singleton_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_409
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f4844]) ).

fof(f27701,plain,
    ( spl0_1236
    | ~ spl0_408
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5396,f4902,f4839,f27699]) ).

fof(f27699,plain,
    ( spl0_1236
  <=> ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).

fof(f5396,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_408
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5377]) ).

fof(f5377,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(intersection(singleton_relation,X0),X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_408
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f4840]) ).

fof(f27697,plain,
    ( spl0_1235
    | ~ spl0_410
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5394,f4902,f4847,f27695]) ).

fof(f27695,plain,
    ( spl0_1235
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).

fof(f5394,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_410
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5379]) ).

fof(f5379,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(X0,intersection(singleton_relation,X1)),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_410
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f4848]) ).

fof(f27693,plain,
    ( spl0_1234
    | ~ spl0_407
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5393,f4902,f4812,f27691]) ).

fof(f27691,plain,
    ( spl0_1234
  <=> ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).

fof(f5393,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_407
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5380]) ).

fof(f5380,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(intersection(X0,singleton_relation),X1),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_407
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f4813]) ).

fof(f27689,plain,
    ( spl0_1233
    | ~ spl0_409
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5389,f4902,f4843,f27687]) ).

fof(f27687,plain,
    ( spl0_1233
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).

fof(f5389,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_409
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5384]) ).

fof(f5384,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(X0,intersection(X1,singleton_relation)),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_409
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f4844]) ).

fof(f27684,plain,
    ( spl0_1232
    | ~ spl0_408
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5362,f4889,f4839,f27682]) ).

fof(f27682,plain,
    ( spl0_1232
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).

fof(f5362,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1)))
    | ~ spl0_408
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5307]) ).

fof(f5307,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X0,intersection(X0,X1))) )
    | ~ spl0_408
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4840]) ).

fof(f27679,plain,
    ( spl0_1231
    | ~ spl0_407
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5358,f4889,f4812,f27677]) ).

fof(f27677,plain,
    ( spl0_1231
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).

fof(f5358,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1)))
    | ~ spl0_407
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5311]) ).

fof(f5311,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1)))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X1,intersection(X0,X1))) )
    | ~ spl0_407
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4813]) ).

fof(f27675,plain,
    ( spl0_1230
    | ~ spl0_1140
    | ~ spl0_1143 ),
    inference(avatar_split_clause,[],[f25642,f25376,f25364,f27672]) ).

fof(f27672,plain,
    ( spl0_1230
  <=> singleton_relation = intersection(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).

fof(f25364,plain,
    ( spl0_1140
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f25376,plain,
    ( spl0_1143
  <=> subclass(singleton_relation,intersection(singleton_relation,subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f25642,plain,
    ( singleton_relation = intersection(singleton_relation,subset_relation)
    | ~ spl0_1140
    | ~ spl0_1143 ),
    inference(resolution,[],[f25365,f25378]) ).

fof(f25378,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,subset_relation))
    | ~ spl0_1143 ),
    inference(avatar_component_clause,[],[f25376]) ).

fof(f25365,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 )
    | ~ spl0_1140 ),
    inference(avatar_component_clause,[],[f25364]) ).

fof(f27669,plain,
    ( spl0_1229
    | ~ spl0_410
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5294,f4885,f4847,f27667]) ).

fof(f27667,plain,
    ( spl0_1229
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).

fof(f5294,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2)))
    | ~ spl0_410
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5245]) ).

fof(f5245,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2)))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X1,intersection(X1,X2))) )
    | ~ spl0_410
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4848]) ).

fof(f27664,plain,
    ( spl0_1228
    | ~ spl0_409
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5289,f4885,f4843,f27662]) ).

fof(f27662,plain,
    ( spl0_1228
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).

fof(f5289,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2)))
    | ~ spl0_409
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5250]) ).

fof(f5250,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2)))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X2,intersection(X1,X2))) )
    | ~ spl0_409
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4844]) ).

fof(f27658,plain,
    ( spl0_1227
    | ~ spl0_352
    | ~ spl0_410 ),
    inference(avatar_split_clause,[],[f5121,f4847,f3533,f27656]) ).

fof(f27656,plain,
    ( spl0_1227
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(null_class,X1)),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).

fof(f3533,plain,
    ( spl0_352
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f5121,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(null_class,X1)),regular(X2))
        | null_class = X2 )
    | ~ spl0_352
    | ~ spl0_410 ),
    inference(duplicate_literal_removal,[],[f5093]) ).

fof(f5093,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(null_class,X1)),regular(X2))
        | null_class = X2
        | subclass(intersection(X0,intersection(null_class,X1)),regular(X2)) )
    | ~ spl0_352
    | ~ spl0_410 ),
    inference(resolution,[],[f4848,f3534]) ).

fof(f3534,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_352 ),
    inference(avatar_component_clause,[],[f3533]) ).

fof(f27652,plain,
    ( spl0_1226
    | ~ spl0_352
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f5063,f4843,f3533,f27650]) ).

fof(f27650,plain,
    ( spl0_1226
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,null_class)),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).

fof(f5063,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,null_class)),regular(X2))
        | null_class = X2 )
    | ~ spl0_352
    | ~ spl0_409 ),
    inference(duplicate_literal_removal,[],[f5035]) ).

fof(f5035,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,null_class)),regular(X2))
        | null_class = X2
        | subclass(intersection(X0,intersection(X1,null_class)),regular(X2)) )
    | ~ spl0_352
    | ~ spl0_409 ),
    inference(resolution,[],[f4844,f3534]) ).

fof(f27646,plain,
    ( spl0_1225
    | ~ spl0_352
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f5004,f4839,f3533,f27644]) ).

fof(f27644,plain,
    ( spl0_1225
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(intersection(null_class,X0),X1),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).

fof(f5004,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(null_class,X0),X1),regular(X2))
        | null_class = X2 )
    | ~ spl0_352
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f4976]) ).

fof(f4976,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(null_class,X0),X1),regular(X2))
        | null_class = X2
        | subclass(intersection(intersection(null_class,X0),X1),regular(X2)) )
    | ~ spl0_352
    | ~ spl0_408 ),
    inference(resolution,[],[f4840,f3534]) ).

fof(f27640,plain,
    ( spl0_1224
    | ~ spl0_352
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f4946,f4812,f3533,f27638]) ).

fof(f27638,plain,
    ( spl0_1224
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,null_class),X1),regular(X2))
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).

fof(f4946,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,null_class),X1),regular(X2))
        | null_class = X2 )
    | ~ spl0_352
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f4918]) ).

fof(f4918,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,null_class),X1),regular(X2))
        | null_class = X2
        | subclass(intersection(intersection(X0,null_class),X1),regular(X2)) )
    | ~ spl0_352
    | ~ spl0_407 ),
    inference(resolution,[],[f4813,f3534]) ).

fof(f27636,plain,
    ( spl0_1223
    | ~ spl0_131
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4760,f4308,f1019,f27634]) ).

fof(f27634,plain,
    ( spl0_1223
  <=> ! [X2,X0,X1] :
        ( subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).

fof(f4760,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | ~ subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4714]) ).

fof(f4714,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_131
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f1020]) ).

fof(f27632,plain,
    ( spl0_1222
    | ~ spl0_305
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4753,f4308,f2966,f27630]) ).

fof(f27630,plain,
    ( spl0_1222
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).

fof(f4753,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_305
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4722]) ).

fof(f4722,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(element_relation,X1))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_305
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f2967]) ).

fof(f27628,plain,
    ( spl0_1221
    | ~ spl0_313
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4747,f4308,f3118,f27626]) ).

fof(f27626,plain,
    ( spl0_1221
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).

fof(f4747,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4736]) ).

fof(f4736,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(subset_relation,X1))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f3119]) ).

fof(f27624,plain,
    ( spl0_1220
    | ~ spl0_381 ),
    inference(avatar_split_clause,[],[f4190,f3857,f27622]) ).

fof(f27622,plain,
    ( spl0_1220
  <=> ! [X0] :
        ( regular(unordered_pair(X0,X0)) = X0
        | unordered_pair(X0,X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).

fof(f3857,plain,
    ( spl0_381
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).

fof(f4190,plain,
    ( ! [X0] :
        ( regular(unordered_pair(X0,X0)) = X0
        | unordered_pair(X0,X0) = null_class )
    | ~ spl0_381 ),
    inference(equality_resolution,[],[f3858]) ).

fof(f3858,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_381 ),
    inference(avatar_component_clause,[],[f3857]) ).

fof(f27620,plain,
    ( spl0_1219
    | ~ spl0_1139
    | ~ spl0_1140 ),
    inference(avatar_split_clause,[],[f25641,f25364,f25281,f27617]) ).

fof(f27617,plain,
    ( spl0_1219
  <=> singleton_relation = intersection(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).

fof(f25281,plain,
    ( spl0_1139
  <=> subclass(singleton_relation,intersection(singleton_relation,element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f25641,plain,
    ( singleton_relation = intersection(singleton_relation,element_relation)
    | ~ spl0_1139
    | ~ spl0_1140 ),
    inference(resolution,[],[f25365,f25283]) ).

fof(f25283,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,element_relation))
    | ~ spl0_1139 ),
    inference(avatar_component_clause,[],[f25281]) ).

fof(f27615,plain,
    ( spl0_1218
    | ~ spl0_4
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f4038,f3829,f220,f27613]) ).

fof(f27613,plain,
    ( spl0_1218
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,X2)
        | member(not_subclass_element(X0,X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).

fof(f4038,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,X2)
        | member(not_subclass_element(X0,X1),universal_class) )
    | ~ spl0_4
    | ~ spl0_374 ),
    inference(resolution,[],[f3830,f221]) ).

fof(f27611,plain,
    ( spl0_1217
    | ~ spl0_318
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3474,f3352,f3170,f27609]) ).

fof(f27609,plain,
    ( spl0_1217
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).

fof(f3170,plain,
    ( spl0_318
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f3474,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_318
    | ~ spl0_338 ),
    inference(duplicate_literal_removal,[],[f3463]) ).

fof(f3463,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_318
    | ~ spl0_338 ),
    inference(resolution,[],[f3353,f3171]) ).

fof(f3171,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2)
        | ~ subclass(X0,complement(X1)) )
    | ~ spl0_318 ),
    inference(avatar_component_clause,[],[f3170]) ).

fof(f27607,plain,
    ( spl0_1216
    | ~ spl0_20
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f3441,f3344,f288,f27605]) ).

fof(f27605,plain,
    ( spl0_1216
  <=> ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ member(not_subclass_element(singleton_relation,X0),compose(element_relation,complement(singleton_relation))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).

fof(f3441,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | ~ member(not_subclass_element(singleton_relation,X0),compose(element_relation,complement(singleton_relation))) )
    | ~ spl0_20
    | ~ spl0_336 ),
    inference(resolution,[],[f3345,f289]) ).

fof(f27603,plain,
    ( spl0_1215
    | ~ spl0_318
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3435,f3330,f3170,f27601]) ).

fof(f27601,plain,
    ( spl0_1215
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).

fof(f3435,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(subset_relation)) )
    | ~ spl0_318
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3424]) ).

fof(f3424,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(subset_relation)) )
    | ~ spl0_318
    | ~ spl0_335 ),
    inference(resolution,[],[f3331,f3171]) ).

fof(f27599,plain,
    ( spl0_1214
    | ~ spl0_318
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3368,f3214,f3170,f27597]) ).

fof(f27597,plain,
    ( spl0_1214
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).

fof(f3368,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_318
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3361]) ).

fof(f3361,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | subclass(intersection(X0,singleton_relation),X1)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_318
    | ~ spl0_327 ),
    inference(resolution,[],[f3215,f3171]) ).

fof(f27595,plain,
    ( spl0_1213
    | ~ spl0_318
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f3341,f3188,f3170,f27593]) ).

fof(f27593,plain,
    ( spl0_1213
  <=> ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).

fof(f3341,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_318
    | ~ spl0_322 ),
    inference(duplicate_literal_removal,[],[f3334]) ).

fof(f3334,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | subclass(intersection(singleton_relation,X0),X1)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_318
    | ~ spl0_322 ),
    inference(resolution,[],[f3189,f3171]) ).

fof(f27591,plain,
    ( spl0_1212
    | ~ spl0_135
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3321,f3170,f1090,f27589]) ).

fof(f27589,plain,
    ( spl0_1212
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).

fof(f3321,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X0)) )
    | ~ spl0_135
    | ~ spl0_318 ),
    inference(duplicate_literal_removal,[],[f3294]) ).

fof(f3294,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X0))
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_135
    | ~ spl0_318 ),
    inference(resolution,[],[f3171,f1091]) ).

fof(f27587,plain,
    ( spl0_1211
    | ~ spl0_136
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3319,f3170,f1094,f27585]) ).

fof(f27585,plain,
    ( spl0_1211
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).

fof(f3319,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X1)) )
    | ~ spl0_136
    | ~ spl0_318 ),
    inference(duplicate_literal_removal,[],[f3296]) ).

fof(f3296,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(intersection(X0,X1),complement(X1))
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_136
    | ~ spl0_318 ),
    inference(resolution,[],[f3171,f1095]) ).

fof(f27559,plain,
    ( spl0_1210
    | spl0_1136
    | ~ spl0_13
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f3284,f3166,f259,f24010,f27557]) ).

fof(f27557,plain,
    ( spl0_1210
  <=> ! [X0,X1] :
        ( member(regular(omega),X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).

fof(f24010,plain,
    ( spl0_1136
  <=> null_class = omega ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).

fof(f3284,plain,
    ( ! [X0,X1] :
        ( null_class = omega
        | member(regular(omega),X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_317 ),
    inference(resolution,[],[f3167,f260]) ).

fof(f27402,plain,
    ( spl0_1209
    | spl0_1136
    | ~ spl0_13
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f3271,f3162,f259,f24010,f27400]) ).

fof(f27400,plain,
    ( spl0_1209
  <=> ! [X0,X1] :
        ( member(regular(omega),X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).

fof(f3162,plain,
    ( spl0_316
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f3271,plain,
    ( ! [X0,X1] :
        ( null_class = omega
        | member(regular(omega),X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_13
    | ~ spl0_316 ),
    inference(resolution,[],[f3163,f260]) ).

fof(f3163,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f3162]) ).

fof(f27398,plain,
    ( spl0_1208
    | ~ spl0_294
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f3156,f3139,f2836,f27396]) ).

fof(f27396,plain,
    ( spl0_1208
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).

fof(f3139,plain,
    ( spl0_314
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f3156,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_294
    | ~ spl0_314 ),
    inference(duplicate_literal_removal,[],[f3151]) ).

fof(f3151,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(subset_relation)) )
    | ~ spl0_294
    | ~ spl0_314 ),
    inference(resolution,[],[f3140,f2837]) ).

fof(f3140,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f3139]) ).

fof(f27394,plain,
    ( spl0_1207
    | ~ spl0_294
    | ~ spl0_303 ),
    inference(avatar_split_clause,[],[f3116,f2956,f2836,f27392]) ).

fof(f27392,plain,
    ( spl0_1207
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).

fof(f2956,plain,
    ( spl0_303
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f3116,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_294
    | ~ spl0_303 ),
    inference(duplicate_literal_removal,[],[f3111]) ).

fof(f3111,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | null_class = intersection(X0,singleton_relation)
        | ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
    | ~ spl0_294
    | ~ spl0_303 ),
    inference(resolution,[],[f2957,f2837]) ).

fof(f2957,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),element_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_303 ),
    inference(avatar_component_clause,[],[f2956]) ).

fof(f27390,plain,
    ( spl0_1206
    | ~ spl0_38
    | ~ spl0_311 ),
    inference(avatar_split_clause,[],[f3109,f3091,f373,f27388]) ).

fof(f27388,plain,
    ( spl0_1206
  <=> ! [X0] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).

fof(f3091,plain,
    ( spl0_311
  <=> member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f3109,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_38
    | ~ spl0_311 ),
    inference(resolution,[],[f3093,f374]) ).

fof(f3093,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_311 ),
    inference(avatar_component_clause,[],[f3091]) ).

fof(f27386,plain,
    ( ~ spl0_1205
    | spl0_232
    | ~ spl0_294
    | ~ spl0_311 ),
    inference(avatar_split_clause,[],[f3105,f3091,f2836,f2289,f27383]) ).

fof(f27383,plain,
    ( spl0_1205
  <=> subclass(singleton_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).

fof(f2289,plain,
    ( spl0_232
  <=> null_class = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f3105,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
    | ~ spl0_294
    | ~ spl0_311 ),
    inference(resolution,[],[f3093,f2837]) ).

fof(f27381,plain,
    ( spl0_1204
    | ~ spl0_38
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3104,f3086,f373,f27379]) ).

fof(f27379,plain,
    ( spl0_1204
  <=> ! [X0] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).

fof(f3086,plain,
    ( spl0_310
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f3104,plain,
    ( ! [X0] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_38
    | ~ spl0_310 ),
    inference(resolution,[],[f3088,f374]) ).

fof(f3088,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_310 ),
    inference(avatar_component_clause,[],[f3086]) ).

fof(f27377,plain,
    ( ~ spl0_1203
    | spl0_232
    | ~ spl0_294
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3100,f3086,f2836,f2289,f27374]) ).

fof(f27374,plain,
    ( spl0_1203
  <=> subclass(singleton_relation,complement(complement(compose(element_relation,complement(singleton_relation))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).

fof(f3100,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,complement(complement(compose(element_relation,complement(singleton_relation)))))
    | ~ spl0_294
    | ~ spl0_310 ),
    inference(resolution,[],[f3088,f2837]) ).

fof(f27246,plain,
    ( spl0_1202
    | ~ spl0_237
    | ~ spl0_294
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f3067,f2840,f2836,f2324,f27244]) ).

fof(f27244,plain,
    ( spl0_1202
  <=> ! [X0] :
        ( ~ subclass(intersection(singleton_relation,X0),complement(subset_relation))
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).

fof(f2840,plain,
    ( spl0_295
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f3067,plain,
    ( ! [X0] :
        ( ~ subclass(intersection(singleton_relation,X0),complement(subset_relation))
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_237
    | ~ spl0_294
    | ~ spl0_295 ),
    inference(forward_demodulation,[],[f3047,f2326]) ).

fof(f3047,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_237
    | ~ spl0_294
    | ~ spl0_295 ),
    inference(forward_demodulation,[],[f3046,f2326]) ).

fof(f3046,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_294
    | ~ spl0_295 ),
    inference(duplicate_literal_removal,[],[f3040]) ).

fof(f3040,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | null_class = intersection(identity_relation,X0)
        | ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
    | ~ spl0_294
    | ~ spl0_295 ),
    inference(resolution,[],[f2841,f2837]) ).

fof(f2841,plain,
    ( ! [X0] :
        ( member(regular(intersection(identity_relation,X0)),subset_relation)
        | null_class = intersection(identity_relation,X0) )
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f2840]) ).

fof(f27242,plain,
    ( spl0_1201
    | ~ spl0_294
    | ~ spl0_296 ),
    inference(avatar_split_clause,[],[f3059,f2844,f2836,f27240]) ).

fof(f27240,plain,
    ( spl0_1201
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).

fof(f2844,plain,
    ( spl0_296
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f3059,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_294
    | ~ spl0_296 ),
    inference(duplicate_literal_removal,[],[f3054]) ).

fof(f3054,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | null_class = intersection(singleton_relation,X0)
        | ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
    | ~ spl0_294
    | ~ spl0_296 ),
    inference(resolution,[],[f2845,f2837]) ).

fof(f2845,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),element_relation)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_296 ),
    inference(avatar_component_clause,[],[f2844]) ).

fof(f27238,plain,
    ( spl0_1200
    | ~ spl0_237
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f3044,f2840,f2324,f27236]) ).

fof(f27236,plain,
    ( spl0_1200
  <=> ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),subset_relation)
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).

fof(f3044,plain,
    ( ! [X0] :
        ( member(regular(intersection(singleton_relation,X0)),subset_relation)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_237
    | ~ spl0_295 ),
    inference(superposition,[],[f2841,f2326]) ).

fof(f27234,plain,
    ( spl0_1199
    | ~ spl0_129
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3012,f2836,f1011,f27232]) ).

fof(f27232,plain,
    ( spl0_1199
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f1011,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f3012,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X0)) )
    | ~ spl0_129
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f2986]) ).

fof(f2986,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X0))
        | intersection(X0,X1) = null_class )
    | ~ spl0_129
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f1012]) ).

fof(f1012,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_129 ),
    inference(avatar_component_clause,[],[f1011]) ).

fof(f27230,plain,
    ( spl0_1198
    | ~ spl0_130
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3010,f2836,f1015,f27228]) ).

fof(f27228,plain,
    ( spl0_1198
  <=> ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f1015,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f3010,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X1)) )
    | ~ spl0_130
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f2988]) ).

fof(f2988,plain,
    ( ! [X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(intersection(X0,X1),complement(X1))
        | intersection(X0,X1) = null_class )
    | ~ spl0_130
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f1016]) ).

fof(f1016,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1015]) ).

fof(f27226,plain,
    ( spl0_1197
    | ~ spl0_53
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2902,f2324,f465,f27224]) ).

fof(f27224,plain,
    ( spl0_1197
  <=> ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).

fof(f465,plain,
    ( spl0_53
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f2902,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | single_valued_class(X0) )
    | ~ spl0_53
    | ~ spl0_237 ),
    inference(superposition,[],[f466,f2326]) ).

fof(f466,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f465]) ).

fof(f27222,plain,
    ( spl0_1196
    | ~ spl0_52
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2901,f2324,f461,f27220]) ).

fof(f27220,plain,
    ( spl0_1196
  <=> ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).

fof(f461,plain,
    ( spl0_52
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f2901,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_237 ),
    inference(superposition,[],[f462,f2326]) ).

fof(f462,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f461]) ).

fof(f27218,plain,
    ( spl0_1195
    | ~ spl0_51
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2900,f2324,f457,f27216]) ).

fof(f27216,plain,
    ( spl0_1195
  <=> ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).

fof(f457,plain,
    ( spl0_51
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f2900,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),singleton_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_237 ),
    inference(superposition,[],[f458,f2326]) ).

fof(f458,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f457]) ).

fof(f27214,plain,
    ( spl0_1193
    | ~ spl0_1194
    | ~ spl0_112
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2587,f2517,f830,f27211,f27208]) ).

fof(f27208,plain,
    ( spl0_1193
  <=> ! [X0,X1] : ~ member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).

fof(f27211,plain,
    ( spl0_1194
  <=> subclass(universal_class,complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).

fof(f2587,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(cross_product(universal_class,universal_class)))
        | ~ member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_112
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f831]) ).

fof(f26802,plain,
    ( ~ spl0_1192
    | spl0_347
    | ~ spl0_22
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f2508,f2475,f296,f3509,f26799]) ).

fof(f26799,plain,
    ( spl0_1192
  <=> function(complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).

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

fof(f2475,plain,
    ( spl0_265
  <=> ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f2508,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ function(complement(cross_product(universal_class,universal_class)))
    | ~ spl0_22
    | ~ spl0_265 ),
    inference(resolution,[],[f2476,f297]) ).

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

fof(f2476,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_265 ),
    inference(avatar_component_clause,[],[f2475]) ).

fof(f26795,plain,
    ( spl0_1191
    | ~ spl0_38
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2491,f2381,f373,f26793]) ).

fof(f26793,plain,
    ( spl0_1191
  <=> ! [X0,X1] :
        ( subclass(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(not_subclass_element(identity_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).

fof(f2491,plain,
    ( ! [X0,X1] :
        ( subclass(identity_relation,X0)
        | ~ subclass(subset_relation,X1)
        | member(not_subclass_element(identity_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_246 ),
    inference(resolution,[],[f2382,f374]) ).

fof(f26791,plain,
    ( spl0_1190
    | ~ spl0_38
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2485,f2377,f373,f26789]) ).

fof(f26789,plain,
    ( spl0_1190
  <=> ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(not_subclass_element(singleton_relation,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).

fof(f2485,plain,
    ( ! [X0,X1] :
        ( subclass(singleton_relation,X0)
        | ~ subclass(element_relation,X1)
        | member(not_subclass_element(singleton_relation,X0),X1) )
    | ~ spl0_38
    | ~ spl0_245 ),
    inference(resolution,[],[f2378,f374]) ).

fof(f26498,plain,
    ( spl0_1189
    | ~ spl0_498
    | ~ spl0_1141 ),
    inference(avatar_split_clause,[],[f25699,f25368,f6737,f26495]) ).

fof(f6737,plain,
    ( spl0_498
  <=> subclass(singleton_relation,intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).

fof(f25368,plain,
    ( spl0_1141
  <=> ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f25699,plain,
    ( singleton_relation = intersection(subset_relation,singleton_relation)
    | ~ spl0_498
    | ~ spl0_1141 ),
    inference(resolution,[],[f25369,f6739]) ).

fof(f6739,plain,
    ( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
    | ~ spl0_498 ),
    inference(avatar_component_clause,[],[f6737]) ).

fof(f25369,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 )
    | ~ spl0_1141 ),
    inference(avatar_component_clause,[],[f25368]) ).

fof(f26121,plain,
    ( spl0_1188
    | ~ spl0_481
    | ~ spl0_1141 ),
    inference(avatar_split_clause,[],[f25696,f25368,f6450,f26118]) ).

fof(f6450,plain,
    ( spl0_481
  <=> subclass(singleton_relation,intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f25696,plain,
    ( singleton_relation = intersection(element_relation,singleton_relation)
    | ~ spl0_481
    | ~ spl0_1141 ),
    inference(resolution,[],[f25369,f6452]) ).

fof(f6452,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_481 ),
    inference(avatar_component_clause,[],[f6450]) ).

fof(f25740,plain,
    ( spl0_1187
    | ~ spl0_492
    | ~ spl0_1140 ),
    inference(avatar_split_clause,[],[f25620,f25364,f6497,f25738]) ).

fof(f25738,plain,
    ( spl0_1187
  <=> ! [X0] : intersection(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f6497,plain,
    ( spl0_492
  <=> ! [X0] : subclass(X0,intersection(X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f25620,plain,
    ( ! [X0] : intersection(X0,X0) = X0
    | ~ spl0_492
    | ~ spl0_1140 ),
    inference(resolution,[],[f25365,f6498]) ).

fof(f6498,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_492 ),
    inference(avatar_component_clause,[],[f6497]) ).

fof(f25619,plain,
    ( spl0_1186
    | ~ spl0_109
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f11201,f11013,f818,f25617]) ).

fof(f25617,plain,
    ( spl0_1186
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).

fof(f11201,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_686 ),
    inference(superposition,[],[f819,f11015]) ).

fof(f25615,plain,
    ( spl0_1185
    | ~ spl0_109
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11127,f11008,f818,f25613]) ).

fof(f25613,plain,
    ( spl0_1185
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).

fof(f11127,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_685 ),
    inference(superposition,[],[f819,f11010]) ).

fof(f25611,plain,
    ( spl0_1184
    | ~ spl0_109
    | ~ spl0_683 ),
    inference(avatar_split_clause,[],[f11053,f10715,f818,f25609]) ).

fof(f25609,plain,
    ( spl0_1184
  <=> ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f11053,plain,
    ( ! [X0] :
        ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),X0)
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_683 ),
    inference(superposition,[],[f819,f10717]) ).

fof(f25607,plain,
    ( spl0_1183
    | ~ spl0_348
    | ~ spl0_684 ),
    inference(avatar_split_clause,[],[f10906,f10885,f3517,f25605]) ).

fof(f25605,plain,
    ( spl0_1183
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).

fof(f10906,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,successor_relation)
        | member(regular(X0),element_relation) )
    | ~ spl0_348
    | ~ spl0_684 ),
    inference(resolution,[],[f10887,f3518]) ).

fof(f25601,plain,
    ( spl0_1182
    | spl0_729
    | ~ spl0_166
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6819,f6485,f1376,f12079,f25599]) ).

fof(f25599,plain,
    ( spl0_1182
  <=> ! [X1] :
        ( ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).

fof(f12079,plain,
    ( spl0_729
  <=> ! [X0] : ~ member(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).

fof(f1376,plain,
    ( spl0_166
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f6819,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1) )
    | ~ spl0_166
    | ~ spl0_489 ),
    inference(duplicate_literal_removal,[],[f6795]) ).

fof(f6795,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(domain_relation,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_166
    | ~ spl0_489 ),
    inference(resolution,[],[f6486,f1377]) ).

fof(f1377,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
        | ~ subclass(domain_relation,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1376]) ).

fof(f25595,plain,
    ( ~ spl0_1181
    | spl0_811
    | ~ spl0_1034 ),
    inference(avatar_split_clause,[],[f21372,f21071,f15357,f25592]) ).

fof(f25592,plain,
    ( spl0_1181
  <=> member(flip(cross_product(subset_relation,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).

fof(f15357,plain,
    ( spl0_811
  <=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).

fof(f21071,plain,
    ( spl0_1034
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).

fof(f21372,plain,
    ( ~ member(flip(cross_product(subset_relation,universal_class)),universal_class)
    | spl0_811
    | ~ spl0_1034 ),
    inference(resolution,[],[f21072,f15359]) ).

fof(f15359,plain,
    ( ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
    | spl0_811 ),
    inference(avatar_component_clause,[],[f15357]) ).

fof(f21072,plain,
    ( ! [X0] :
        ( member(domain_of(X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_1034 ),
    inference(avatar_component_clause,[],[f21071]) ).

fof(f25590,plain,
    ( spl0_1180
    | spl0_729
    | ~ spl0_109
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6796,f6485,f818,f12079,f25588]) ).

fof(f25588,plain,
    ( spl0_1180
  <=> ! [X1] :
        ( ~ subclass(domain_relation,complement(X1))
        | ~ subclass(universal_class,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).

fof(f6796,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(X1))
        | ~ subclass(universal_class,X1) )
    | ~ spl0_109
    | ~ spl0_489 ),
    inference(resolution,[],[f6486,f819]) ).

fof(f25577,plain,
    ( ~ spl0_277
    | spl0_1179
    | ~ spl0_186
    | ~ spl0_470 ),
    inference(avatar_split_clause,[],[f6246,f6240,f1563,f25574,f2555]) ).

fof(f2555,plain,
    ( spl0_277
  <=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f25574,plain,
    ( spl0_1179
  <=> member(regular(subset_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).

fof(f1563,plain,
    ( spl0_186
  <=> ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f6246,plain,
    ( member(regular(subset_relation),subset_relation)
    | ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_186
    | ~ spl0_470 ),
    inference(resolution,[],[f6242,f1564]) ).

fof(f1564,plain,
    ( ! [X0] :
        ( ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1563]) ).

fof(f25572,plain,
    ( spl0_1178
    | ~ spl0_131
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5416,f4906,f1019,f25570]) ).

fof(f25570,plain,
    ( spl0_1178
  <=> ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f5416,plain,
    ( ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_131
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5405]) ).

fof(f5405,plain,
    ( ! [X0] :
        ( subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_131
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f1020]) ).

fof(f25568,plain,
    ( spl0_1177
    | ~ spl0_131
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5392,f4902,f1019,f25566]) ).

fof(f25566,plain,
    ( spl0_1177
  <=> ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).

fof(f5392,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_131
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5381]) ).

fof(f5381,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_131
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f1020]) ).

fof(f25563,plain,
    ( spl0_1176
    | ~ spl0_392
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5357,f4889,f4269,f25561]) ).

fof(f25561,plain,
    ( spl0_1176
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,null_class))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f5357,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_392
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5312]) ).

fof(f5312,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,null_class))
        | subclass(intersection(null_class,X0),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_392
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4270]) ).

fof(f25558,plain,
    ( spl0_1175
    | ~ spl0_394
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5356,f4889,f4277,f25556]) ).

fof(f25556,plain,
    ( spl0_1175
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X0))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).

fof(f5356,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_394
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5313]) ).

fof(f5313,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,X0))
        | subclass(intersection(X0,null_class),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_394
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4278]) ).

fof(f25554,plain,
    ( spl0_1174
    | ~ spl0_393
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5353,f4889,f4273,f25552]) ).

fof(f25552,plain,
    ( spl0_1174
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).

fof(f5353,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2) )
    | ~ spl0_393
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5316]) ).

fof(f5316,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X1,X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_393
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4274]) ).

fof(f25550,plain,
    ( spl0_1173
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5352,f4889,f4265,f25548]) ).

fof(f25548,plain,
    ( spl0_1173
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f5352,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2) )
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5317]) ).

fof(f5317,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X0))
        | ~ subclass(X0,X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_391
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4266]) ).

fof(f25545,plain,
    ( spl0_1172
    | ~ spl0_392
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5292,f4885,f4269,f25543]) ).

fof(f25543,plain,
    ( spl0_1172
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X0))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).

fof(f5292,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_392
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5247]) ).

fof(f5247,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),intersection(X1,X0))
        | subclass(intersection(null_class,X0),intersection(X1,X0))
        | null_class = X1 )
    | ~ spl0_392
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4270]) ).

fof(f25541,plain,
    ( ~ spl0_1171
    | ~ spl0_1022
    | spl0_1029 ),
    inference(avatar_split_clause,[],[f21297,f21049,f21017,f25538]) ).

fof(f25538,plain,
    ( spl0_1171
  <=> subclass(element_relation,compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).

fof(f21017,plain,
    ( spl0_1022
  <=> ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f21049,plain,
    ( spl0_1029
  <=> member(regular(singleton_relation),compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).

fof(f21297,plain,
    ( ~ subclass(element_relation,compose(element_relation,complement(singleton_relation)))
    | ~ spl0_1022
    | spl0_1029 ),
    inference(resolution,[],[f21051,f21018]) ).

fof(f21018,plain,
    ( ! [X0] :
        ( member(regular(singleton_relation),X0)
        | ~ subclass(element_relation,X0) )
    | ~ spl0_1022 ),
    inference(avatar_component_clause,[],[f21017]) ).

fof(f21051,plain,
    ( ~ member(regular(singleton_relation),compose(element_relation,complement(singleton_relation)))
    | spl0_1029 ),
    inference(avatar_component_clause,[],[f21049]) ).

fof(f25535,plain,
    ( spl0_1170
    | ~ spl0_394
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5291,f4885,f4277,f25533]) ).

fof(f25533,plain,
    ( spl0_1170
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,null_class))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f5291,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_394
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5248]) ).

fof(f5248,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),intersection(X1,null_class))
        | subclass(intersection(X0,null_class),intersection(X1,null_class))
        | null_class = X1 )
    | ~ spl0_394
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4278]) ).

fof(f25531,plain,
    ( spl0_1169
    | ~ spl0_393
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5288,f4885,f4273,f25529]) ).

fof(f25529,plain,
    ( spl0_1169
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f5288,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2) )
    | ~ spl0_393
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5251]) ).

fof(f5251,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X1,X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_393
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4274]) ).

fof(f25527,plain,
    ( spl0_1168
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5287,f4885,f4265,f25525]) ).

fof(f25525,plain,
    ( spl0_1168
  <=> ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f5287,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2) )
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5252]) ).

fof(f5252,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X2,X1))
        | ~ subclass(X0,X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_391
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4266]) ).

fof(f25523,plain,
    ( spl0_1167
    | ~ spl0_288
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4755,f4308,f2753,f25521]) ).

fof(f25521,plain,
    ( spl0_1167
  <=> ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f4755,plain,
    ( ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0) )
    | ~ spl0_288
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4719]) ).

fof(f4719,plain,
    ( ! [X0] :
        ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0))
        | ~ subclass(subset_relation,X0)
        | subclass(subset_relation,intersection(cross_product(universal_class,universal_class),X0)) )
    | ~ spl0_288
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f2754]) ).

fof(f25518,plain,
    ( spl0_276
    | spl0_1166
    | ~ spl0_315
    | ~ spl0_394 ),
    inference(avatar_split_clause,[],[f4670,f4277,f3158,f25516,f2551]) ).

fof(f2551,plain,
    ( spl0_276
  <=> null_class = subset_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f25516,plain,
    ( spl0_1166
  <=> ! [X0] : subclass(intersection(X0,null_class),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).

fof(f3158,plain,
    ( spl0_315
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f4670,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,null_class),cross_product(universal_class,universal_class))
        | null_class = subset_relation )
    | ~ spl0_315
    | ~ spl0_394 ),
    inference(duplicate_literal_removal,[],[f4638]) ).

fof(f4638,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,null_class),cross_product(universal_class,universal_class))
        | null_class = subset_relation
        | subclass(intersection(X0,null_class),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_394 ),
    inference(resolution,[],[f4278,f3159]) ).

fof(f3159,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f3158]) ).

fof(f25514,plain,
    ( spl0_1165
    | ~ spl0_377
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4622,f4273,f3841,f25512]) ).

fof(f25512,plain,
    ( spl0_1165
  <=> ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).

fof(f4622,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2) )
    | ~ spl0_377
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4583]) ).

fof(f4583,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(X1,complement(X0)),X2)
        | subclass(intersection(X1,complement(X0)),X2) )
    | ~ spl0_377
    | ~ spl0_393 ),
    inference(resolution,[],[f4274,f3842]) ).

fof(f25510,plain,
    ( spl0_1164
    | ~ spl0_315
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4621,f4273,f3158,f25508]) ).

fof(f25508,plain,
    ( spl0_1164
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f4621,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4584]) ).

fof(f4584,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_393 ),
    inference(resolution,[],[f4274,f3159]) ).

fof(f25505,plain,
    ( spl0_276
    | spl0_1163
    | ~ spl0_315
    | ~ spl0_392 ),
    inference(avatar_split_clause,[],[f4572,f4269,f3158,f25503,f2551]) ).

fof(f25503,plain,
    ( spl0_1163
  <=> ! [X0] : subclass(intersection(null_class,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f4572,plain,
    ( ! [X0] :
        ( subclass(intersection(null_class,X0),cross_product(universal_class,universal_class))
        | null_class = subset_relation )
    | ~ spl0_315
    | ~ spl0_392 ),
    inference(duplicate_literal_removal,[],[f4540]) ).

fof(f4540,plain,
    ( ! [X0] :
        ( subclass(intersection(null_class,X0),cross_product(universal_class,universal_class))
        | null_class = subset_relation
        | subclass(intersection(null_class,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_392 ),
    inference(resolution,[],[f4270,f3159]) ).

fof(f25501,plain,
    ( spl0_1162
    | ~ spl0_376
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4527,f4265,f3837,f25499]) ).

fof(f25499,plain,
    ( spl0_1162
  <=> ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f4527,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_376
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4486]) ).

fof(f4486,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(intersection(complement(X0),X1),X2)
        | subclass(intersection(complement(X0),X1),X2) )
    | ~ spl0_376
    | ~ spl0_391 ),
    inference(resolution,[],[f4266,f3838]) ).

fof(f25497,plain,
    ( spl0_1161
    | ~ spl0_315
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4525,f4265,f3158,f25495]) ).

fof(f25495,plain,
    ( spl0_1161
  <=> ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f4525,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4488]) ).

fof(f4488,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,subset_relation)
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_391 ),
    inference(resolution,[],[f4266,f3159]) ).

fof(f25481,plain,
    ( spl0_1160
    | ~ spl0_356
    | ~ spl0_372 ),
    inference(avatar_split_clause,[],[f4003,f3821,f3551,f25479]) ).

fof(f25479,plain,
    ( spl0_1160
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f3821,plain,
    ( spl0_372
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f4003,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0)) )
    | ~ spl0_356
    | ~ spl0_372 ),
    inference(duplicate_literal_removal,[],[f3974]) ).

fof(f3974,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(X1,complement(X0))
        | null_class = intersection(X1,complement(X0)) )
    | ~ spl0_356
    | ~ spl0_372 ),
    inference(resolution,[],[f3822,f3552]) ).

fof(f3822,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X1,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_372 ),
    inference(avatar_component_clause,[],[f3821]) ).

fof(f25477,plain,
    ( spl0_1159
    | ~ spl0_355
    | ~ spl0_370 ),
    inference(avatar_split_clause,[],[f3937,f3813,f3547,f25475]) ).

fof(f25475,plain,
    ( spl0_1159
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f3813,plain,
    ( spl0_370
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).

fof(f3937,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_355
    | ~ spl0_370 ),
    inference(duplicate_literal_removal,[],[f3906]) ).

fof(f3906,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | null_class = intersection(complement(X0),X1)
        | null_class = intersection(complement(X0),X1) )
    | ~ spl0_355
    | ~ spl0_370 ),
    inference(resolution,[],[f3814,f3548]) ).

fof(f3814,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,X1)),X2)
        | ~ subclass(X0,X2)
        | intersection(X0,X1) = null_class )
    | ~ spl0_370 ),
    inference(avatar_component_clause,[],[f3813]) ).

fof(f25473,plain,
    ( spl0_1158
    | ~ spl0_6
    | ~ spl0_363 ),
    inference(avatar_split_clause,[],[f3785,f3655,f229,f25471]) ).

fof(f229,plain,
    ( spl0_6
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f3655,plain,
    ( spl0_363
  <=> ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f3785,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_6
    | ~ spl0_363 ),
    inference(resolution,[],[f3656,f230]) ).

fof(f230,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f3656,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_363 ),
    inference(avatar_component_clause,[],[f3655]) ).

fof(f25469,plain,
    ( spl0_1157
    | ~ spl0_4
    | ~ spl0_348 ),
    inference(avatar_split_clause,[],[f3575,f3517,f220,f25467]) ).

fof(f25467,plain,
    ( spl0_1157
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f3575,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | member(regular(X0),universal_class) )
    | ~ spl0_4
    | ~ spl0_348 ),
    inference(resolution,[],[f3518,f221]) ).

fof(f25465,plain,
    ( spl0_1156
    | ~ spl0_131
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3318,f3170,f1019,f25463]) ).

fof(f25463,plain,
    ( spl0_1156
  <=> ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f3318,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_131
    | ~ spl0_318 ),
    inference(duplicate_literal_removal,[],[f3297]) ).

fof(f3297,plain,
    ( ! [X2,X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X2))
        | ~ subclass(X0,X2)
        | subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_318 ),
    inference(resolution,[],[f3171,f1020]) ).

fof(f25461,plain,
    ( spl0_1155
    | ~ spl0_305
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3315,f3170,f2966,f25459]) ).

fof(f25459,plain,
    ( spl0_1155
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f3315,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_305
    | ~ spl0_318 ),
    inference(duplicate_literal_removal,[],[f3303]) ).

fof(f3303,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(element_relation))
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_305
    | ~ spl0_318 ),
    inference(resolution,[],[f3171,f2967]) ).

fof(f25457,plain,
    ( spl0_1154
    | ~ spl0_313
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3313,f3170,f3118,f25455]) ).

fof(f25455,plain,
    ( spl0_1154
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f3313,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_318 ),
    inference(duplicate_literal_removal,[],[f3312]) ).

fof(f3312,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(subset_relation))
        | subclass(X0,X1)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_318 ),
    inference(resolution,[],[f3171,f3119]) ).

fof(f25453,plain,
    ( spl0_1153
    | ~ spl0_237
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3068,f2836,f2745,f2324,f25451]) ).

fof(f25451,plain,
    ( spl0_1153
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(subset_relation)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).

fof(f3068,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ subclass(X0,complement(subset_relation)) )
    | ~ spl0_237
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(forward_demodulation,[],[f3008,f2326]) ).

fof(f3008,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(subset_relation))
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f3003]) ).

fof(f3003,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(subset_relation))
        | null_class = X0
        | ~ subclass(X0,identity_relation) )
    | ~ spl0_286
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f2746]) ).

fof(f25449,plain,
    ( spl0_1152
    | ~ spl0_117
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3011,f2836,f926,f25447]) ).

fof(f25447,plain,
    ( spl0_1152
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).

fof(f3011,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_117
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f2987]) ).

fof(f2987,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ subclass(X0,X1)
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f927]) ).

fof(f25445,plain,
    ( spl0_1151
    | ~ spl0_287
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3009,f2836,f2749,f25443]) ).

fof(f25443,plain,
    ( spl0_1151
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f3009,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_287
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f2994]) ).

fof(f2994,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(element_relation))
        | null_class = X0
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_287
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f2750]) ).

fof(f25429,plain,
    ( spl0_1150
    | ~ spl0_125
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2905,f2324,f962,f25427]) ).

fof(f2905,plain,
    ( ! [X0] :
        ( member(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_125
    | ~ spl0_237 ),
    inference(superposition,[],[f963,f2326]) ).

fof(f25420,plain,
    ( spl0_1149
    | spl0_1147
    | ~ spl0_103
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f2825,f2757,f764,f25399,f25417]) ).

fof(f25417,plain,
    ( spl0_1149
  <=> member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f25399,plain,
    ( spl0_1147
  <=> subclass(universal_class,complement(singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f2825,plain,
    ( subclass(universal_class,complement(singleton_relation))
    | member(not_subclass_element(universal_class,complement(singleton_relation)),element_relation)
    | ~ spl0_103
    | ~ spl0_289 ),
    inference(resolution,[],[f2758,f765]) ).

fof(f25407,plain,
    ( spl0_1148
    | ~ spl0_237
    | ~ spl0_1145 ),
    inference(avatar_split_clause,[],[f25397,f25388,f2324,f25404]) ).

fof(f25388,plain,
    ( spl0_1145
  <=> member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f25397,plain,
    ( member(not_subclass_element(universal_class,complement(singleton_relation)),subset_relation)
    | ~ spl0_237
    | ~ spl0_1145 ),
    inference(forward_demodulation,[],[f25390,f2326]) ).

fof(f25390,plain,
    ( member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
    | ~ spl0_1145 ),
    inference(avatar_component_clause,[],[f25388]) ).

fof(f25402,plain,
    ( ~ spl0_1147
    | ~ spl0_237
    | spl0_1146 ),
    inference(avatar_split_clause,[],[f25396,f25392,f2324,f25399]) ).

fof(f25392,plain,
    ( spl0_1146
  <=> subclass(universal_class,complement(identity_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).

fof(f25396,plain,
    ( ~ subclass(universal_class,complement(singleton_relation))
    | ~ spl0_237
    | spl0_1146 ),
    inference(forward_demodulation,[],[f25393,f2326]) ).

fof(f25393,plain,
    ( ~ subclass(universal_class,complement(identity_relation))
    | spl0_1146 ),
    inference(avatar_component_clause,[],[f25392]) ).

fof(f25395,plain,
    ( spl0_1145
    | spl0_1146
    | ~ spl0_104
    | ~ spl0_289 ),
    inference(avatar_split_clause,[],[f2823,f2757,f768,f25392,f25388]) ).

fof(f2823,plain,
    ( subclass(universal_class,complement(identity_relation))
    | member(not_subclass_element(universal_class,complement(identity_relation)),subset_relation)
    | ~ spl0_104
    | ~ spl0_289 ),
    inference(resolution,[],[f2758,f769]) ).

fof(f25386,plain,
    ( spl0_1144
    | ~ spl0_38
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2743,f2719,f373,f25384]) ).

fof(f25384,plain,
    ( spl0_1144
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f2719,plain,
    ( spl0_283
  <=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f2743,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_283 ),
    inference(resolution,[],[f2721,f374]) ).

fof(f2721,plain,
    ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_283 ),
    inference(avatar_component_clause,[],[f2719]) ).

fof(f25379,plain,
    ( spl0_1143
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_1123 ),
    inference(avatar_split_clause,[],[f24956,f23956,f2324,f394,f25376]) ).

fof(f23956,plain,
    ( spl0_1123
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f24956,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_1123 ),
    inference(forward_demodulation,[],[f24950,f2326]) ).

fof(f24950,plain,
    ( subclass(identity_relation,intersection(identity_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_1123 ),
    inference(superposition,[],[f23957,f396]) ).

fof(f23957,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
    | ~ spl0_1123 ),
    inference(avatar_component_clause,[],[f23956]) ).

fof(f25374,plain,
    ( spl0_729
    | spl0_1142
    | ~ spl0_166
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2579,f2517,f1376,f25372,f12079]) ).

fof(f25372,plain,
    ( spl0_1142
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(domain_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f2579,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class) )
    | ~ spl0_166
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f1377]) ).

fof(f25370,plain,
    ( spl0_1141
    | ~ spl0_39
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2250,f2234,f377,f25368]) ).

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

fof(f2250,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X1,X0))
        | intersection(X1,X0) = X0 )
    | ~ spl0_39
    | ~ spl0_225 ),
    inference(resolution,[],[f2235,f378]) ).

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

fof(f25366,plain,
    ( spl0_1140
    | ~ spl0_39
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2239,f2230,f377,f25364]) ).

fof(f2239,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,intersection(X0,X1))
        | intersection(X0,X1) = X0 )
    | ~ spl0_39
    | ~ spl0_224 ),
    inference(resolution,[],[f2231,f378]) ).

fof(f25284,plain,
    ( spl0_1139
    | ~ spl0_41
    | ~ spl0_1123 ),
    inference(avatar_split_clause,[],[f24943,f23956,f385,f25281]) ).

fof(f24943,plain,
    ( subclass(singleton_relation,intersection(singleton_relation,element_relation))
    | ~ spl0_41
    | ~ spl0_1123 ),
    inference(superposition,[],[f23957,f387]) ).

fof(f24023,plain,
    ( spl0_1138
    | ~ spl0_9
    | ~ spl0_744 ),
    inference(avatar_split_clause,[],[f12778,f12573,f241,f24020]) ).

fof(f24020,plain,
    ( spl0_1138
  <=> member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f12778,plain,
    ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function),universal_class)
    | ~ spl0_9
    | ~ spl0_744 ),
    inference(superposition,[],[f242,f12575]) ).

fof(f24018,plain,
    ( spl0_1137
    | ~ spl0_9
    | ~ spl0_742 ),
    inference(avatar_split_clause,[],[f12700,f12509,f241,f24015]) ).

fof(f24015,plain,
    ( spl0_1137
  <=> member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f12700,plain,
    ( member(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function),universal_class)
    | ~ spl0_9
    | ~ spl0_742 ),
    inference(superposition,[],[f242,f12511]) ).

fof(f24013,plain,
    ( ~ spl0_1135
    | spl0_1136
    | ~ spl0_13
    | ~ spl0_1027 ),
    inference(avatar_split_clause,[],[f21292,f21040,f259,f24010,f24006]) ).

fof(f24006,plain,
    ( spl0_1135
  <=> inductive(complement(omega)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).

fof(f21040,plain,
    ( spl0_1027
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f21292,plain,
    ( null_class = omega
    | ~ inductive(complement(omega))
    | ~ spl0_13
    | ~ spl0_1027 ),
    inference(resolution,[],[f21041,f260]) ).

fof(f21041,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(X0))
        | null_class = X0 )
    | ~ spl0_1027 ),
    inference(avatar_component_clause,[],[f21040]) ).

fof(f24004,plain,
    ( spl0_1134
    | ~ spl0_67
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10636,f10535,f557,f24002]) ).

fof(f24002,plain,
    ( spl0_1134
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,flip(cross_product(X0,X1)))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f10535,plain,
    ( spl0_680
  <=> ! [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_680])]) ).

fof(f10636,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,flip(cross_product(X0,X1)))
        | member(X2,X1) )
    | ~ spl0_67
    | ~ spl0_680 ),
    inference(resolution,[],[f10536,f558]) ).

fof(f10536,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_680 ),
    inference(avatar_component_clause,[],[f10535]) ).

fof(f24000,plain,
    ( spl0_1133
    | ~ spl0_67
    | ~ spl0_679 ),
    inference(avatar_split_clause,[],[f10549,f10531,f557,f23998]) ).

fof(f23998,plain,
    ( spl0_1133
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f10531,plain,
    ( spl0_679
  <=> ! [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_679])]) ).

fof(f10549,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,rotate(cross_product(X0,X1)))
        | member(X2,X1) )
    | ~ spl0_67
    | ~ spl0_679 ),
    inference(resolution,[],[f10532,f558]) ).

fof(f10532,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_679 ),
    inference(avatar_component_clause,[],[f10531]) ).

fof(f23996,plain,
    ( spl0_1132
    | ~ spl0_135
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5421,f4906,f1090,f23994]) ).

fof(f23994,plain,
    ( spl0_1132
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f5421,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_135
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5400]) ).

fof(f5400,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_135
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f1091]) ).

fof(f23992,plain,
    ( spl0_1131
    | ~ spl0_136
    | ~ spl0_421 ),
    inference(avatar_split_clause,[],[f5419,f4906,f1094,f23990]) ).

fof(f23990,plain,
    ( spl0_1131
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f5419,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_136
    | ~ spl0_421 ),
    inference(duplicate_literal_removal,[],[f5402]) ).

fof(f5402,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(intersection(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_136
    | ~ spl0_421 ),
    inference(resolution,[],[f4907,f1095]) ).

fof(f23988,plain,
    ( spl0_1130
    | ~ spl0_135
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5397,f4902,f1090,f23986]) ).

fof(f23986,plain,
    ( spl0_1130
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f5397,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_135
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5376]) ).

fof(f5376,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_135
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f1091]) ).

fof(f23984,plain,
    ( spl0_1129
    | ~ spl0_136
    | ~ spl0_420 ),
    inference(avatar_split_clause,[],[f5395,f4902,f1094,f23982]) ).

fof(f23982,plain,
    ( spl0_1129
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f5395,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_136
    | ~ spl0_420 ),
    inference(duplicate_literal_removal,[],[f5378]) ).

fof(f5378,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(intersection(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_136
    | ~ spl0_420 ),
    inference(resolution,[],[f4903,f1095]) ).

fof(f23980,plain,
    ( spl0_1128
    | ~ spl0_27
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5361,f4889,f320,f23978]) ).

fof(f23978,plain,
    ( spl0_1128
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

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

fof(f5361,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
    | ~ spl0_27
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5308]) ).

fof(f5308,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0))
        | subclass(intersection(X0,X1),intersection(intersection(X0,X1),X0)) )
    | ~ spl0_27
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f321]) ).

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

fof(f23976,plain,
    ( spl0_1127
    | ~ spl0_410
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5359,f4889,f4847,f23974]) ).

fof(f23974,plain,
    ( spl0_1127
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f5359,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
    | ~ spl0_410
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5310]) ).

fof(f5310,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X1,X0)) )
    | ~ spl0_410
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4848]) ).

fof(f23972,plain,
    ( spl0_1126
    | ~ spl0_409
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5354,f4889,f4843,f23970]) ).

fof(f23970,plain,
    ( spl0_1126
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f5354,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
    | ~ spl0_409
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5315]) ).

fof(f5315,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0))
        | subclass(intersection(X0,intersection(X1,X2)),intersection(X2,X0)) )
    | ~ spl0_409
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f4844]) ).

fof(f23968,plain,
    ( spl0_1125
    | ~ spl0_408
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5297,f4885,f4839,f23966]) ).

fof(f23966,plain,
    ( spl0_1125
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f5297,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
    | ~ spl0_408
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5242]) ).

fof(f5242,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X0,X2)) )
    | ~ spl0_408
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4840]) ).

fof(f23963,plain,
    ( spl0_1124
    | ~ spl0_289
    | ~ spl0_961 ),
    inference(avatar_split_clause,[],[f19517,f19434,f2757,f23960]) ).

fof(f23960,plain,
    ( spl0_1124
  <=> subclass(universal_class,complement(domain_of(null_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f19434,plain,
    ( spl0_961
  <=> ! [X0] : ~ member(X0,domain_of(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f19517,plain,
    ( subclass(universal_class,complement(domain_of(null_class)))
    | ~ spl0_289
    | ~ spl0_961 ),
    inference(resolution,[],[f19435,f2758]) ).

fof(f19435,plain,
    ( ! [X0] : ~ member(X0,domain_of(null_class))
    | ~ spl0_961 ),
    inference(avatar_component_clause,[],[f19434]) ).

fof(f23958,plain,
    ( spl0_1123
    | ~ spl0_27
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5296,f4885,f320,f23956]) ).

fof(f5296,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
    | ~ spl0_27
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5243]) ).

fof(f5243,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1))
        | subclass(intersection(X0,X1),intersection(intersection(X0,X1),X1)) )
    | ~ spl0_27
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f321]) ).

fof(f23954,plain,
    ( spl0_1122
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5293,f4885,f4812,f23952]) ).

fof(f23952,plain,
    ( spl0_1122
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f5293,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5246]) ).

fof(f5246,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2))
        | subclass(intersection(intersection(X0,X1),X2),intersection(X1,X2)) )
    | ~ spl0_407
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f4813]) ).

fof(f23950,plain,
    ( spl0_1121
    | ~ spl0_315
    | ~ spl0_410 ),
    inference(avatar_split_clause,[],[f5127,f4847,f3158,f23948]) ).

fof(f23948,plain,
    ( spl0_1121
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f5127,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_410 ),
    inference(duplicate_literal_removal,[],[f5087]) ).

fof(f5087,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(subset_relation,X1)),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_410 ),
    inference(resolution,[],[f4848,f3159]) ).

fof(f23946,plain,
    ( spl0_1120
    | ~ spl0_315
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f5069,f4843,f3158,f23944]) ).

fof(f23944,plain,
    ( spl0_1120
  <=> ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).

fof(f5069,plain,
    ( ! [X0,X1] : subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_409 ),
    inference(duplicate_literal_removal,[],[f5029]) ).

fof(f5029,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,intersection(X1,subset_relation)),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_409 ),
    inference(resolution,[],[f4844,f3159]) ).

fof(f23942,plain,
    ( spl0_1119
    | ~ spl0_315
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f5010,f4839,f3158,f23940]) ).

fof(f23940,plain,
    ( spl0_1119
  <=> ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).

fof(f5010,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f4970]) ).

fof(f4970,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(subset_relation,X0),X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_408 ),
    inference(resolution,[],[f4840,f3159]) ).

fof(f23938,plain,
    ( spl0_1118
    | ~ spl0_315
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f4952,f4812,f3158,f23936]) ).

fof(f23936,plain,
    ( spl0_1118
  <=> ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).

fof(f4952,plain,
    ( ! [X0,X1] : subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f4912]) ).

fof(f4912,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class))
        | subclass(intersection(intersection(X0,subset_relation),X1),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_407 ),
    inference(resolution,[],[f4813,f3159]) ).

fof(f23933,plain,
    ( spl0_1117
    | ~ spl0_376
    | ~ spl0_394 ),
    inference(avatar_split_clause,[],[f4671,f4277,f3837,f23931]) ).

fof(f23931,plain,
    ( spl0_1117
  <=> ! [X0,X1] :
        ( subclass(intersection(complement(X0),null_class),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f4671,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(X0),null_class),X1)
        | null_class = X0 )
    | ~ spl0_376
    | ~ spl0_394 ),
    inference(duplicate_literal_removal,[],[f4637]) ).

fof(f4637,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(complement(X0),null_class),X1)
        | null_class = X0
        | subclass(intersection(complement(X0),null_class),X1) )
    | ~ spl0_376
    | ~ spl0_394 ),
    inference(resolution,[],[f4278,f3838]) ).

fof(f23929,plain,
    ( spl0_1116
    | ~ spl0_376
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4623,f4273,f3837,f23927]) ).

fof(f23927,plain,
    ( spl0_1116
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).

fof(f4623,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2) )
    | ~ spl0_376
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4582]) ).

fof(f4582,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(complement(X1),X0),X2)
        | subclass(intersection(complement(X1),X0),X2) )
    | ~ spl0_376
    | ~ spl0_393 ),
    inference(resolution,[],[f4274,f3838]) ).

fof(f23924,plain,
    ( spl0_1115
    | ~ spl0_377
    | ~ spl0_392 ),
    inference(avatar_split_clause,[],[f4573,f4269,f3841,f23922]) ).

fof(f23922,plain,
    ( spl0_1115
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,complement(X0)),X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).

fof(f4573,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,complement(X0)),X1)
        | null_class = X0 )
    | ~ spl0_377
    | ~ spl0_392 ),
    inference(duplicate_literal_removal,[],[f4539]) ).

fof(f4539,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,complement(X0)),X1)
        | null_class = X0
        | subclass(intersection(null_class,complement(X0)),X1) )
    | ~ spl0_377
    | ~ spl0_392 ),
    inference(resolution,[],[f4270,f3842]) ).

fof(f23920,plain,
    ( spl0_1114
    | ~ spl0_377
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4526,f4265,f3841,f23918]) ).

fof(f23918,plain,
    ( spl0_1114
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).

fof(f4526,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_377
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4487]) ).

fof(f4487,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,complement(X1)),X2)
        | subclass(intersection(X0,complement(X1)),X2) )
    | ~ spl0_377
    | ~ spl0_391 ),
    inference(resolution,[],[f4266,f3842]) ).

fof(f23658,plain,
    ( spl0_1113
    | ~ spl0_355
    | ~ spl0_372 ),
    inference(avatar_split_clause,[],[f4004,f3821,f3547,f23656]) ).

fof(f4004,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0) )
    | ~ spl0_355
    | ~ spl0_372 ),
    inference(duplicate_literal_removal,[],[f3973]) ).

fof(f3973,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(complement(X1),X0)
        | null_class = intersection(complement(X1),X0) )
    | ~ spl0_355
    | ~ spl0_372 ),
    inference(resolution,[],[f3822,f3548]) ).

fof(f23654,plain,
    ( spl0_1112
    | ~ spl0_356
    | ~ spl0_370 ),
    inference(avatar_split_clause,[],[f3936,f3813,f3551,f23652]) ).

fof(f3936,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_356
    | ~ spl0_370 ),
    inference(duplicate_literal_removal,[],[f3907]) ).

fof(f3907,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = intersection(X0,complement(X1))
        | null_class = intersection(X0,complement(X1)) )
    | ~ spl0_356
    | ~ spl0_370 ),
    inference(resolution,[],[f3814,f3552]) ).

fof(f23649,plain,
    ( spl0_1111
    | ~ spl0_135
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3648,f3533,f1090,f23647]) ).

fof(f23647,plain,
    ( spl0_1111
  <=> ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(null_class,X1),regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f3648,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(null_class,X1),regular(X0)) )
    | ~ spl0_135
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3639]) ).

fof(f3639,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(null_class,X1),regular(X0))
        | subclass(intersection(null_class,X1),regular(X0)) )
    | ~ spl0_135
    | ~ spl0_352 ),
    inference(resolution,[],[f3534,f1091]) ).

fof(f23644,plain,
    ( spl0_1110
    | ~ spl0_136
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f3647,f3533,f1094,f23642]) ).

fof(f23642,plain,
    ( spl0_1110
  <=> ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(X1,null_class),regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f3647,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(X1,null_class),regular(X0)) )
    | ~ spl0_136
    | ~ spl0_352 ),
    inference(duplicate_literal_removal,[],[f3640]) ).

fof(f3640,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | subclass(intersection(X1,null_class),regular(X0))
        | subclass(intersection(X1,null_class),regular(X0)) )
    | ~ spl0_136
    | ~ spl0_352 ),
    inference(resolution,[],[f3534,f1095]) ).

fof(f23640,plain,
    ( spl0_1109
    | ~ spl0_330
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3471,f3352,f3231,f23638]) ).

fof(f23638,plain,
    ( spl0_1109
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f3471,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation)))
    | ~ spl0_330
    | ~ spl0_338 ),
    inference(duplicate_literal_removal,[],[f3466]) ).

fof(f3466,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation)))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,intersection(X0,singleton_relation))) )
    | ~ spl0_330
    | ~ spl0_338 ),
    inference(resolution,[],[f3353,f3232]) ).

fof(f23636,plain,
    ( spl0_1108
    | ~ spl0_330
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f3457,f3348,f3231,f23633]) ).

fof(f23633,plain,
    ( spl0_1108
  <=> subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f3457,plain,
    ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
    | ~ spl0_330
    | ~ spl0_337 ),
    inference(duplicate_literal_removal,[],[f3452]) ).

fof(f3452,plain,
    ( subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
    | subclass(singleton_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),singleton_relation))
    | ~ spl0_330
    | ~ spl0_337 ),
    inference(resolution,[],[f3349,f3232]) ).

fof(f23631,plain,
    ( spl0_1107
    | ~ spl0_330
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f3445,f3344,f3231,f23628]) ).

fof(f23628,plain,
    ( spl0_1107
  <=> subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f3445,plain,
    ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
    | ~ spl0_330
    | ~ spl0_336 ),
    inference(duplicate_literal_removal,[],[f3440]) ).

fof(f3440,plain,
    ( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
    | subclass(singleton_relation,intersection(complement(compose(element_relation,complement(singleton_relation))),singleton_relation))
    | ~ spl0_330
    | ~ spl0_336 ),
    inference(resolution,[],[f3345,f3232]) ).

fof(f23626,plain,
    ( spl0_1106
    | ~ spl0_330
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3432,f3330,f3231,f23624]) ).

fof(f23624,plain,
    ( spl0_1106
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).

fof(f3432,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0)))
    | ~ spl0_330
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3427]) ).

fof(f3427,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0)))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,intersection(singleton_relation,X0))) )
    | ~ spl0_330
    | ~ spl0_335 ),
    inference(resolution,[],[f3331,f3232]) ).

fof(f23622,plain,
    ( spl0_1105
    | ~ spl0_135
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3404,f3231,f1090,f23620]) ).

fof(f23620,plain,
    ( spl0_1105
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).

fof(f3404,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
    | ~ spl0_135
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3371]) ).

fof(f3371,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1)))
        | subclass(intersection(X0,X1),intersection(X0,intersection(X0,X1))) )
    | ~ spl0_135
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f1091]) ).

fof(f23618,plain,
    ( spl0_1104
    | ~ spl0_136
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3403,f3231,f1094,f23616]) ).

fof(f23616,plain,
    ( spl0_1104
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).

fof(f3403,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
    | ~ spl0_136
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3372]) ).

fof(f3372,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1)))
        | subclass(intersection(X0,X1),intersection(X1,intersection(X0,X1))) )
    | ~ spl0_136
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f1095]) ).

fof(f23604,plain,
    ( spl0_1103
    | ~ spl0_322
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3398,f3231,f3188,f23602]) ).

fof(f23602,plain,
    ( spl0_1103
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).

fof(f3398,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0)))
    | ~ spl0_322
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3378]) ).

fof(f3378,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0)))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,intersection(singleton_relation,X0))) )
    | ~ spl0_322
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f3189]) ).

fof(f23600,plain,
    ( spl0_1102
    | ~ spl0_327
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3397,f3231,f3214,f23598]) ).

fof(f23598,plain,
    ( spl0_1102
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f3397,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation)))
    | ~ spl0_327
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3379]) ).

fof(f3379,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation)))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,intersection(X0,singleton_relation))) )
    | ~ spl0_327
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f3215]) ).

fof(f23596,plain,
    ( ~ spl0_1101
    | spl0_276
    | ~ spl0_277
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f2991,f2836,f2555,f2551,f23593]) ).

fof(f23593,plain,
    ( spl0_1101
  <=> subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).

fof(f2991,plain,
    ( null_class = subset_relation
    | ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class)))
    | ~ spl0_277
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f2557]) ).

fof(f2557,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_277 ),
    inference(avatar_component_clause,[],[f2555]) ).

fof(f23591,plain,
    ( spl0_1100
    | ~ spl0_237
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2917,f2547,f2324,f23589]) ).

fof(f23589,plain,
    ( spl0_1100
  <=> ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).

fof(f2917,plain,
    ( ! [X0] :
        ( ~ member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,singleton_relation) )
    | ~ spl0_237
    | ~ spl0_275 ),
    inference(superposition,[],[f2548,f2326]) ).

fof(f23587,plain,
    ( spl0_1099
    | ~ spl0_41
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2899,f2324,f385,f23584]) ).

fof(f23584,plain,
    ( spl0_1099
  <=> singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f2899,plain,
    ( singleton_relation = intersection(complement(compose(element_relation,complement(singleton_relation))),element_relation)
    | ~ spl0_41
    | ~ spl0_237 ),
    inference(superposition,[],[f387,f2326]) ).

fof(f23582,plain,
    ( spl0_1098
    | ~ spl0_38
    | ~ spl0_277 ),
    inference(avatar_split_clause,[],[f2739,f2555,f373,f23580]) ).

fof(f23580,plain,
    ( spl0_1098
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f2739,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(regular(subset_relation),X0) )
    | ~ spl0_38
    | ~ spl0_277 ),
    inference(resolution,[],[f2557,f374]) ).

fof(f23578,plain,
    ( spl0_1097
    | ~ spl0_111
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2252,f2234,f826,f23576]) ).

fof(f23576,plain,
    ( spl0_1097
  <=> ! [X0] :
        ( omega = intersection(X0,omega)
        | ~ inductive(intersection(X0,omega)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f826,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f2252,plain,
    ( ! [X0] :
        ( omega = intersection(X0,omega)
        | ~ inductive(intersection(X0,omega)) )
    | ~ spl0_111
    | ~ spl0_225 ),
    inference(resolution,[],[f2235,f827]) ).

fof(f827,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f826]) ).

fof(f23574,plain,
    ( spl0_1096
    | ~ spl0_111
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2241,f2230,f826,f23572]) ).

fof(f23572,plain,
    ( spl0_1096
  <=> ! [X0] :
        ( omega = intersection(omega,X0)
        | ~ inductive(intersection(omega,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f2241,plain,
    ( ! [X0] :
        ( omega = intersection(omega,X0)
        | ~ inductive(intersection(omega,X0)) )
    | ~ spl0_111
    | ~ spl0_224 ),
    inference(resolution,[],[f2231,f827]) ).

fof(f22844,plain,
    ( ~ spl0_1095
    | spl0_819
    | ~ spl0_1076 ),
    inference(avatar_split_clause,[],[f22647,f22494,f15396,f22841]) ).

fof(f22841,plain,
    ( spl0_1095
  <=> subclass(composition_function,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f15396,plain,
    ( spl0_819
  <=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f22494,plain,
    ( spl0_1076
  <=> ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).

fof(f22647,plain,
    ( ~ subclass(composition_function,subset_relation)
    | spl0_819
    | ~ spl0_1076 ),
    inference(resolution,[],[f22495,f15398]) ).

fof(f15398,plain,
    ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
    | spl0_819 ),
    inference(avatar_component_clause,[],[f15396]) ).

fof(f22495,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_1076 ),
    inference(avatar_component_clause,[],[f22494]) ).

fof(f22581,plain,
    ( spl0_1094
    | ~ spl0_270
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10667,f10535,f2517,f22579]) ).

fof(f22579,plain,
    ( spl0_1094
  <=> ! [X0] :
        ( ~ subclass(universal_class,flip(X0))
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f10667,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(X0))
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270
    | ~ spl0_680 ),
    inference(resolution,[],[f10536,f2518]) ).

fof(f22577,plain,
    ( spl0_1093
    | ~ spl0_270
    | ~ spl0_679 ),
    inference(avatar_split_clause,[],[f10580,f10531,f2517,f22575]) ).

fof(f22575,plain,
    ( spl0_1093
  <=> ! [X0] :
        ( ~ subclass(universal_class,rotate(X0))
        | ~ subclass(universal_class,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).

fof(f10580,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(X0))
        | ~ subclass(universal_class,complement(X0)) )
    | ~ spl0_270
    | ~ spl0_679 ),
    inference(resolution,[],[f10532,f2518]) ).

fof(f22573,plain,
    ( spl0_1092
    | ~ spl0_237
    | ~ spl0_246
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4769,f4308,f2381,f2324,f22571]) ).

fof(f22571,plain,
    ( spl0_1092
  <=> ! [X0] :
        ( ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(subset_relation,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).

fof(f4769,plain,
    ( ! [X0] :
        ( ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(subset_relation,X0)) )
    | ~ spl0_237
    | ~ spl0_246
    | ~ spl0_401 ),
    inference(forward_demodulation,[],[f4768,f2326]) ).

fof(f4768,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0) )
    | ~ spl0_237
    | ~ spl0_246
    | ~ spl0_401 ),
    inference(forward_demodulation,[],[f4748,f2326]) ).

fof(f4748,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0) )
    | ~ spl0_246
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4735]) ).

fof(f4735,plain,
    ( ! [X0] :
        ( subclass(identity_relation,intersection(subset_relation,X0))
        | ~ subclass(identity_relation,X0)
        | subclass(identity_relation,intersection(subset_relation,X0)) )
    | ~ spl0_246
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f2382]) ).

fof(f22559,plain,
    ( spl0_1091
    | ~ spl0_27
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4763,f4308,f320,f22557]) ).

fof(f22557,plain,
    ( spl0_1091
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f4763,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4711]) ).

fof(f4711,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X0,X1))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X0,X1)) )
    | ~ spl0_27
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f321]) ).

fof(f22555,plain,
    ( spl0_1090
    | ~ spl0_245
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f4754,f4308,f2377,f22553]) ).

fof(f22553,plain,
    ( spl0_1090
  <=> ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f4754,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0) )
    | ~ spl0_245
    | ~ spl0_401 ),
    inference(duplicate_literal_removal,[],[f4721]) ).

fof(f4721,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,intersection(element_relation,X0))
        | ~ subclass(singleton_relation,X0)
        | subclass(singleton_relation,intersection(element_relation,X0)) )
    | ~ spl0_245
    | ~ spl0_401 ),
    inference(resolution,[],[f4309,f2378]) ).

fof(f22550,plain,
    ( spl0_1089
    | ~ spl0_28
    | ~ spl0_394 ),
    inference(avatar_split_clause,[],[f4673,f4277,f324,f22548]) ).

fof(f22548,plain,
    ( spl0_1089
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).

fof(f324,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f4673,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X1 )
    | ~ spl0_28
    | ~ spl0_394 ),
    inference(duplicate_literal_removal,[],[f4635]) ).

fof(f4635,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | null_class = X1
        | subclass(intersection(X0,null_class),X1) )
    | ~ spl0_28
    | ~ spl0_394 ),
    inference(resolution,[],[f4278,f325]) ).

fof(f325,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f324]) ).

fof(f22546,plain,
    ( spl0_1088
    | ~ spl0_28
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f4625,f4273,f324,f22544]) ).

fof(f4625,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1) )
    | ~ spl0_28
    | ~ spl0_393 ),
    inference(duplicate_literal_removal,[],[f4580]) ).

fof(f4580,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X2,X0),X1)
        | subclass(intersection(X2,X0),X1) )
    | ~ spl0_28
    | ~ spl0_393 ),
    inference(resolution,[],[f4274,f325]) ).

fof(f22541,plain,
    ( spl0_1087
    | ~ spl0_28
    | ~ spl0_392 ),
    inference(avatar_split_clause,[],[f4575,f4269,f324,f22539]) ).

fof(f22539,plain,
    ( spl0_1087
  <=> ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).

fof(f4575,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X1 )
    | ~ spl0_28
    | ~ spl0_392 ),
    inference(duplicate_literal_removal,[],[f4537]) ).

fof(f4537,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | null_class = X1
        | subclass(intersection(null_class,X0),X1) )
    | ~ spl0_28
    | ~ spl0_392 ),
    inference(resolution,[],[f4270,f325]) ).

fof(f22537,plain,
    ( spl0_1086
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(avatar_split_clause,[],[f4529,f4265,f324,f22535]) ).

fof(f22535,plain,
    ( spl0_1086
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).

fof(f4529,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1) )
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(duplicate_literal_removal,[],[f4484]) ).

fof(f4484,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(intersection(X0,X2),X1)
        | subclass(intersection(X0,X2),X1) )
    | ~ spl0_28
    | ~ spl0_391 ),
    inference(resolution,[],[f4266,f325]) ).

fof(f22533,plain,
    ( spl0_1085
    | ~ spl0_355
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f4472,f4257,f3547,f22531]) ).

fof(f22531,plain,
    ( spl0_1085
  <=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).

fof(f4472,plain,
    ( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X0,X1))
    | ~ spl0_355
    | ~ spl0_390 ),
    inference(duplicate_literal_removal,[],[f4442]) ).

fof(f4442,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),intersection(X0,X1))
        | null_class = intersection(complement(X0),intersection(X0,X1)) )
    | ~ spl0_355
    | ~ spl0_390 ),
    inference(resolution,[],[f4258,f3548]) ).

fof(f22529,plain,
    ( spl0_1084
    | ~ spl0_355
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f4431,f4253,f3547,f22527]) ).

fof(f22527,plain,
    ( spl0_1084
  <=> ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f4253,plain,
    ( spl0_389
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f4431,plain,
    ( ! [X0,X1] : null_class = intersection(complement(X0),intersection(X1,X0))
    | ~ spl0_355
    | ~ spl0_389 ),
    inference(duplicate_literal_removal,[],[f4401]) ).

fof(f4401,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),intersection(X1,X0))
        | null_class = intersection(complement(X0),intersection(X1,X0)) )
    | ~ spl0_355
    | ~ spl0_389 ),
    inference(resolution,[],[f4254,f3548]) ).

fof(f4254,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(X0,intersection(X1,X2))),X2)
        | null_class = intersection(X0,intersection(X1,X2)) )
    | ~ spl0_389 ),
    inference(avatar_component_clause,[],[f4253]) ).

fof(f22525,plain,
    ( spl0_1083
    | ~ spl0_356
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f4389,f4249,f3551,f22523]) ).

fof(f22523,plain,
    ( spl0_1083
  <=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f4389,plain,
    ( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X0))
    | ~ spl0_356
    | ~ spl0_388 ),
    inference(duplicate_literal_removal,[],[f4359]) ).

fof(f4359,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,X1),complement(X0))
        | null_class = intersection(intersection(X0,X1),complement(X0)) )
    | ~ spl0_356
    | ~ spl0_388 ),
    inference(resolution,[],[f4250,f3552]) ).

fof(f22521,plain,
    ( spl0_1082
    | ~ spl0_356
    | ~ spl0_387 ),
    inference(avatar_split_clause,[],[f4350,f4245,f3551,f22519]) ).

fof(f22519,plain,
    ( spl0_1082
  <=> ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f4245,plain,
    ( spl0_387
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f4350,plain,
    ( ! [X0,X1] : null_class = intersection(intersection(X0,X1),complement(X1))
    | ~ spl0_356
    | ~ spl0_387 ),
    inference(duplicate_literal_removal,[],[f4320]) ).

fof(f4320,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(intersection(X0,X1),complement(X1))
        | null_class = intersection(intersection(X0,X1),complement(X1)) )
    | ~ spl0_356
    | ~ spl0_387 ),
    inference(resolution,[],[f4246,f3552]) ).

fof(f4246,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(intersection(intersection(X0,X1),X2)),X1)
        | null_class = intersection(intersection(X0,X1),X2) )
    | ~ spl0_387 ),
    inference(avatar_component_clause,[],[f4245]) ).

fof(f22517,plain,
    ( spl0_1081
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f21814,f21130,f2324,f394,f22514]) ).

fof(f22514,plain,
    ( spl0_1081
  <=> subclass(singleton_relation,intersection(subset_relation,subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f21130,plain,
    ( spl0_1048
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).

fof(f21814,plain,
    ( subclass(singleton_relation,intersection(subset_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_237
    | ~ spl0_1048 ),
    inference(forward_demodulation,[],[f21809,f2326]) ).

fof(f21809,plain,
    ( subclass(identity_relation,intersection(subset_relation,subset_relation))
    | ~ spl0_43
    | ~ spl0_1048 ),
    inference(superposition,[],[f21131,f396]) ).

fof(f21131,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1))
    | ~ spl0_1048 ),
    inference(avatar_component_clause,[],[f21130]) ).

fof(f22512,plain,
    ( spl0_1080
    | ~ spl0_131
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3402,f3231,f1019,f22510]) ).

fof(f22510,plain,
    ( spl0_1080
  <=> ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f3402,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3373]) ).

fof(f3373,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,X0))
        | ~ subclass(X0,X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_131
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f1020]) ).

fof(f22508,plain,
    ( spl0_1079
    | ~ spl0_305
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3399,f3231,f2966,f22506]) ).

fof(f22506,plain,
    ( spl0_1079
  <=> ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f3399,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_305
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3377]) ).

fof(f3377,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(element_relation,X0))
        | subclass(X0,intersection(element_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_305
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f2967]) ).

fof(f22504,plain,
    ( spl0_1078
    | ~ spl0_313
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3395,f3231,f3118,f22502]) ).

fof(f22502,plain,
    ( spl0_1078
  <=> ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).

fof(f3395,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3388]) ).

fof(f3388,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(subset_relation,X0))
        | subclass(X0,intersection(subset_relation,X0))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f3119]) ).

fof(f22500,plain,
    ( spl0_1077
    | ~ spl0_313
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3256,f3158,f3118,f22498]) ).

fof(f22498,plain,
    ( spl0_1077
  <=> ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).

fof(f3256,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3247]) ).

fof(f3247,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_313
    | ~ spl0_315 ),
    inference(resolution,[],[f3159,f3119]) ).

fof(f22496,plain,
    ( spl0_1076
    | ~ spl0_131
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3252,f3158,f1019,f22494]) ).

fof(f3252,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation) )
    | ~ spl0_131
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3251]) ).

fof(f3251,plain,
    ( ! [X0] :
        ( subclass(X0,cross_product(universal_class,universal_class))
        | ~ subclass(X0,subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_131
    | ~ spl0_315 ),
    inference(resolution,[],[f3159,f1020]) ).

fof(f22483,plain,
    ( ~ spl0_402
    | spl0_1075
    | ~ spl0_145
    | ~ spl0_237
    | ~ spl0_311 ),
    inference(avatar_split_clause,[],[f3110,f3091,f2324,f1174,f22480,f4631]) ).

fof(f4631,plain,
    ( spl0_402
  <=> member(regular(singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f22480,plain,
    ( spl0_1075
  <=> member(regular(singleton_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).

fof(f1174,plain,
    ( spl0_145
  <=> ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f3110,plain,
    ( member(regular(singleton_relation),singleton_relation)
    | ~ member(regular(singleton_relation),subset_relation)
    | ~ spl0_145
    | ~ spl0_237
    | ~ spl0_311 ),
    inference(forward_demodulation,[],[f3106,f2326]) ).

fof(f3106,plain,
    ( ~ member(regular(singleton_relation),subset_relation)
    | member(regular(singleton_relation),identity_relation)
    | ~ spl0_145
    | ~ spl0_311 ),
    inference(resolution,[],[f3093,f1175]) ).

fof(f1175,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1174]) ).

fof(f22478,plain,
    ( spl0_1074
    | ~ spl0_37
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2947,f2521,f360,f22476]) ).

fof(f22476,plain,
    ( spl0_1074
  <=> ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).

fof(f360,plain,
    ( spl0_37
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f2521,plain,
    ( spl0_271
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f2947,plain,
    ( ! [X0] :
        ( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_37
    | ~ spl0_271 ),
    inference(resolution,[],[f2522,f361]) ).

fof(f361,plain,
    ( ! [X8] :
        ( function(domain_of(flip(cross_product(X8,universal_class))))
        | ~ one_to_one(X8) )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f360]) ).

fof(f2522,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ inductive(X0) )
    | ~ spl0_271 ),
    inference(avatar_component_clause,[],[f2521]) ).

fof(f22474,plain,
    ( spl0_1073
    | ~ spl0_237
    | ~ spl0_246 ),
    inference(avatar_split_clause,[],[f2911,f2381,f2324,f22472]) ).

fof(f22472,plain,
    ( spl0_1073
  <=> ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),subset_relation)
        | subclass(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).

fof(f2911,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),subset_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_237
    | ~ spl0_246 ),
    inference(superposition,[],[f2382,f2326]) ).

fof(f22470,plain,
    ( ~ spl0_1071
    | spl0_1072
    | ~ spl0_113
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2797,f2749,f891,f22467,f22463]) ).

fof(f22463,plain,
    ( spl0_1071
  <=> subclass(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).

fof(f22467,plain,
    ( spl0_1072
  <=> null_class = complement(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).

fof(f891,plain,
    ( spl0_113
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f2797,plain,
    ( null_class = complement(element_relation)
    | ~ subclass(complement(element_relation),singleton_relation)
    | ~ spl0_113
    | ~ spl0_287 ),
    inference(duplicate_literal_removal,[],[f2789]) ).

fof(f2789,plain,
    ( null_class = complement(element_relation)
    | ~ subclass(complement(element_relation),singleton_relation)
    | null_class = complement(element_relation)
    | ~ spl0_113
    | ~ spl0_287 ),
    inference(resolution,[],[f2750,f892]) ).

fof(f892,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(X0)),X0)
        | complement(X0) = null_class )
    | ~ spl0_113 ),
    inference(avatar_component_clause,[],[f891]) ).

fof(f22461,plain,
    ( ~ spl0_1070
    | ~ spl0_237
    | spl0_1068 ),
    inference(avatar_split_clause,[],[f22456,f22448,f2324,f22458]) ).

fof(f22458,plain,
    ( spl0_1070
  <=> subclass(complement(subset_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).

fof(f22448,plain,
    ( spl0_1068
  <=> subclass(complement(subset_relation),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).

fof(f22456,plain,
    ( ~ subclass(complement(subset_relation),singleton_relation)
    | ~ spl0_237
    | spl0_1068 ),
    inference(forward_demodulation,[],[f22450,f2326]) ).

fof(f22450,plain,
    ( ~ subclass(complement(subset_relation),identity_relation)
    | spl0_1068 ),
    inference(avatar_component_clause,[],[f22448]) ).

fof(f22455,plain,
    ( ~ spl0_1068
    | spl0_1069
    | ~ spl0_113
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2788,f2745,f891,f22452,f22448]) ).

fof(f22452,plain,
    ( spl0_1069
  <=> null_class = complement(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).

fof(f2788,plain,
    ( null_class = complement(subset_relation)
    | ~ subclass(complement(subset_relation),identity_relation)
    | ~ spl0_113
    | ~ spl0_286 ),
    inference(duplicate_literal_removal,[],[f2780]) ).

fof(f2780,plain,
    ( null_class = complement(subset_relation)
    | ~ subclass(complement(subset_relation),identity_relation)
    | null_class = complement(subset_relation)
    | ~ spl0_113
    | ~ spl0_286 ),
    inference(resolution,[],[f2746,f892]) ).

fof(f22429,plain,
    ( spl0_1066
    | spl0_1067
    | ~ spl0_277
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2737,f2576,f2555,f22427,f22423]) ).

fof(f22423,plain,
    ( spl0_1066
  <=> member(regular(subset_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).

fof(f22427,plain,
    ( spl0_1067
  <=> ! [X0] : ~ member(regular(subset_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f2737,plain,
    ( ! [X0] :
        ( ~ member(regular(subset_relation),X0)
        | member(regular(subset_relation),universal_class) )
    | ~ spl0_277
    | ~ spl0_278 ),
    inference(resolution,[],[f2557,f2577]) ).

fof(f22079,plain,
    ( ~ spl0_757
    | ~ spl0_1065 ),
    inference(avatar_contradiction_clause,[],[f22053]) ).

fof(f22053,plain,
    ( $false
    | ~ spl0_757
    | ~ spl0_1065 ),
    inference(resolution,[],[f22048,f13345]) ).

fof(f13345,plain,
    ( member(regular(singleton_relation),universal_class)
    | ~ spl0_757 ),
    inference(avatar_component_clause,[],[f13343]) ).

fof(f13343,plain,
    ( spl0_757
  <=> member(regular(singleton_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f22048,plain,
    ( ! [X0] : ~ member(regular(singleton_relation),X0)
    | ~ spl0_1065 ),
    inference(avatar_component_clause,[],[f22047]) ).

fof(f22047,plain,
    ( spl0_1065
  <=> ! [X0] : ~ member(regular(singleton_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).

fof(f22078,plain,
    ( ~ spl0_233
    | ~ spl0_1065 ),
    inference(avatar_contradiction_clause,[],[f22059]) ).

fof(f22059,plain,
    ( $false
    | ~ spl0_233
    | ~ spl0_1065 ),
    inference(resolution,[],[f22048,f2295]) ).

fof(f2295,plain,
    ( member(regular(singleton_relation),element_relation)
    | ~ spl0_233 ),
    inference(avatar_component_clause,[],[f2293]) ).

fof(f2293,plain,
    ( spl0_233
  <=> member(regular(singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f22077,plain,
    ( ~ spl0_310
    | ~ spl0_1065 ),
    inference(avatar_contradiction_clause,[],[f22063]) ).

fof(f22063,plain,
    ( $false
    | ~ spl0_310
    | ~ spl0_1065 ),
    inference(resolution,[],[f22048,f3088]) ).

fof(f22076,plain,
    ( ~ spl0_311
    | ~ spl0_1065 ),
    inference(avatar_contradiction_clause,[],[f22068]) ).

fof(f22068,plain,
    ( $false
    | ~ spl0_311
    | ~ spl0_1065 ),
    inference(resolution,[],[f22048,f3093]) ).

fof(f22075,plain,
    ( ~ spl0_402
    | ~ spl0_1065 ),
    inference(avatar_contradiction_clause,[],[f22073]) ).

fof(f22073,plain,
    ( $false
    | ~ spl0_402
    | ~ spl0_1065 ),
    inference(resolution,[],[f22048,f4633]) ).

fof(f4633,plain,
    ( member(regular(singleton_relation),subset_relation)
    | ~ spl0_402 ),
    inference(avatar_component_clause,[],[f4631]) ).

fof(f22049,plain,
    ( spl0_1065
    | ~ spl0_237
    | ~ spl0_1064 ),
    inference(avatar_split_clause,[],[f22044,f22041,f2324,f22047]) ).

fof(f22041,plain,
    ( spl0_1064
  <=> ! [X0] : ~ member(regular(identity_relation),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).

fof(f22044,plain,
    ( ! [X0] : ~ member(regular(singleton_relation),X0)
    | ~ spl0_237
    | ~ spl0_1064 ),
    inference(forward_demodulation,[],[f22042,f2326]) ).

fof(f22042,plain,
    ( ! [X0] : ~ member(regular(identity_relation),X0)
    | ~ spl0_1064 ),
    inference(avatar_component_clause,[],[f22041]) ).

fof(f22043,plain,
    ( spl0_1063
    | spl0_1064
    | ~ spl0_236
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2694,f2576,f2318,f22041,f22037]) ).

fof(f22037,plain,
    ( spl0_1063
  <=> member(regular(identity_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).

fof(f2318,plain,
    ( spl0_236
  <=> member(regular(identity_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f2694,plain,
    ( ! [X0] :
        ( ~ member(regular(identity_relation),X0)
        | member(regular(identity_relation),universal_class) )
    | ~ spl0_236
    | ~ spl0_278 ),
    inference(resolution,[],[f2577,f2320]) ).

fof(f2320,plain,
    ( member(regular(identity_relation),subset_relation)
    | ~ spl0_236 ),
    inference(avatar_component_clause,[],[f2318]) ).

fof(f21952,plain,
    ( spl0_1062
    | ~ spl0_41
    | ~ spl0_1048 ),
    inference(avatar_split_clause,[],[f21804,f21130,f385,f21949]) ).

fof(f21949,plain,
    ( spl0_1062
  <=> subclass(singleton_relation,intersection(element_relation,element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).

fof(f21804,plain,
    ( subclass(singleton_relation,intersection(element_relation,element_relation))
    | ~ spl0_41
    | ~ spl0_1048 ),
    inference(superposition,[],[f21131,f387]) ).

fof(f21343,plain,
    ( ~ spl0_1061
    | ~ spl0_998
    | ~ spl0_1022 ),
    inference(avatar_split_clause,[],[f21256,f21017,f20458,f21340]) ).

fof(f21340,plain,
    ( spl0_1061
  <=> subclass(element_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).

fof(f21256,plain,
    ( ~ subclass(element_relation,null_class)
    | ~ spl0_998
    | ~ spl0_1022 ),
    inference(resolution,[],[f21018,f20459]) ).

fof(f21227,plain,
    ( spl0_1060
    | ~ spl0_9
    | ~ spl0_686 ),
    inference(avatar_split_clause,[],[f11197,f11013,f241,f21224]) ).

fof(f21224,plain,
    ( spl0_1060
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).

fof(f11197,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),domain_relation),universal_class)
    | ~ spl0_9
    | ~ spl0_686 ),
    inference(superposition,[],[f242,f11015]) ).

fof(f21222,plain,
    ( spl0_1059
    | ~ spl0_9
    | ~ spl0_685 ),
    inference(avatar_split_clause,[],[f11123,f11008,f241,f21219]) ).

fof(f21219,plain,
    ( spl0_1059
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).

fof(f11123,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),successor_relation),universal_class)
    | ~ spl0_9
    | ~ spl0_685 ),
    inference(superposition,[],[f242,f11010]) ).

fof(f21217,plain,
    ( spl0_1058
    | ~ spl0_9
    | ~ spl0_683 ),
    inference(avatar_split_clause,[],[f11049,f10715,f241,f21214]) ).

fof(f21214,plain,
    ( spl0_1058
  <=> member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).

fof(f11049,plain,
    ( member(not_subclass_element(cross_product(universal_class,universal_class),element_relation),universal_class)
    | ~ spl0_9
    | ~ spl0_683 ),
    inference(superposition,[],[f242,f10717]) ).

fof(f21212,plain,
    ( spl0_717
    | ~ spl0_1057
    | ~ spl0_366
    | ~ spl0_680 ),
    inference(avatar_split_clause,[],[f10648,f10535,f3796,f21209,f11894]) ).

fof(f11894,plain,
    ( spl0_717
  <=> ! [X0] : member(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).

fof(f21209,plain,
    ( spl0_1057
  <=> subclass(universal_class,flip(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).

fof(f10648,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,flip(subset_relation))
        | member(X0,universal_class) )
    | ~ spl0_366
    | ~ spl0_680 ),
    inference(resolution,[],[f10536,f3797]) ).

fof(f21207,plain,
    ( spl0_717
    | ~ spl0_1056
    | ~ spl0_366
    | ~ spl0_679 ),
    inference(avatar_split_clause,[],[f10561,f10531,f3796,f21204,f11894]) ).

fof(f21204,plain,
    ( spl0_1056
  <=> subclass(universal_class,rotate(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).

fof(f10561,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,rotate(subset_relation))
        | member(X0,universal_class) )
    | ~ spl0_366
    | ~ spl0_679 ),
    inference(resolution,[],[f10532,f3797]) ).

fof(f21202,plain,
    ( ~ spl0_1055
    | spl0_729
    | ~ spl0_66
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6817,f6485,f553,f12079,f21199]) ).

fof(f21199,plain,
    ( spl0_1055
  <=> subclass(domain_relation,complement(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).

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

fof(f6817,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(domain_relation)) )
    | ~ spl0_66
    | ~ spl0_489 ),
    inference(duplicate_literal_removal,[],[f6816]) ).

fof(f6816,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(domain_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_66
    | ~ spl0_489 ),
    inference(resolution,[],[f6486,f554]) ).

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

fof(f21197,plain,
    ( spl0_1054
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5363,f4889,f1090,f21195]) ).

fof(f21195,plain,
    ( spl0_1054
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).

fof(f5363,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X0,X0))
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5306]) ).

fof(f5306,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X0,X0))
        | subclass(intersection(X0,X1),intersection(X0,X0)) )
    | ~ spl0_135
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f1091]) ).

fof(f21193,plain,
    ( spl0_1053
    | ~ spl0_136
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5360,f4889,f1094,f21191]) ).

fof(f21191,plain,
    ( spl0_1053
  <=> ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).

fof(f5360,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X0))
    | ~ spl0_136
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5309]) ).

fof(f5309,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X0))
        | subclass(intersection(X0,X1),intersection(X1,X0)) )
    | ~ spl0_136
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f1095]) ).

fof(f21189,plain,
    ( spl0_1052
    | ~ spl0_322
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5351,f4889,f3188,f21187]) ).

fof(f21187,plain,
    ( spl0_1052
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).

fof(f5351,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
    | ~ spl0_322
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5319]) ).

fof(f5319,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,singleton_relation)) )
    | ~ spl0_322
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f3189]) ).

fof(f21185,plain,
    ( spl0_1051
    | ~ spl0_327
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5350,f4889,f3214,f21183]) ).

fof(f5350,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
    | ~ spl0_327
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5320]) ).

fof(f5320,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,X0))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,X0)) )
    | ~ spl0_327
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f3215]) ).

fof(f21181,plain,
    ( spl0_1050
    | ~ spl0_335
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5348,f4889,f3330,f21179]) ).

fof(f21179,plain,
    ( spl0_1050
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).

fof(f5348,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
    | ~ spl0_335
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5331]) ).

fof(f5331,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,singleton_relation)) )
    | ~ spl0_335
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f3331]) ).

fof(f21136,plain,
    ( spl0_1049
    | ~ spl0_338
    | ~ spl0_419 ),
    inference(avatar_split_clause,[],[f5347,f4889,f3352,f21134]) ).

fof(f5347,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
    | ~ spl0_338
    | ~ spl0_419 ),
    inference(duplicate_literal_removal,[],[f5332]) ).

fof(f5332,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,X0)) )
    | ~ spl0_338
    | ~ spl0_419 ),
    inference(resolution,[],[f4890,f3353]) ).

fof(f21132,plain,
    ( spl0_1048
    | ~ spl0_136
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5295,f4885,f1094,f21130]) ).

fof(f5295,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),intersection(X1,X1))
    | ~ spl0_136
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5244]) ).

fof(f5244,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),intersection(X1,X1))
        | subclass(intersection(X0,X1),intersection(X1,X1)) )
    | ~ spl0_136
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f1095]) ).

fof(f21128,plain,
    ( spl0_1047
    | ~ spl0_322
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5286,f4885,f3188,f21126]) ).

fof(f21126,plain,
    ( spl0_1047
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).

fof(f5286,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
    | ~ spl0_322
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5254]) ).

fof(f5254,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(element_relation,X0))
        | subclass(intersection(singleton_relation,X0),intersection(element_relation,X0)) )
    | ~ spl0_322
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f3189]) ).

fof(f21124,plain,
    ( spl0_1046
    | ~ spl0_327
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5285,f4885,f3214,f21122]) ).

fof(f21122,plain,
    ( spl0_1046
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f5285,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
    | ~ spl0_327
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5255]) ).

fof(f5255,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation))
        | subclass(intersection(X0,singleton_relation),intersection(element_relation,singleton_relation)) )
    | ~ spl0_327
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f3215]) ).

fof(f21120,plain,
    ( spl0_1045
    | ~ spl0_335
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5283,f4885,f3330,f21118]) ).

fof(f21118,plain,
    ( spl0_1045
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).

fof(f5283,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
    | ~ spl0_335
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5266]) ).

fof(f5266,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0))
        | subclass(intersection(singleton_relation,X0),intersection(subset_relation,X0)) )
    | ~ spl0_335
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f3331]) ).

fof(f21116,plain,
    ( spl0_1044
    | ~ spl0_338
    | ~ spl0_418 ),
    inference(avatar_split_clause,[],[f5282,f4885,f3352,f21114]) ).

fof(f21114,plain,
    ( spl0_1044
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f5282,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
    | ~ spl0_338
    | ~ spl0_418 ),
    inference(duplicate_literal_removal,[],[f5267]) ).

fof(f5267,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation))
        | subclass(intersection(X0,singleton_relation),intersection(subset_relation,singleton_relation)) )
    | ~ spl0_338
    | ~ spl0_418 ),
    inference(resolution,[],[f4886,f3353]) ).

fof(f21112,plain,
    ( spl0_1043
    | ~ spl0_28
    | ~ spl0_410 ),
    inference(avatar_split_clause,[],[f5130,f4847,f324,f21110]) ).

fof(f21110,plain,
    ( spl0_1043
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).

fof(f5130,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X1)
    | ~ spl0_28
    | ~ spl0_410 ),
    inference(duplicate_literal_removal,[],[f5084]) ).

fof(f5084,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X1)
        | subclass(intersection(X0,intersection(X1,X2)),X1) )
    | ~ spl0_28
    | ~ spl0_410 ),
    inference(resolution,[],[f4848,f325]) ).

fof(f21108,plain,
    ( spl0_1042
    | ~ spl0_28
    | ~ spl0_409 ),
    inference(avatar_split_clause,[],[f5072,f4843,f324,f21106]) ).

fof(f21106,plain,
    ( spl0_1042
  <=> ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).

fof(f5072,plain,
    ( ! [X2,X0,X1] : subclass(intersection(X0,intersection(X1,X2)),X2)
    | ~ spl0_28
    | ~ spl0_409 ),
    inference(duplicate_literal_removal,[],[f5026]) ).

fof(f5026,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X2)
        | subclass(intersection(X0,intersection(X1,X2)),X2) )
    | ~ spl0_28
    | ~ spl0_409 ),
    inference(resolution,[],[f4844,f325]) ).

fof(f21104,plain,
    ( spl0_1041
    | ~ spl0_28
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f5013,f4839,f324,f21102]) ).

fof(f21102,plain,
    ( spl0_1041
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f5013,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X0)
    | ~ spl0_28
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f4967]) ).

fof(f4967,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X0)
        | subclass(intersection(intersection(X0,X1),X2),X0) )
    | ~ spl0_28
    | ~ spl0_408 ),
    inference(resolution,[],[f4840,f325]) ).

fof(f21100,plain,
    ( spl0_1040
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f4955,f4812,f324,f21098]) ).

fof(f21098,plain,
    ( spl0_1040
  <=> ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).

fof(f4955,plain,
    ( ! [X2,X0,X1] : subclass(intersection(intersection(X0,X1),X2),X1)
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f4909]) ).

fof(f4909,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X1)
        | subclass(intersection(intersection(X0,X1),X2),X1) )
    | ~ spl0_28
    | ~ spl0_407 ),
    inference(resolution,[],[f4813,f325]) ).

fof(f21096,plain,
    ( spl0_1039
    | ~ spl0_55
    | ~ spl0_1009 ),
    inference(avatar_split_clause,[],[f20853,f20710,f478,f21093]) ).

fof(f21093,plain,
    ( spl0_1039
  <=> universal_class = complement(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).

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

fof(f20710,plain,
    ( spl0_1009
  <=> subclass(universal_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f20853,plain,
    ( universal_class = complement(null_class)
    | ~ spl0_55
    | ~ spl0_1009 ),
    inference(resolution,[],[f20712,f479]) ).

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

fof(f20712,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_1009 ),
    inference(avatar_component_clause,[],[f20710]) ).

fof(f21091,plain,
    ( spl0_1038
    | ~ spl0_315
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3473,f3352,f3158,f21089]) ).

fof(f21089,plain,
    ( spl0_1038
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).

fof(f3473,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_338 ),
    inference(duplicate_literal_removal,[],[f3464]) ).

fof(f3464,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,singleton_relation),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_338 ),
    inference(resolution,[],[f3353,f3159]) ).

fof(f21087,plain,
    ( spl0_1037
    | ~ spl0_28
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f3460,f3348,f324,f21084]) ).

fof(f21084,plain,
    ( spl0_1037
  <=> subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).

fof(f3460,plain,
    ( subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_28
    | ~ spl0_337 ),
    inference(duplicate_literal_removal,[],[f3449]) ).

fof(f3449,plain,
    ( subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | subclass(singleton_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_28
    | ~ spl0_337 ),
    inference(resolution,[],[f3349,f325]) ).

fof(f21082,plain,
    ( spl0_1036
    | ~ spl0_28
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f3448,f3344,f324,f21079]) ).

fof(f21079,plain,
    ( spl0_1036
  <=> subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f3448,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_28
    | ~ spl0_336 ),
    inference(duplicate_literal_removal,[],[f3437]) ).

fof(f3437,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | subclass(singleton_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_28
    | ~ spl0_336 ),
    inference(resolution,[],[f3345,f325]) ).

fof(f21077,plain,
    ( spl0_1035
    | ~ spl0_315
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3434,f3330,f3158,f21075]) ).

fof(f21075,plain,
    ( spl0_1035
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).

fof(f3434,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class))
    | ~ spl0_315
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3425]) ).

fof(f3425,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class))
        | subclass(intersection(singleton_relation,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_315
    | ~ spl0_335 ),
    inference(resolution,[],[f3331,f3159]) ).

fof(f21073,plain,
    ( spl0_1034
    | ~ spl0_14
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f3415,f3235,f263,f21071]) ).

fof(f3235,plain,
    ( spl0_331
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f3415,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(X0),universal_class) )
    | ~ spl0_14
    | ~ spl0_331 ),
    inference(resolution,[],[f3236,f265]) ).

fof(f3236,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f3235]) ).

fof(f21069,plain,
    ( spl0_1033
    | ~ spl0_50
    | ~ spl0_288
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3406,f3231,f2753,f453,f21066]) ).

fof(f21066,plain,
    ( spl0_1033
  <=> subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).

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

fof(f3406,plain,
    ( subclass(subset_relation,intersection(subset_relation,cross_product(universal_class,universal_class)))
    | ~ spl0_50
    | ~ spl0_288
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f3401,f454]) ).

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

fof(f3401,plain,
    ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
    | ~ spl0_288
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3374]) ).

fof(f3374,plain,
    ( subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
    | subclass(subset_relation,intersection(cross_product(universal_class,universal_class),subset_relation))
    | ~ spl0_288
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f2754]) ).

fof(f21064,plain,
    ( spl0_1032
    | ~ spl0_27
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f3322,f3170,f320,f21062]) ).

fof(f21062,plain,
    ( spl0_1032
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).

fof(f3322,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_318 ),
    inference(duplicate_literal_removal,[],[f3293]) ).

fof(f3293,plain,
    ( ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ subclass(X0,complement(X0))
        | subclass(X0,X1) )
    | ~ spl0_27
    | ~ spl0_318 ),
    inference(resolution,[],[f3171,f321]) ).

fof(f21060,plain,
    ( spl0_1031
    | ~ spl0_135
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3254,f3158,f1090,f21058]) ).

fof(f21058,plain,
    ( spl0_1031
  <=> ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).

fof(f3254,plain,
    ( ! [X0] : subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class))
    | ~ spl0_135
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3249]) ).

fof(f3249,plain,
    ( ! [X0] :
        ( subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(intersection(subset_relation,X0),cross_product(universal_class,universal_class)) )
    | ~ spl0_135
    | ~ spl0_315 ),
    inference(resolution,[],[f3159,f1091]) ).

fof(f21056,plain,
    ( spl0_1030
    | ~ spl0_136
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3253,f3158,f1094,f21054]) ).

fof(f21054,plain,
    ( spl0_1030
  <=> ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).

fof(f3253,plain,
    ( ! [X0] : subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class))
    | ~ spl0_136
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3250]) ).

fof(f3250,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(intersection(X0,subset_relation),cross_product(universal_class,universal_class)) )
    | ~ spl0_136
    | ~ spl0_315 ),
    inference(resolution,[],[f3159,f1095]) ).

fof(f21052,plain,
    ( ~ spl0_1029
    | ~ spl0_20
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3101,f3086,f288,f21049]) ).

fof(f3101,plain,
    ( ~ member(regular(singleton_relation),compose(element_relation,complement(singleton_relation)))
    | ~ spl0_20
    | ~ spl0_310 ),
    inference(resolution,[],[f3088,f289]) ).

fof(f21047,plain,
    ( spl0_232
    | ~ spl0_1028
    | ~ spl0_236
    | ~ spl0_237
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3069,f2836,f2324,f2318,f21044,f2289]) ).

fof(f21044,plain,
    ( spl0_1028
  <=> subclass(singleton_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f3069,plain,
    ( ~ subclass(singleton_relation,complement(subset_relation))
    | null_class = singleton_relation
    | ~ spl0_236
    | ~ spl0_237
    | ~ spl0_294 ),
    inference(forward_demodulation,[],[f3035,f2326]) ).

fof(f3035,plain,
    ( null_class = singleton_relation
    | ~ subclass(identity_relation,complement(subset_relation))
    | ~ spl0_236
    | ~ spl0_237
    | ~ spl0_294 ),
    inference(forward_demodulation,[],[f3002,f2326]) ).

fof(f3002,plain,
    ( null_class = identity_relation
    | ~ subclass(identity_relation,complement(subset_relation))
    | ~ spl0_236
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f2320]) ).

fof(f21042,plain,
    ( spl0_1027
    | ~ spl0_23
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f3013,f2836,f300,f21040]) ).

fof(f3013,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0)) )
    | ~ spl0_23
    | ~ spl0_294 ),
    inference(duplicate_literal_removal,[],[f2985]) ).

fof(f2985,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(X0))
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f301]) ).

fof(f21038,plain,
    ( ~ spl0_1026
    | spl0_232
    | ~ spl0_233
    | ~ spl0_294 ),
    inference(avatar_split_clause,[],[f2993,f2836,f2293,f2289,f21035]) ).

fof(f21035,plain,
    ( spl0_1026
  <=> subclass(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f2993,plain,
    ( null_class = singleton_relation
    | ~ subclass(singleton_relation,complement(element_relation))
    | ~ spl0_233
    | ~ spl0_294 ),
    inference(resolution,[],[f2837,f2295]) ).

fof(f21033,plain,
    ( spl0_729
    | ~ spl0_1025
    | ~ spl0_66
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2602,f2517,f553,f21030,f12079]) ).

fof(f21030,plain,
    ( spl0_1025
  <=> subclass(universal_class,complement(domain_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f2602,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(domain_relation))
        | ~ member(X0,universal_class) )
    | ~ spl0_66
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f554]) ).

fof(f21028,plain,
    ( spl0_1024
    | ~ spl0_109
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2580,f2517,f818,f21026]) ).

fof(f21026,plain,
    ( spl0_1024
  <=> ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(universal_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f2580,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ subclass(universal_class,X0) )
    | ~ spl0_109
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f819]) ).

fof(f21023,plain,
    ( spl0_1023
    | ~ spl0_38
    | ~ spl0_236 ),
    inference(avatar_split_clause,[],[f2455,f2318,f373,f21021]) ).

fof(f21021,plain,
    ( spl0_1023
  <=> ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).

fof(f2455,plain,
    ( ! [X0] :
        ( ~ subclass(subset_relation,X0)
        | member(regular(identity_relation),X0) )
    | ~ spl0_38
    | ~ spl0_236 ),
    inference(resolution,[],[f2320,f374]) ).

fof(f21019,plain,
    ( spl0_1022
    | ~ spl0_38
    | ~ spl0_233 ),
    inference(avatar_split_clause,[],[f2343,f2293,f373,f21017]) ).

fof(f2343,plain,
    ( ! [X0] :
        ( ~ subclass(element_relation,X0)
        | member(regular(singleton_relation),X0) )
    | ~ spl0_38
    | ~ spl0_233 ),
    inference(resolution,[],[f2295,f374]) ).

fof(f21014,plain,
    ( spl0_1021
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2247,f2230,f394,f21011]) ).

fof(f21011,plain,
    ( spl0_1021
  <=> subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).

fof(f2247,plain,
    ( subclass(identity_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_43
    | ~ spl0_224 ),
    inference(superposition,[],[f2231,f396]) ).

fof(f21008,plain,
    ( spl0_1020
    | ~ spl0_229
    | ~ spl0_1009 ),
    inference(avatar_split_clause,[],[f20852,f20710,f2272,f21005]) ).

fof(f21005,plain,
    ( spl0_1020
  <=> member(null_class,complement(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).

fof(f2272,plain,
    ( spl0_229
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f20852,plain,
    ( member(null_class,complement(null_class))
    | ~ spl0_229
    | ~ spl0_1009 ),
    inference(resolution,[],[f20712,f2273]) ).

fof(f2273,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_229 ),
    inference(avatar_component_clause,[],[f2272]) ).

fof(f21002,plain,
    ( spl0_1019
    | ~ spl0_41
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2246,f2230,f385,f20999]) ).

fof(f20999,plain,
    ( spl0_1019
  <=> subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f2246,plain,
    ( subclass(singleton_relation,complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_41
    | ~ spl0_224 ),
    inference(superposition,[],[f2231,f387]) ).

fof(f20967,plain,
    ( spl0_1018
    | ~ spl0_89
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1849,f1819,f684,f20965]) ).

fof(f20965,plain,
    ( spl0_1018
  <=> ! [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_1018])]) ).

fof(f684,plain,
    ( spl0_89
  <=> ! [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_89])]) ).

fof(f1819,plain,
    ( spl0_205
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f1849,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_89
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f685]) ).

fof(f685,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_89 ),
    inference(avatar_component_clause,[],[f684]) ).

fof(f1820,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_205 ),
    inference(avatar_component_clause,[],[f1819]) ).

fof(f20963,plain,
    ( spl0_1017
    | ~ spl0_89
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1823,f1815,f684,f20961]) ).

fof(f20961,plain,
    ( spl0_1017
  <=> ! [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_1017])]) ).

fof(f1815,plain,
    ( spl0_204
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f1823,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_89
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f685]) ).

fof(f1816,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_204 ),
    inference(avatar_component_clause,[],[f1815]) ).

fof(f20924,plain,
    ( spl0_1016
    | ~ spl0_112
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2135,f2131,f830,f20922]) ).

fof(f20922,plain,
    ( spl0_1016
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(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_1016])]) ).

fof(f2131,plain,
    ( spl0_222
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f2135,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_222 ),
    inference(resolution,[],[f2132,f831]) ).

fof(f2132,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_222 ),
    inference(avatar_component_clause,[],[f2131]) ).

fof(f20891,plain,
    ( spl0_1015
    | ~ spl0_101
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1886,f1875,f752,f20889]) ).

fof(f20889,plain,
    ( spl0_1015
  <=> ! [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_1015])]) ).

fof(f752,plain,
    ( spl0_101
  <=> ! [X10,X11,X0,X9,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
        | ~ homomorphism(X9,X10,X11)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f1875,plain,
    ( spl0_206
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f1886,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ homomorphism(X3,X0,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f753]) ).

fof(f753,plain,
    ( ! [X10,X0,X11,X1,X9] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
        | ~ homomorphism(X9,X10,X11)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f752]) ).

fof(f1876,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2)
        | ~ subclass(composition_function,X2)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_206 ),
    inference(avatar_component_clause,[],[f1875]) ).

fof(f20850,plain,
    ( spl0_1014
    | ~ spl0_198
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2023,f2001,f1712,f20848]) ).

fof(f20848,plain,
    ( spl0_1014
  <=> ! [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_1014])]) ).

fof(f1712,plain,
    ( spl0_198
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f2001,plain,
    ( spl0_212
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f2023,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_198
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1713]) ).

fof(f1713,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_198 ),
    inference(avatar_component_clause,[],[f1712]) ).

fof(f2002,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_212 ),
    inference(avatar_component_clause,[],[f2001]) ).

fof(f20809,plain,
    ( spl0_1013
    | ~ spl0_77
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2134,f2131,f615,f20807]) ).

fof(f20807,plain,
    ( spl0_1013
  <=> ! [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_1013])]) ).

fof(f2134,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_222 ),
    inference(resolution,[],[f2132,f616]) ).

fof(f20790,plain,
    ( spl0_1012
    | ~ spl0_40
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2138,f2131,f381,f20788]) ).

fof(f20788,plain,
    ( spl0_1012
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f2138,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ operation(X3)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_222 ),
    inference(superposition,[],[f2132,f382]) ).

fof(f20760,plain,
    ( spl0_1011
    | ~ spl0_206
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2009,f2001,f1875,f20758]) ).

fof(f20758,plain,
    ( spl0_1011
  <=> ! [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_1011])]) ).

fof(f2009,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_206
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1876]) ).

fof(f20730,plain,
    ( spl0_1010
    | ~ spl0_93
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2028,f2001,f702,f20728]) ).

fof(f20728,plain,
    ( spl0_1010
  <=> ! [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_1010])]) ).

fof(f702,plain,
    ( spl0_93
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f2028,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f703]) ).

fof(f703,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f702]) ).

fof(f20713,plain,
    ( spl0_1009
    | ~ spl0_289
    | ~ spl0_998 ),
    inference(avatar_split_clause,[],[f20510,f20458,f2757,f20710]) ).

fof(f20510,plain,
    ( subclass(universal_class,complement(null_class))
    | ~ spl0_289
    | ~ spl0_998 ),
    inference(resolution,[],[f20459,f2758]) ).

fof(f20708,plain,
    ( spl0_1008
    | ~ spl0_101
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1759,f1752,f752,f20706]) ).

fof(f20706,plain,
    ( spl0_1008
  <=> ! [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_1008])]) ).

fof(f1752,plain,
    ( spl0_200
  <=> ! [X0,X3,X2,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f1759,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(X3))
        | ~ operation(X2)
        | ~ homomorphism(X4,X3,X5)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f753]) ).

fof(f1753,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | ~ operation(X0) )
    | ~ spl0_200 ),
    inference(avatar_component_clause,[],[f1752]) ).

fof(f20698,plain,
    ( spl0_1007
    | ~ spl0_199
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2125,f2117,f1718,f20696]) ).

fof(f20696,plain,
    ( spl0_1007
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f1718,plain,
    ( spl0_199
  <=> ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f2117,plain,
    ( spl0_220
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f2125,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(regular(cross_product(X0,X1)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199
    | ~ spl0_220 ),
    inference(superposition,[],[f2118,f1719]) ).

fof(f1719,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f1718]) ).

fof(f2118,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_220 ),
    inference(avatar_component_clause,[],[f2117]) ).

fof(f20681,plain,
    ( spl0_1006
    | ~ spl0_101
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1738,f1718,f752,f20679]) ).

fof(f20679,plain,
    ( spl0_1006
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
        | ~ homomorphism(X3,X2,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).

fof(f1738,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
        | ~ homomorphism(X3,X2,X4)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_101
    | ~ spl0_199 ),
    inference(superposition,[],[f753,f1719]) ).

fof(f20488,plain,
    ( spl0_1005
    | ~ spl0_196
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1862,f1819,f1663,f20486]) ).

fof(f20486,plain,
    ( spl0_1005
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).

fof(f1663,plain,
    ( spl0_196
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f1862,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class) )
    | ~ spl0_196
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1664]) ).

fof(f1664,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class) )
    | ~ spl0_196 ),
    inference(avatar_component_clause,[],[f1663]) ).

fof(f20484,plain,
    ( spl0_1004
    | ~ spl0_197
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1854,f1819,f1667,f20482]) ).

fof(f20482,plain,
    ( spl0_1004
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).

fof(f1667,plain,
    ( spl0_197
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f1854,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class) )
    | ~ spl0_197
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1668]) ).

fof(f1668,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
        | intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class) )
    | ~ spl0_197 ),
    inference(avatar_component_clause,[],[f1667]) ).

fof(f20480,plain,
    ( spl0_1003
    | ~ spl0_196
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1836,f1815,f1663,f20478]) ).

fof(f20478,plain,
    ( spl0_1003
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f1836,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class) )
    | ~ spl0_196
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1664]) ).

fof(f20476,plain,
    ( spl0_1002
    | ~ spl0_197
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1828,f1815,f1667,f20474]) ).

fof(f20474,plain,
    ( spl0_1002
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f1828,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class) )
    | ~ spl0_197
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1668]) ).

fof(f20472,plain,
    ( spl0_1001
    | ~ spl0_94
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1700,f1667,f708,f20470]) ).

fof(f20470,plain,
    ( spl0_1001
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f708,plain,
    ( spl0_94
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f1700,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f709]) ).

fof(f709,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f708]) ).

fof(f20468,plain,
    ( spl0_1000
    | ~ spl0_94
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1679,f1663,f708,f20466]) ).

fof(f20466,plain,
    ( spl0_1000
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f1679,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f709]) ).

fof(f20464,plain,
    ( spl0_999
    | ~ spl0_9
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f2120,f2117,f241,f20462]) ).

fof(f20462,plain,
    ( spl0_999
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f2120,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
        | ~ homomorphism(X3,X2,X4)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) )
    | ~ spl0_9
    | ~ spl0_220 ),
    inference(resolution,[],[f2118,f242]) ).

fof(f20460,plain,
    ( spl0_998
    | ~ spl0_961
    | ~ spl0_985 ),
    inference(avatar_split_clause,[],[f20293,f20074,f19434,f20458]) ).

fof(f20074,plain,
    ( spl0_985
  <=> null_class = domain_of(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f20293,plain,
    ( ! [X0] : ~ member(X0,null_class)
    | ~ spl0_961
    | ~ spl0_985 ),
    inference(superposition,[],[f19435,f20076]) ).

fof(f20076,plain,
    ( null_class = domain_of(null_class)
    | ~ spl0_985 ),
    inference(avatar_component_clause,[],[f20074]) ).

fof(f20456,plain,
    ( spl0_997
    | ~ spl0_101
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1420,f1376,f752,f20454]) ).

fof(f20454,plain,
    ( spl0_997
  <=> ! [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_997])]) ).

fof(f1420,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(domain_relation,domain_of(X0))
        | ~ member(X1,universal_class)
        | ~ homomorphism(X2,X0,X3)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f753]) ).

fof(f20425,plain,
    ( spl0_996
    | ~ spl0_237
    | ~ spl0_995 ),
    inference(avatar_split_clause,[],[f20421,f20418,f2324,f20423]) ).

fof(f20423,plain,
    ( spl0_996
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),singleton_relation)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f20418,plain,
    ( spl0_995
  <=> ! [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_995])]) ).

fof(f20421,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),singleton_relation)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
    | ~ spl0_237
    | ~ spl0_995 ),
    inference(forward_demodulation,[],[f20419,f2326]) ).

fof(f20419,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_995 ),
    inference(avatar_component_clause,[],[f20418]) ).

fof(f20420,plain,
    ( spl0_995
    | ~ spl0_50
    | ~ spl0_101
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1009,f966,f752,f453,f20418]) ).

fof(f1009,plain,
    ( ! [X2,X3,X0,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
    | ~ spl0_50
    | ~ spl0_101
    | ~ spl0_126 ),
    inference(forward_demodulation,[],[f1007,f454]) ).

fof(f1007,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
        | ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_126 ),
    inference(resolution,[],[f967,f753]) ).

fof(f20386,plain,
    ( spl0_994
    | ~ spl0_83
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1853,f1819,f652,f20384]) ).

fof(f20384,plain,
    ( spl0_994
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f652,plain,
    ( spl0_83
  <=> ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f1853,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_83
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f653]) ).

fof(f653,plain,
    ( ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f652]) ).

fof(f20382,plain,
    ( spl0_993
    | ~ spl0_83
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1827,f1815,f652,f20380]) ).

fof(f20380,plain,
    ( spl0_993
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).

fof(f1827,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_83
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f653]) ).

fof(f20346,plain,
    ( spl0_992
    | ~ spl0_112
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2108,f2104,f830,f20344]) ).

fof(f20344,plain,
    ( spl0_992
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f2104,plain,
    ( spl0_219
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f2108,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_219 ),
    inference(resolution,[],[f2105,f831]) ).

fof(f2105,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f2104]) ).

fof(f20292,plain,
    ( spl0_991
    | ~ spl0_101
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f837,f818,f752,f20290]) ).

fof(f20290,plain,
    ( spl0_991
  <=> ! [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_991])]) ).

fof(f837,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(universal_class,domain_of(X0))
        | ~ homomorphism(X1,X0,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) )
    | ~ spl0_101
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f753]) ).

fof(f20288,plain,
    ( ~ spl0_989
    | spl0_990
    | ~ spl0_40
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f2141,f2131,f381,f20286,f20282]) ).

fof(f20282,plain,
    ( spl0_989
  <=> operation(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f20286,plain,
    ( spl0_990
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
        | homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ operation(X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f2141,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(null_class,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ operation(X3)
        | ~ compatible(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | homomorphism(X2,domain_of(flip(cross_product(null_class,universal_class))),X3)
        | ~ operation(domain_of(flip(cross_product(null_class,universal_class))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_222 ),
    inference(superposition,[],[f2132,f382]) ).

fof(f20263,plain,
    ( spl0_988
    | ~ spl0_40
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2111,f2104,f381,f20261]) ).

fof(f20261,plain,
    ( spl0_988
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f2111,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_219 ),
    inference(superposition,[],[f2105,f382]) ).

fof(f20119,plain,
    ( spl0_987
    | ~ spl0_96
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1891,f1875,f729,f20117]) ).

fof(f20117,plain,
    ( spl0_987
  <=> ! [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_987])]) ).

fof(f729,plain,
    ( spl0_96
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1891,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) )
    | ~ spl0_96
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f730]) ).

fof(f730,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f729]) ).

fof(f20081,plain,
    ( spl0_986
    | ~ spl0_77
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f2107,f2104,f615,f20079]) ).

fof(f20079,plain,
    ( spl0_986
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f2107,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_219 ),
    inference(resolution,[],[f2105,f616]) ).

fof(f20077,plain,
    ( spl0_985
    | ~ spl0_23
    | ~ spl0_961 ),
    inference(avatar_split_clause,[],[f19522,f19434,f300,f20074]) ).

fof(f19522,plain,
    ( null_class = domain_of(null_class)
    | ~ spl0_23
    | ~ spl0_961 ),
    inference(resolution,[],[f19435,f301]) ).

fof(f20072,plain,
    ( spl0_983
    | ~ spl0_984
    | ~ spl0_99
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1893,f1875,f741,f20069,f20066]) ).

fof(f20066,plain,
    ( spl0_983
  <=> ! [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_983])]) ).

fof(f20069,plain,
    ( spl0_984
  <=> subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).

fof(f741,plain,
    ( spl0_99
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f1893,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),X3) )
    | ~ spl0_99
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f742]) ).

fof(f742,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f741]) ).

fof(f20038,plain,
    ( spl0_982
    | ~ spl0_187
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2027,f2001,f1585,f20036]) ).

fof(f20036,plain,
    ( spl0_982
  <=> ! [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_982])]) ).

fof(f2027,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose_class(X0)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_187
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1586]) ).

fof(f20016,plain,
    ( spl0_981
    | ~ spl0_205
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1906,f1875,f1819,f20014]) ).

fof(f20014,plain,
    ( spl0_981
  <=> ! [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_981])]) ).

fof(f1906,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X0,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_205
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1820]) ).

fof(f20012,plain,
    ( spl0_980
    | ~ spl0_204
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1905,f1875,f1815,f20010]) ).

fof(f20010,plain,
    ( spl0_980
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(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_980])]) ).

fof(f1905,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_204
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1816]) ).

fof(f20008,plain,
    ( spl0_979
    | ~ spl0_94
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1904,f1875,f708,f20006]) ).

fof(f20006,plain,
    ( spl0_979
  <=> ! [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_979])]) ).

fof(f1904,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f709]) ).

fof(f20003,plain,
    ( spl0_978
    | ~ spl0_27
    | ~ spl0_961 ),
    inference(avatar_split_clause,[],[f19514,f19434,f320,f20001]) ).

fof(f20001,plain,
    ( spl0_978
  <=> ! [X0] : subclass(domain_of(null_class),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f19514,plain,
    ( ! [X0] : subclass(domain_of(null_class),X0)
    | ~ spl0_27
    | ~ spl0_961 ),
    inference(resolution,[],[f19435,f321]) ).

fof(f19983,plain,
    ( spl0_977
    | ~ spl0_100
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1737,f1718,f747,f19981]) ).

fof(f19981,plain,
    ( spl0_977
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f747,plain,
    ( spl0_100
  <=> ! [X4,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f1737,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_100
    | ~ spl0_199 ),
    inference(superposition,[],[f748,f1719]) ).

fof(f748,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f747]) ).

fof(f19934,plain,
    ( spl0_976
    | ~ spl0_206
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2037,f2005,f1875,f19932]) ).

fof(f19932,plain,
    ( spl0_976
  <=> ! [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_976])]) ).

fof(f2005,plain,
    ( spl0_213
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f2037,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_206
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1876]) ).

fof(f2006,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_213 ),
    inference(avatar_component_clause,[],[f2005]) ).

fof(f19893,plain,
    ( spl0_975
    | ~ spl0_166
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2008,f2001,f1376,f19891]) ).

fof(f19891,plain,
    ( spl0_975
  <=> ! [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_975])]) ).

fof(f2008,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X2))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_166
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1377]) ).

fof(f19889,plain,
    ( spl0_974
    | ~ spl0_79
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1693,f1667,f630,f19887]) ).

fof(f19887,plain,
    ( spl0_974
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).

fof(f630,plain,
    ( spl0_79
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f1693,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | ~ member(intersection(cross_product(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f631]) ).

fof(f631,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f630]) ).

fof(f19885,plain,
    ( spl0_973
    | ~ spl0_79
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1672,f1663,f630,f19883]) ).

fof(f19883,plain,
    ( spl0_973
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f1672,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f631]) ).

fof(f19880,plain,
    ( ~ spl0_972
    | ~ spl0_12
    | ~ spl0_961 ),
    inference(avatar_split_clause,[],[f19518,f19434,f255,f19877]) ).

fof(f19877,plain,
    ( spl0_972
  <=> inductive(domain_of(null_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).

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

fof(f19518,plain,
    ( ~ inductive(domain_of(null_class))
    | ~ spl0_12
    | ~ spl0_961 ),
    inference(resolution,[],[f19435,f256]) ).

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

fof(f19830,plain,
    ( spl0_971
    | ~ spl0_93
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2056,f2005,f702,f19828]) ).

fof(f19828,plain,
    ( spl0_971
  <=> ! [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_971])]) ).

fof(f2056,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f703]) ).

fof(f19784,plain,
    ( spl0_970
    | ~ spl0_199
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2072,f2063,f1718,f19782]) ).

fof(f19782,plain,
    ( spl0_970
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | ~ member(X2,universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f2063,plain,
    ( spl0_215
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f2072,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
        | ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | ~ member(X2,universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199
    | ~ spl0_215 ),
    inference(superposition,[],[f2064,f1719]) ).

fof(f2064,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(X0,domain_of(X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_215 ),
    inference(avatar_component_clause,[],[f2063]) ).

fof(f19780,plain,
    ( spl0_969
    | ~ spl0_66
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2029,f2001,f553,f19778]) ).

fof(f19778,plain,
    ( spl0_969
  <=> ! [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_969])]) ).

fof(f2029,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(domain_relation))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
    | ~ spl0_66
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f554]) ).

fof(f19485,plain,
    ( spl0_968
    | ~ spl0_200
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2071,f2063,f1752,f19483]) ).

fof(f19483,plain,
    ( spl0_968
  <=> ! [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_968])]) ).

fof(f2071,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(not_homomorphism1(X1,X2,X3),domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),cross_product(universal_class,universal_class))
        | ~ operation(X3) )
    | ~ spl0_200
    | ~ spl0_215 ),
    inference(resolution,[],[f2064,f1753]) ).

fof(f19481,plain,
    ( spl0_967
    | ~ spl0_210
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2053,f2005,f1942,f19479]) ).

fof(f19479,plain,
    ( spl0_967
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).

fof(f1942,plain,
    ( spl0_210
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f2053,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_210
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1943]) ).

fof(f1943,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_210 ),
    inference(avatar_component_clause,[],[f1942]) ).

fof(f19477,plain,
    ( spl0_966
    | ~ spl0_70
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2049,f2005,f569,f19475]) ).

fof(f19475,plain,
    ( spl0_966
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f569,plain,
    ( spl0_70
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,domain_of(X0))
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f2049,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) )
    | ~ spl0_70
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f570]) ).

fof(f570,plain,
    ( ! [X0,X4] :
        ( member(X4,domain_of(X0))
        | ~ member(X4,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f569]) ).

fof(f19473,plain,
    ( spl0_965
    | ~ spl0_210
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2025,f2001,f1942,f19471]) ).

fof(f19471,plain,
    ( spl0_965
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f2025,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
    | ~ spl0_210
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1943]) ).

fof(f19469,plain,
    ( spl0_964
    | ~ spl0_70
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2021,f2001,f569,f19467]) ).

fof(f19467,plain,
    ( spl0_964
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).

fof(f2021,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) )
    | ~ spl0_70
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f570]) ).

fof(f19444,plain,
    ( spl0_963
    | ~ spl0_199
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2058,f2005,f1718,f19442]) ).

fof(f19442,plain,
    ( spl0_963
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).

fof(f2058,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199
    | ~ spl0_213 ),
    inference(superposition,[],[f2006,f1719]) ).

fof(f19440,plain,
    ( spl0_962
    | ~ spl0_159
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1908,f1875,f1301,f19438]) ).

fof(f19438,plain,
    ( spl0_962
  <=> ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).

fof(f1301,plain,
    ( spl0_159
  <=> ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f1908,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) )
    | ~ spl0_159
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1302]) ).

fof(f1302,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1301]) ).

fof(f19436,plain,
    ( spl0_961
    | ~ spl0_146
    | ~ spl0_946 ),
    inference(avatar_split_clause,[],[f19259,f18817,f1178,f19434]) ).

fof(f1178,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f18817,plain,
    ( spl0_946
  <=> ! [X0] : null_class = intersection(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f19259,plain,
    ( ! [X0] : ~ member(X0,domain_of(null_class))
    | ~ spl0_146
    | ~ spl0_946 ),
    inference(trivial_inequality_removal,[],[f19193]) ).

fof(f19193,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(null_class)) )
    | ~ spl0_146
    | ~ spl0_946 ),
    inference(superposition,[],[f1179,f18818]) ).

fof(f18818,plain,
    ( ! [X0] : null_class = intersection(null_class,X0)
    | ~ spl0_946 ),
    inference(avatar_component_clause,[],[f18817]) ).

fof(f1179,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1178]) ).

fof(f19391,plain,
    ( spl0_960
    | ~ spl0_198
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2060,f2005,f1712,f19389]) ).

fof(f19389,plain,
    ( spl0_960
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_960])]) ).

fof(f2060,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_198
    | ~ spl0_213 ),
    inference(duplicate_literal_removal,[],[f2051]) ).

fof(f2051,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_198
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1713]) ).

fof(f19369,plain,
    ( spl0_959
    | ~ spl0_200
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1868,f1819,f1752,f19367]) ).

fof(f19367,plain,
    ( spl0_959
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(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_959])]) ).

fof(f1868,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_200
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1753]) ).

fof(f19365,plain,
    ( spl0_958
    | ~ spl0_200
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1842,f1815,f1752,f19363]) ).

fof(f19363,plain,
    ( spl0_958
  <=> ! [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_958])]) ).

fof(f1842,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
        | ~ compatible(X1,X2,X3)
        | homomorphism(X1,X2,X3)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
        | ~ operation(X3) )
    | ~ spl0_200
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1753]) ).

fof(f19361,plain,
    ( spl0_957
    | ~ spl0_94
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1773,f1752,f708,f19359]) ).

fof(f19359,plain,
    ( spl0_957
  <=> ! [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_957])]) ).

fof(f1773,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f709]) ).

fof(f19118,plain,
    ( spl0_956
    | ~ spl0_207
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2052,f2005,f1913,f19116]) ).

fof(f19116,plain,
    ( spl0_956
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f1913,plain,
    ( spl0_207
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f2052,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
    | ~ spl0_207
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1914]) ).

fof(f1914,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_207 ),
    inference(avatar_component_clause,[],[f1913]) ).

fof(f19114,plain,
    ( spl0_955
    | ~ spl0_207
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2024,f2001,f1913,f19112]) ).

fof(f19112,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(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f2024,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
    | ~ spl0_207
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1914]) ).

fof(f19007,plain,
    ( spl0_954
    | ~ spl0_136
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1857,f1819,f1094,f19005]) ).

fof(f19005,plain,
    ( spl0_954
  <=> ! [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_954])]) ).

fof(f1857,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) )
    | ~ spl0_136
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1095]) ).

fof(f19003,plain,
    ( spl0_953
    | ~ spl0_135
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1851,f1819,f1090,f19001]) ).

fof(f19001,plain,
    ( spl0_953
  <=> ! [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_953])]) ).

fof(f1851,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) )
    | ~ spl0_135
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1091]) ).

fof(f18999,plain,
    ( spl0_952
    | ~ spl0_225
    | ~ spl0_903 ),
    inference(avatar_split_clause,[],[f18714,f17507,f2234,f18997]) ).

fof(f17507,plain,
    ( spl0_903
  <=> ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f18714,plain,
    ( ! [X0] : null_class = intersection(X0,null_class)
    | ~ spl0_225
    | ~ spl0_903 ),
    inference(resolution,[],[f17508,f2235]) ).

fof(f17508,plain,
    ( ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 )
    | ~ spl0_903 ),
    inference(avatar_component_clause,[],[f17507]) ).

fof(f18995,plain,
    ( spl0_951
    | ~ spl0_136
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1831,f1815,f1094,f18993]) ).

fof(f18993,plain,
    ( spl0_951
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f1831,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) )
    | ~ spl0_136
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1095]) ).

fof(f18991,plain,
    ( spl0_950
    | ~ spl0_135
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1825,f1815,f1090,f18989]) ).

fof(f18989,plain,
    ( spl0_950
  <=> ! [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_950])]) ).

fof(f1825,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
        | subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) )
    | ~ spl0_135
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1091]) ).

fof(f18987,plain,
    ( spl0_949
    | ~ spl0_94
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1144,f1094,f708,f18985]) ).

fof(f18985,plain,
    ( spl0_949
  <=> ! [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_949])]) ).

fof(f1144,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f709]) ).

fof(f18983,plain,
    ( spl0_948
    | ~ spl0_94
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1126,f1090,f708,f18981]) ).

fof(f18981,plain,
    ( spl0_948
  <=> ! [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_948])]) ).

fof(f1126,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f709]) ).

fof(f18909,plain,
    ( spl0_947
    | ~ spl0_99
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1736,f1718,f741,f18907]) ).

fof(f18907,plain,
    ( spl0_947
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f1736,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_99
    | ~ spl0_199 ),
    inference(superposition,[],[f742,f1719]) ).

fof(f18819,plain,
    ( spl0_946
    | ~ spl0_224
    | ~ spl0_903 ),
    inference(avatar_split_clause,[],[f18713,f17507,f2230,f18817]) ).

fof(f18713,plain,
    ( ! [X0] : null_class = intersection(null_class,X0)
    | ~ spl0_224
    | ~ spl0_903 ),
    inference(resolution,[],[f17508,f2231]) ).

fof(f18774,plain,
    ( spl0_945
    | ~ spl0_130
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1864,f1819,f1015,f18772]) ).

fof(f18772,plain,
    ( spl0_945
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f1864,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_130
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1016]) ).

fof(f18770,plain,
    ( spl0_944
    | ~ spl0_129
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1856,f1819,f1011,f18768]) ).

fof(f18768,plain,
    ( spl0_944
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f1856,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_129
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1012]) ).

fof(f18766,plain,
    ( spl0_943
    | ~ spl0_130
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1838,f1815,f1015,f18764]) ).

fof(f18764,plain,
    ( spl0_943
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f1838,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
        | null_class = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_130
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1016]) ).

fof(f18762,plain,
    ( spl0_942
    | ~ spl0_129
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1830,f1815,f1011,f18760]) ).

fof(f18760,plain,
    ( spl0_942
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f1830,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
        | null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_129
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1012]) ).

fof(f18758,plain,
    ( spl0_941
    | ~ spl0_94
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1057,f1015,f708,f18756]) ).

fof(f18756,plain,
    ( spl0_941
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f1057,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f709]) ).

fof(f18754,plain,
    ( spl0_940
    | ~ spl0_94
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1041,f1011,f708,f18752]) ).

fof(f18752,plain,
    ( spl0_940
  <=> ! [X0,X3,X2,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f1041,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f709]) ).

fof(f18709,plain,
    ( spl0_939
    | ~ spl0_27
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1850,f1819,f320,f18707]) ).

fof(f18707,plain,
    ( spl0_939
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f1850,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f321]) ).

fof(f18705,plain,
    ( spl0_938
    | ~ spl0_27
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1824,f1815,f320,f18703]) ).

fof(f18703,plain,
    ( spl0_938
  <=> ! [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_938])]) ).

fof(f1824,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f321]) ).

fof(f18673,plain,
    ( spl0_937
    | ~ spl0_112
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2091,f2087,f830,f18671]) ).

fof(f18671,plain,
    ( spl0_937
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(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_937])]) ).

fof(f2087,plain,
    ( spl0_217
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f2091,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_217 ),
    inference(resolution,[],[f2088,f831]) ).

fof(f2088,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_217 ),
    inference(avatar_component_clause,[],[f2087]) ).

fof(f18641,plain,
    ( spl0_936
    | ~ spl0_23
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1855,f1819,f300,f18639]) ).

fof(f18639,plain,
    ( spl0_936
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f1855,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f301]) ).

fof(f18637,plain,
    ( spl0_935
    | ~ spl0_23
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1829,f1815,f300,f18635]) ).

fof(f18635,plain,
    ( spl0_935
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f1829,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f301]) ).

fof(f18502,plain,
    ( spl0_934
    | ~ spl0_97
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1892,f1875,f733,f18500]) ).

fof(f18500,plain,
    ( spl0_934
  <=> ! [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_934])]) ).

fof(f733,plain,
    ( spl0_97
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1892,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) )
    | ~ spl0_97
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f734]) ).

fof(f734,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f733]) ).

fof(f18498,plain,
    ( spl0_933
    | ~ spl0_32
    | ~ spl0_682 ),
    inference(avatar_split_clause,[],[f14503,f10626,f340,f18496]) ).

fof(f18496,plain,
    ( spl0_933
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f10626,plain,
    ( spl0_682
  <=> ! [X0] : null_class = intersection(complement(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).

fof(f14503,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0) )
    | ~ spl0_32
    | ~ spl0_682 ),
    inference(superposition,[],[f341,f10627]) ).

fof(f10627,plain,
    ( ! [X0] : null_class = intersection(complement(X0),X0)
    | ~ spl0_682 ),
    inference(avatar_component_clause,[],[f10626]) ).

fof(f18466,plain,
    ( spl0_932
    | ~ spl0_112
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2078,f2074,f830,f18464]) ).

fof(f18464,plain,
    ( spl0_932
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f2074,plain,
    ( spl0_216
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f2078,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_216 ),
    inference(resolution,[],[f2075,f831]) ).

fof(f2075,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f2074]) ).

fof(f18420,plain,
    ( spl0_931
    | ~ spl0_98
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1735,f1718,f737,f18418]) ).

fof(f18418,plain,
    ( spl0_931
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f737,plain,
    ( spl0_98
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1735,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_98
    | ~ spl0_199 ),
    inference(superposition,[],[f738,f1719]) ).

fof(f738,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f737]) ).

fof(f18416,plain,
    ( spl0_929
    | ~ spl0_930
    | ~ spl0_99
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1427,f1376,f741,f18413,f18410]) ).

fof(f18410,plain,
    ( spl0_929
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f18413,plain,
    ( spl0_930
  <=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f1427,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2) )
    | ~ spl0_99
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f742]) ).

fof(f18228,plain,
    ( spl0_928
    | ~ spl0_49
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2045,f2005,f449,f18226]) ).

fof(f18226,plain,
    ( spl0_928
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

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

fof(f2045,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_49
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f450]) ).

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

fof(f18224,plain,
    ( spl0_927
    | ~ spl0_49
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2017,f2001,f449,f18222]) ).

fof(f18222,plain,
    ( spl0_927
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f2017,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
    | ~ spl0_49
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f450]) ).

fof(f18220,plain,
    ( spl0_926
    | ~ spl0_20
    | ~ spl0_400 ),
    inference(avatar_split_clause,[],[f4815,f4303,f288,f18218]) ).

fof(f18218,plain,
    ( spl0_926
  <=> ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f4303,plain,
    ( spl0_400
  <=> null_class = complement(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f4815,plain,
    ( ! [X0] :
        ( ~ member(X0,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_20
    | ~ spl0_400 ),
    inference(superposition,[],[f289,f4305]) ).

fof(f4305,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_400 ),
    inference(avatar_component_clause,[],[f4303]) ).

fof(f18138,plain,
    ( spl0_925
    | ~ spl0_44
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2047,f2005,f425,f18136]) ).

fof(f18136,plain,
    ( spl0_925
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

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

fof(f2047,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_44
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f426]) ).

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

fof(f18134,plain,
    ( spl0_924
    | ~ spl0_44
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2019,f2001,f425,f18132]) ).

fof(f18132,plain,
    ( spl0_924
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f2019,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_44
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f426]) ).

fof(f18130,plain,
    ( spl0_923
    | ~ spl0_79
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1632,f1627,f630,f18128]) ).

fof(f18128,plain,
    ( spl0_923
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).

fof(f1627,plain,
    ( spl0_194
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f1632,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,cross_product(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f631]) ).

fof(f1628,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f1627]) ).

fof(f17824,plain,
    ( spl0_922
    | ~ spl0_30
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2041,f2005,f332,f17822]) ).

fof(f17822,plain,
    ( spl0_922
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).

fof(f2041,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_30
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f333]) ).

fof(f17820,plain,
    ( spl0_921
    | ~ spl0_29
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2040,f2005,f328,f17818]) ).

fof(f17818,plain,
    ( spl0_921
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f2040,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_29
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f329]) ).

fof(f17816,plain,
    ( spl0_920
    | ~ spl0_199
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2030,f2001,f1718,f17814]) ).

fof(f17814,plain,
    ( spl0_920
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f2030,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199
    | ~ spl0_212 ),
    inference(superposition,[],[f2002,f1719]) ).

fof(f17812,plain,
    ( spl0_919
    | ~ spl0_30
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2013,f2001,f332,f17810]) ).

fof(f17810,plain,
    ( spl0_919
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f2013,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_30
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f333]) ).

fof(f17808,plain,
    ( spl0_918
    | ~ spl0_29
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2012,f2001,f328,f17806]) ).

fof(f17806,plain,
    ( spl0_918
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).

fof(f2012,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_29
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f329]) ).

fof(f17804,plain,
    ( spl0_917
    | ~ spl0_159
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1775,f1752,f1301,f17802]) ).

fof(f17802,plain,
    ( spl0_917
  <=> ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
        | ~ operation(X2)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).

fof(f1775,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
        | ~ operation(X2)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) )
    | ~ spl0_159
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f1302]) ).

fof(f17800,plain,
    ( spl0_916
    | ~ spl0_97
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1734,f1718,f733,f17798]) ).

fof(f17798,plain,
    ( spl0_916
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).

fof(f1734,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_97
    | ~ spl0_199 ),
    inference(superposition,[],[f734,f1719]) ).

fof(f17754,plain,
    ( spl0_915
    | ~ spl0_40
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2094,f2087,f381,f17752]) ).

fof(f17752,plain,
    ( spl0_915
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).

fof(f2094,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))),X2)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_217 ),
    inference(superposition,[],[f2088,f382]) ).

fof(f17750,plain,
    ( spl0_914
    | ~ spl0_194
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1861,f1819,f1627,f17748]) ).

fof(f17748,plain,
    ( spl0_914
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).

fof(f1861,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_194
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1628]) ).

fof(f17746,plain,
    ( spl0_913
    | ~ spl0_194
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1835,f1815,f1627,f17744]) ).

fof(f17744,plain,
    ( spl0_913
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).

fof(f1835,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | null_class = X1
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_194
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1628]) ).

fof(f17742,plain,
    ( spl0_912
    | ~ spl0_94
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1639,f1627,f708,f17740]) ).

fof(f17740,plain,
    ( spl0_912
  <=> ! [X0,X3,X2,X1] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f1639,plain,
    ( ! [X2,X3,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f709]) ).

fof(f17726,plain,
    ( spl0_911
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2081,f2074,f381,f17724]) ).

fof(f17724,plain,
    ( spl0_911
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f2081,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(superposition,[],[f2075,f382]) ).

fof(f17722,plain,
    ( spl0_909
    | ~ spl0_910
    | ~ spl0_39
    | ~ spl0_369 ),
    inference(avatar_split_clause,[],[f4263,f3808,f377,f17719,f17715]) ).

fof(f17715,plain,
    ( spl0_909
  <=> subset_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f3808,plain,
    ( spl0_369
  <=> subclass(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f4263,plain,
    ( ~ subclass(subset_relation,singleton_relation)
    | subset_relation = singleton_relation
    | ~ spl0_39
    | ~ spl0_369 ),
    inference(resolution,[],[f3810,f378]) ).

fof(f3810,plain,
    ( subclass(singleton_relation,subset_relation)
    | ~ spl0_369 ),
    inference(avatar_component_clause,[],[f3808]) ).

fof(f17700,plain,
    ( spl0_908
    | ~ spl0_24
    | ~ spl0_100
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1881,f1875,f747,f304,f17698]) ).

fof(f17698,plain,
    ( spl0_908
  <=> ! [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_908])]) ).

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

fof(f1881,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_100
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f748]) ).

fof(f17671,plain,
    ( spl0_907
    | ~ spl0_112
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2067,f2063,f830,f17669]) ).

fof(f17669,plain,
    ( spl0_907
  <=> ! [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_907])]) ).

fof(f2067,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_215 ),
    inference(resolution,[],[f2064,f831]) ).

fof(f17640,plain,
    ( spl0_906
    | ~ spl0_77
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2090,f2087,f615,f17638]) ).

fof(f17638,plain,
    ( spl0_906
  <=> ! [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_906])]) ).

fof(f2090,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
        | ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_217 ),
    inference(resolution,[],[f2088,f616]) ).

fof(f17517,plain,
    ( spl0_905
    | ~ spl0_77
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2077,f2074,f615,f17515]) ).

fof(f17515,plain,
    ( spl0_905
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).

fof(f2077,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_216 ),
    inference(resolution,[],[f2075,f616]) ).

fof(f17513,plain,
    ( spl0_904
    | ~ spl0_96
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1733,f1718,f729,f17511]) ).

fof(f17511,plain,
    ( spl0_904
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).

fof(f1733,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_96
    | ~ spl0_199 ),
    inference(superposition,[],[f730,f1719]) ).

fof(f17509,plain,
    ( spl0_903
    | ~ spl0_39
    | ~ spl0_349 ),
    inference(avatar_split_clause,[],[f3898,f3521,f377,f17507]) ).

fof(f3521,plain,
    ( spl0_349
  <=> ! [X0] : subclass(null_class,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f3898,plain,
    ( ! [X0] :
        ( ~ subclass(X0,null_class)
        | null_class = X0 )
    | ~ spl0_39
    | ~ spl0_349 ),
    inference(resolution,[],[f3522,f378]) ).

fof(f3522,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_349 ),
    inference(avatar_component_clause,[],[f3521]) ).

fof(f17367,plain,
    ( spl0_729
    | spl0_902
    | ~ spl0_77
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f2066,f2063,f615,f17365,f12079]) ).

fof(f17365,plain,
    ( spl0_902
  <=> ! [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_902])]) ).

fof(f2066,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(X0,universal_class)
        | ~ member(X2,universal_class)
        | ~ member(X1,universal_class) )
    | ~ spl0_77
    | ~ spl0_215 ),
    inference(resolution,[],[f2064,f616]) ).

fof(f17363,plain,
    ( spl0_901
    | ~ spl0_96
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1425,f1376,f729,f17361]) ).

fof(f17361,plain,
    ( spl0_901
  <=> ! [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_901])]) ).

fof(f1425,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,rotate(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) )
    | ~ spl0_96
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f730]) ).

fof(f17359,plain,
    ( ~ spl0_899
    | spl0_900
    | ~ spl0_89
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1212,f1174,f684,f17357,f17353]) ).

fof(f17353,plain,
    ( spl0_899
  <=> operation(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).

fof(f17357,plain,
    ( spl0_900
  <=> ! [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_900])]) ).

fof(f1212,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_89
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f685]) ).

fof(f17351,plain,
    ( spl0_897
    | ~ spl0_898
    | ~ spl0_100
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f845,f818,f747,f17348,f17345]) ).

fof(f17345,plain,
    ( spl0_897
  <=> ! [X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).

fof(f17348,plain,
    ( spl0_898
  <=> subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).

fof(f845,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function) )
    | ~ spl0_100
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f748]) ).

fof(f17343,plain,
    ( spl0_895
    | ~ spl0_896
    | ~ spl0_186
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1900,f1875,f1563,f17340,f17337]) ).

fof(f17337,plain,
    ( spl0_895
  <=> ! [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_895])]) ).

fof(f17340,plain,
    ( spl0_896
  <=> 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_896])]) ).

fof(f1900,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_186
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1564]) ).

fof(f17290,plain,
    ( spl0_894
    | ~ spl0_163
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2046,f2005,f1358,f17288]) ).

fof(f17288,plain,
    ( spl0_894
  <=> ! [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_894])]) ).

fof(f1358,plain,
    ( spl0_163
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f2046,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_163
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1359]) ).

fof(f1359,plain,
    ( ! [X0] :
        ( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,subset_relation) )
    | ~ spl0_163 ),
    inference(avatar_component_clause,[],[f1358]) ).

fof(f17286,plain,
    ( spl0_893
    | ~ spl0_163
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2018,f2001,f1358,f17284]) ).

fof(f17284,plain,
    ( spl0_893
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_893])]) ).

fof(f2018,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_163
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1359]) ).

fof(f17267,plain,
    ( spl0_892
    | ~ spl0_172
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1859,f1819,f1463,f17265]) ).

fof(f17265,plain,
    ( spl0_892
  <=> ! [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_892])]) ).

fof(f1463,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f1859,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_172
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1464]) ).

fof(f1464,plain,
    ( ! [X0,X1] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_172 ),
    inference(avatar_component_clause,[],[f1463]) ).

fof(f17263,plain,
    ( spl0_891
    | ~ spl0_172
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1833,f1815,f1463,f17261]) ).

fof(f17261,plain,
    ( spl0_891
  <=> ! [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_891])]) ).

fof(f1833,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_172
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1464]) ).

fof(f17259,plain,
    ( spl0_890
    | ~ spl0_94
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1513,f1463,f708,f17257]) ).

fof(f17257,plain,
    ( spl0_890
  <=> ! [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_890])]) ).

fof(f1513,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f709]) ).

fof(f17218,plain,
    ( spl0_889
    | ~ spl0_187
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2059,f2005,f1585,f17216]) ).

fof(f17216,plain,
    ( spl0_889
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_889])]) ).

fof(f2059,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_187
    | ~ spl0_213 ),
    inference(duplicate_literal_removal,[],[f2055]) ).

fof(f2055,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
        | ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_187
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1586]) ).

fof(f17173,plain,
    ( spl0_888
    | ~ spl0_166
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2036,f2005,f1376,f17171]) ).

fof(f17171,plain,
    ( spl0_888
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_888])]) ).

fof(f2036,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
        | ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_166
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1377]) ).

fof(f17125,plain,
    ( spl0_887
    | ~ spl0_40
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2097,f2087,f381,f17123]) ).

fof(f17123,plain,
    ( spl0_887
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).

fof(f2097,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | subclass(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),X2)
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_217 ),
    inference(superposition,[],[f2088,f382]) ).

fof(f17121,plain,
    ( spl0_885
    | ~ spl0_886
    | ~ spl0_39
    | ~ spl0_325 ),
    inference(avatar_split_clause,[],[f3734,f3203,f377,f17118,f17114]) ).

fof(f17114,plain,
    ( spl0_885
  <=> element_relation = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).

fof(f3203,plain,
    ( spl0_325
  <=> subclass(singleton_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f3734,plain,
    ( ~ subclass(element_relation,singleton_relation)
    | element_relation = singleton_relation
    | ~ spl0_39
    | ~ spl0_325 ),
    inference(resolution,[],[f3205,f378]) ).

fof(f3205,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_325 ),
    inference(avatar_component_clause,[],[f3203]) ).

fof(f17112,plain,
    ( spl0_884
    | ~ spl0_200
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1938,f1930,f1752,f17110]) ).

fof(f17110,plain,
    ( spl0_884
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).

fof(f1930,plain,
    ( spl0_209
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f1938,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
        | ~ member(not_homomorphism2(X0,X1,X2),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
        | ~ operation(X2) )
    | ~ spl0_200
    | ~ spl0_209 ),
    inference(resolution,[],[f1931,f1753]) ).

fof(f1931,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_209 ),
    inference(avatar_component_clause,[],[f1930]) ).

fof(f17108,plain,
    ( spl0_883
    | ~ spl0_166
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1858,f1819,f1376,f17106]) ).

fof(f17106,plain,
    ( spl0_883
  <=> ! [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_883])]) ).

fof(f1858,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_166
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1377]) ).

fof(f17104,plain,
    ( spl0_882
    | ~ spl0_166
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1832,f1815,f1376,f17102]) ).

fof(f17102,plain,
    ( spl0_882
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(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_882])]) ).

fof(f1832,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_166
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1377]) ).

fof(f17100,plain,
    ( spl0_881
    | ~ spl0_94
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1437,f1376,f708,f17098]) ).

fof(f17098,plain,
    ( spl0_881
  <=> ! [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_881])]) ).

fof(f1437,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f709]) ).

fof(f16982,plain,
    ( spl0_880
    | ~ spl0_237
    | ~ spl0_875 ),
    inference(avatar_split_clause,[],[f16893,f16890,f2324,f16980]) ).

fof(f16980,plain,
    ( spl0_880
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).

fof(f16890,plain,
    ( spl0_875
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_875])]) ).

fof(f16893,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_237
    | ~ spl0_875 ),
    inference(forward_demodulation,[],[f16891,f2326]) ).

fof(f16891,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_875 ),
    inference(avatar_component_clause,[],[f16890]) ).

fof(f16930,plain,
    ( spl0_879
    | ~ spl0_237
    | ~ spl0_874 ),
    inference(avatar_split_clause,[],[f16888,f16885,f2324,f16928]) ).

fof(f16928,plain,
    ( spl0_879
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f16885,plain,
    ( spl0_874
  <=> ! [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_874])]) ).

fof(f16888,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_874 ),
    inference(forward_demodulation,[],[f16886,f2326]) ).

fof(f16886,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_874 ),
    inference(avatar_component_clause,[],[f16885]) ).

fof(f16905,plain,
    ( spl0_878
    | ~ spl0_237
    | ~ spl0_872 ),
    inference(avatar_split_clause,[],[f16879,f16876,f2324,f16903]) ).

fof(f16903,plain,
    ( spl0_878
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).

fof(f16876,plain,
    ( spl0_872
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_872])]) ).

fof(f16879,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_237
    | ~ spl0_872 ),
    inference(forward_demodulation,[],[f16877,f2326]) ).

fof(f16877,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_872 ),
    inference(avatar_component_clause,[],[f16876]) ).

fof(f16901,plain,
    ( spl0_877
    | ~ spl0_237
    | ~ spl0_871 ),
    inference(avatar_split_clause,[],[f16874,f16871,f2324,f16899]) ).

fof(f16899,plain,
    ( spl0_877
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f16871,plain,
    ( spl0_871
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_871])]) ).

fof(f16874,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_871 ),
    inference(forward_demodulation,[],[f16872,f2326]) ).

fof(f16872,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_871 ),
    inference(avatar_component_clause,[],[f16871]) ).

fof(f16897,plain,
    ( spl0_876
    | ~ spl0_124
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2054,f2005,f958,f16895]) ).

fof(f16895,plain,
    ( spl0_876
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f958,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f2054,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),null_class)
        | null_class = X3 )
    | ~ spl0_124
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f959]) ).

fof(f959,plain,
    ( ! [X0,X1] :
        ( member(X1,regular(X0))
        | ~ member(X1,null_class)
        | null_class = X0 )
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f958]) ).

fof(f16892,plain,
    ( spl0_875
    | ~ spl0_126
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2050,f2005,f966,f16890]) ).

fof(f2050,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
    | ~ spl0_126
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f967]) ).

fof(f16887,plain,
    ( spl0_874
    | ~ spl0_125
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2048,f2005,f962,f16885]) ).

fof(f2048,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
    | ~ spl0_125
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f963]) ).

fof(f16883,plain,
    ( spl0_873
    | ~ spl0_124
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2026,f2001,f958,f16881]) ).

fof(f16881,plain,
    ( spl0_873
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f2026,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(regular(X3)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),null_class)
        | null_class = X3 )
    | ~ spl0_124
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f959]) ).

fof(f16878,plain,
    ( spl0_872
    | ~ spl0_126
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2022,f2001,f966,f16876]) ).

fof(f2022,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
    | ~ spl0_126
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f967]) ).

fof(f16873,plain,
    ( spl0_871
    | ~ spl0_125
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2020,f2001,f962,f16871]) ).

fof(f2020,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
    | ~ spl0_125
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f963]) ).

fof(f16685,plain,
    ( spl0_870
    | ~ spl0_66
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2057,f2005,f553,f16683]) ).

fof(f16683,plain,
    ( spl0_870
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_870])]) ).

fof(f2057,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
        | ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_66
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f554]) ).

fof(f16681,plain,
    ( spl0_869
    | ~ spl0_143
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1910,f1875,f1166,f16679]) ).

fof(f16679,plain,
    ( spl0_869
  <=> ! [X2,X0,X1] :
        ( ~ subclass(composition_function,regular(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f1166,plain,
    ( spl0_143
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1910,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,regular(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
        | null_class = X0 )
    | ~ spl0_143
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1167]) ).

fof(f1167,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,regular(X0))
        | member(X1,null_class)
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1166]) ).

fof(f16676,plain,
    ( spl0_867
    | ~ spl0_868
    | ~ spl0_145
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1907,f1875,f1174,f16673,f16670]) ).

fof(f16670,plain,
    ( spl0_867
  <=> ! [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_867])]) ).

fof(f16673,plain,
    ( spl0_868
  <=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f1907,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation) )
    | ~ spl0_145
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1175]) ).

fof(f16604,plain,
    ( ~ spl0_866
    | ~ spl0_237
    | spl0_865 ),
    inference(avatar_split_clause,[],[f16599,f16595,f2324,f16601]) ).

fof(f16601,plain,
    ( spl0_866
  <=> subclass(composition_function,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).

fof(f16595,plain,
    ( spl0_865
  <=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).

fof(f16599,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_237
    | spl0_865 ),
    inference(forward_demodulation,[],[f16597,f2326]) ).

fof(f16597,plain,
    ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
    | spl0_865 ),
    inference(avatar_component_clause,[],[f16595]) ).

fof(f16598,plain,
    ( spl0_864
    | ~ spl0_865
    | ~ spl0_144
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1902,f1875,f1170,f16595,f16592]) ).

fof(f16592,plain,
    ( spl0_864
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),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_864])]) ).

fof(f1902,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f1171]) ).

fof(f16590,plain,
    ( spl0_863
    | ~ spl0_171
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1867,f1819,f1459,f16588]) ).

fof(f16588,plain,
    ( spl0_863
  <=> ! [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_863])]) ).

fof(f1459,plain,
    ( spl0_171
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f1867,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_171
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1460]) ).

fof(f1460,plain,
    ( ! [X2,X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1459]) ).

fof(f16586,plain,
    ( spl0_862
    | ~ spl0_171
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1841,f1815,f1459,f16584]) ).

fof(f16584,plain,
    ( spl0_862
  <=> ! [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_862])]) ).

fof(f1841,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
        | ~ function(X2)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_171
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1460]) ).

fof(f16523,plain,
    ( spl0_861
    | spl0_629
    | ~ spl0_79
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1507,f1463,f630,f9626,f16521]) ).

fof(f16521,plain,
    ( spl0_861
  <=> ! [X2] :
        ( ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))),unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),unordered_pair(second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).

fof(f9626,plain,
    ( spl0_629
  <=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f1507,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))),unordered_pair(first(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),unordered_pair(second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class)))))),second(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))))))) )
    | ~ spl0_79
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f631]) ).

fof(f16519,plain,
    ( spl0_860
    | ~ spl0_94
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1495,f1459,f708,f16517]) ).

fof(f16517,plain,
    ( spl0_860
  <=> ! [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_860])]) ).

fof(f1495,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | ~ member(X4,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f709]) ).

fof(f16479,plain,
    ( ~ spl0_91
    | spl0_180
    | ~ spl0_856 ),
    inference(avatar_split_clause,[],[f16364,f16357,f1529,f693]) ).

fof(f693,plain,
    ( spl0_91
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f1529,plain,
    ( spl0_180
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f16357,plain,
    ( spl0_856
  <=> null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f16364,plain,
    ( ~ member(null_class,universal_class)
    | spl0_180
    | ~ spl0_856 ),
    inference(superposition,[],[f1530,f16359]) ).

fof(f16359,plain,
    ( null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
    | ~ spl0_856 ),
    inference(avatar_component_clause,[],[f16357]) ).

fof(f1530,plain,
    ( ~ member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | spl0_180 ),
    inference(avatar_component_clause,[],[f1529]) ).

fof(f16457,plain,
    ( spl0_859
    | ~ spl0_112
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2043,f2005,f830,f16455]) ).

fof(f16455,plain,
    ( spl0_859
  <=> ! [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_859])]) ).

fof(f2043,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f831]) ).

fof(f16453,plain,
    ( spl0_858
    | ~ spl0_112
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2015,f2001,f830,f16451]) ).

fof(f16451,plain,
    ( spl0_858
  <=> ! [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_858])]) ).

fof(f2015,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f831]) ).

fof(f16363,plain,
    ( spl0_856
    | spl0_857
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2084,f2074,f381,f16361,f16357]) ).

fof(f16361,plain,
    ( spl0_857
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f2084,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(null_class,universal_class))))),regular(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | null_class = domain_of(domain_of(flip(cross_product(null_class,universal_class))))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_216 ),
    inference(superposition,[],[f2075,f382]) ).

fof(f16355,plain,
    ( spl0_855
    | ~ spl0_48
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1896,f1875,f445,f16353]) ).

fof(f16353,plain,
    ( spl0_855
  <=> ! [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_855])]) ).

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

fof(f1896,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,unordered_pair(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 )
    | ~ spl0_48
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f446]) ).

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

fof(f16334,plain,
    ( spl0_854
    | ~ spl0_159
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1641,f1627,f1301,f16332]) ).

fof(f16332,plain,
    ( spl0_854
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).

fof(f1641,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) )
    | ~ spl0_159
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f1302]) ).

fof(f16324,plain,
    ( spl0_853
    | ~ spl0_400
    | ~ spl0_694 ),
    inference(avatar_split_clause,[],[f16054,f11645,f4303,f16321]) ).

fof(f16321,plain,
    ( spl0_853
  <=> null_class = intersection(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).

fof(f11645,plain,
    ( spl0_694
  <=> ! [X0] : null_class = intersection(X0,complement(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f16054,plain,
    ( null_class = intersection(universal_class,null_class)
    | ~ spl0_400
    | ~ spl0_694 ),
    inference(superposition,[],[f11646,f4305]) ).

fof(f11646,plain,
    ( ! [X0] : null_class = intersection(X0,complement(X0))
    | ~ spl0_694 ),
    inference(avatar_component_clause,[],[f11645]) ).

fof(f16313,plain,
    ( spl0_852
    | ~ spl0_186
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1769,f1752,f1563,f16311]) ).

fof(f16311,plain,
    ( spl0_852
  <=> ! [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_852])]) ).

fof(f1769,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_186
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f1564]) ).

fof(f16309,plain,
    ( spl0_851
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1661,f1646,f569,f453,f16307]) ).

fof(f16307,plain,
    ( spl0_851
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f1646,plain,
    ( spl0_195
  <=> ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f1661,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_195 ),
    inference(forward_demodulation,[],[f1657,f454]) ).

fof(f1657,plain,
    ( ! [X0] :
        ( null_class = complement(domain_of(X0))
        | ~ member(complement(domain_of(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class),X0) )
    | ~ spl0_70
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f570]) ).

fof(f1647,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
        | complement(X0) = null_class
        | ~ member(complement(X0),universal_class) )
    | ~ spl0_195 ),
    inference(avatar_component_clause,[],[f1646]) ).

fof(f16213,plain,
    ( spl0_850
    | ~ spl0_237
    | ~ spl0_846 ),
    inference(avatar_split_clause,[],[f16049,f16046,f2324,f16211]) ).

fof(f16211,plain,
    ( spl0_850
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),singleton_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).

fof(f16046,plain,
    ( spl0_846
  <=> ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f16049,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),singleton_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_846 ),
    inference(forward_demodulation,[],[f16047,f2326]) ).

fof(f16047,plain,
    ( ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_846 ),
    inference(avatar_component_clause,[],[f16046]) ).

fof(f16209,plain,
    ( spl0_849
    | ~ spl0_237
    | ~ spl0_845 ),
    inference(avatar_split_clause,[],[f16044,f16038,f2324,f16207]) ).

fof(f16207,plain,
    ( spl0_849
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).

fof(f16038,plain,
    ( spl0_845
  <=> ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f16044,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0) )
    | ~ spl0_237
    | ~ spl0_845 ),
    inference(forward_demodulation,[],[f16043,f2326]) ).

fof(f16043,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),intersection(complement(compose(element_relation,complement(singleton_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_845 ),
    inference(forward_demodulation,[],[f16042,f2326]) ).

fof(f16042,plain,
    ( ! [X0] :
        ( ~ member(intersection(complement(compose(element_relation,complement(singleton_relation))),X0),universal_class)
        | null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_845 ),
    inference(forward_demodulation,[],[f16041,f2326]) ).

fof(f16041,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(singleton_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_845 ),
    inference(forward_demodulation,[],[f16039,f2326]) ).

fof(f16039,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_845 ),
    inference(avatar_component_clause,[],[f16038]) ).

fof(f16205,plain,
    ( spl0_848
    | ~ spl0_237
    | ~ spl0_844 ),
    inference(avatar_split_clause,[],[f16036,f16033,f2324,f16203]) ).

fof(f16203,plain,
    ( spl0_848
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f16033,plain,
    ( spl0_844
  <=> ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f16036,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_844 ),
    inference(forward_demodulation,[],[f16034,f2326]) ).

fof(f16034,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_844 ),
    inference(avatar_component_clause,[],[f16033]) ).

fof(f16053,plain,
    ( spl0_847
    | ~ spl0_237
    | ~ spl0_843 ),
    inference(avatar_split_clause,[],[f16031,f16025,f2324,f16051]) ).

fof(f16051,plain,
    ( spl0_847
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).

fof(f16025,plain,
    ( spl0_843
  <=> ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f16031,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation)))) )
    | ~ spl0_237
    | ~ spl0_843 ),
    inference(forward_demodulation,[],[f16030,f2326]) ).

fof(f16030,plain,
    ( ! [X0] :
        ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),intersection(X0,complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),element_relation)
        | ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_843 ),
    inference(forward_demodulation,[],[f16029,f2326]) ).

fof(f16029,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,complement(compose(element_relation,complement(singleton_relation)))),universal_class)
        | null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_843 ),
    inference(forward_demodulation,[],[f16028,f2326]) ).

fof(f16028,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_843 ),
    inference(forward_demodulation,[],[f16026,f2326]) ).

fof(f16026,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_843 ),
    inference(avatar_component_clause,[],[f16025]) ).

fof(f16048,plain,
    ( spl0_846
    | ~ spl0_145
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1701,f1667,f1174,f16046]) ).

fof(f1701,plain,
    ( ! [X0] :
        ( null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
        | ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_145
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f1175]) ).

fof(f16040,plain,
    ( spl0_845
    | ~ spl0_144
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1698,f1667,f1170,f16038]) ).

fof(f1698,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
        | ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f1171]) ).

fof(f16035,plain,
    ( spl0_844
    | ~ spl0_145
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1680,f1663,f1174,f16033]) ).

fof(f1680,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_145
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f1175]) ).

fof(f16027,plain,
    ( spl0_843
    | ~ spl0_144
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1677,f1663,f1170,f16025]) ).

fof(f1677,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f1171]) ).

fof(f15964,plain,
    ( spl0_629
    | spl0_842
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1489,f1459,f630,f15962,f9626]) ).

fof(f15962,plain,
    ( spl0_842
  <=> ! [X0,X3] :
        ( ~ function(X0)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))))))
        | ~ member(X3,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f1489,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,cross_product(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = unordered_pair(unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))),unordered_pair(first(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),unordered_pair(second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class))))),second(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))))))) )
    | ~ spl0_79
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f631]) ).

fof(f15950,plain,
    ( spl0_841
    | ~ spl0_199
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1947,f1942,f1718,f15948]) ).

fof(f15948,plain,
    ( spl0_841
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).

fof(f1947,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199
    | ~ spl0_210 ),
    inference(superposition,[],[f1943,f1719]) ).

fof(f15873,plain,
    ( spl0_839
    | ~ spl0_840
    | ~ spl0_99
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f850,f818,f741,f15870,f15867]) ).

fof(f15867,plain,
    ( spl0_839
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).

fof(f15870,plain,
    ( spl0_840
  <=> subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).

fof(f850,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
    | ~ spl0_99
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f742]) ).

fof(f15839,plain,
    ( spl0_838
    | ~ spl0_177
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2016,f2001,f1484,f15837]) ).

fof(f15837,plain,
    ( spl0_838
  <=> ! [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_838])]) ).

fof(f1484,plain,
    ( spl0_177
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f2016,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
    | ~ spl0_177
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f1485]) ).

fof(f1485,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f1484]) ).

fof(f15832,plain,
    ( ~ spl0_836
    | ~ spl0_837
    | spl0_630
    | ~ spl0_163
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1654,f1646,f1358,f9700,f15829,f15825]) ).

fof(f15825,plain,
    ( spl0_836
  <=> 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_836])]) ).

fof(f15829,plain,
    ( spl0_837
  <=> 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_837])]) ).

fof(f9700,plain,
    ( spl0_630
  <=> null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f1654,plain,
    ( null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_163
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f1359]) ).

fof(f15773,plain,
    ( spl0_835
    | ~ spl0_177
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2061,f2005,f1484,f15771]) ).

fof(f15771,plain,
    ( spl0_835
  <=> ! [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_835])]) ).

fof(f2061,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_177
    | ~ spl0_213 ),
    inference(duplicate_literal_removal,[],[f2044]) ).

fof(f2044,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
    | ~ spl0_177
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f1485]) ).

fof(f15769,plain,
    ( spl0_834
    | ~ spl0_88
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1945,f1942,f680,f15767]) ).

fof(f15767,plain,
    ( spl0_834
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f680,plain,
    ( spl0_88
  <=> ! [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_88])]) ).

fof(f1945,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
    | ~ spl0_88
    | ~ spl0_210 ),
    inference(resolution,[],[f1943,f681]) ).

fof(f681,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_88 ),
    inference(avatar_component_clause,[],[f680]) ).

fof(f15685,plain,
    ( spl0_833
    | ~ spl0_237
    | ~ spl0_827 ),
    inference(avatar_split_clause,[],[f15654,f15651,f2324,f15683]) ).

fof(f15683,plain,
    ( spl0_833
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f15651,plain,
    ( spl0_827
  <=> ! [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_827])]) ).

fof(f15654,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_827 ),
    inference(forward_demodulation,[],[f15652,f2326]) ).

fof(f15652,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_827 ),
    inference(avatar_component_clause,[],[f15651]) ).

fof(f15681,plain,
    ( spl0_832
    | ~ spl0_237
    | ~ spl0_826 ),
    inference(avatar_split_clause,[],[f15649,f15646,f2324,f15679]) ).

fof(f15679,plain,
    ( spl0_832
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f15646,plain,
    ( spl0_826
  <=> ! [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_826])]) ).

fof(f15649,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),complement(compose(element_relation,complement(singleton_relation))))
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_826 ),
    inference(forward_demodulation,[],[f15647,f2326]) ).

fof(f15647,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_826 ),
    inference(avatar_component_clause,[],[f15646]) ).

fof(f15670,plain,
    ( spl0_831
    | ~ spl0_199
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1939,f1930,f1718,f15668]) ).

fof(f15668,plain,
    ( spl0_831
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),compose(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f1939,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),compose(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199
    | ~ spl0_209 ),
    inference(superposition,[],[f1931,f1719]) ).

fof(f15666,plain,
    ( spl0_830
    | ~ spl0_153
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1860,f1819,f1254,f15664]) ).

fof(f15664,plain,
    ( spl0_830
  <=> ! [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_830])]) ).

fof(f1254,plain,
    ( spl0_153
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f1860,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_153
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1255]) ).

fof(f1255,plain,
    ( ! [X0,X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
        | ~ subclass(universal_class,X1)
        | ~ member(X0,universal_class) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1254]) ).

fof(f15662,plain,
    ( spl0_829
    | ~ spl0_153
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1834,f1815,f1254,f15660]) ).

fof(f15660,plain,
    ( spl0_829
  <=> ! [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_829])]) ).

fof(f1834,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X1,universal_class) )
    | ~ spl0_153
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1255]) ).

fof(f15658,plain,
    ( spl0_828
    | ~ spl0_143
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1777,f1752,f1166,f15656]) ).

fof(f15656,plain,
    ( spl0_828
  <=> ! [X0,X3,X2,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),regular(X3))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
        | null_class = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f1777,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),regular(X3))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),null_class)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
        | null_class = X3 )
    | ~ spl0_143
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f1167]) ).

fof(f15653,plain,
    ( spl0_827
    | ~ spl0_145
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1774,f1752,f1174,f15651]) ).

fof(f1774,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) )
    | ~ spl0_145
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f1175]) ).

fof(f15648,plain,
    ( spl0_826
    | ~ spl0_144
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1771,f1752,f1170,f15646]) ).

fof(f1771,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f1171]) ).

fof(f15644,plain,
    ( spl0_825
    | ~ spl0_94
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1274,f1254,f708,f15642]) ).

fof(f15642,plain,
    ( spl0_825
  <=> ! [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_825])]) ).

fof(f1274,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(X3,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f709]) ).

fof(f15618,plain,
    ( spl0_824
    | ~ spl0_199
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1918,f1913,f1718,f15616]) ).

fof(f15616,plain,
    ( spl0_824
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).

fof(f1918,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
        | ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_199
    | ~ spl0_207 ),
    inference(superposition,[],[f1914,f1719]) ).

fof(f15614,plain,
    ( spl0_823
    | ~ spl0_48
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1765,f1752,f445,f15612]) ).

fof(f15612,plain,
    ( spl0_823
  <=> ! [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_823])]) ).

fof(f1765,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),unordered_pair(X3,X4))
        | ~ operation(X2)
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
        | unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 )
    | ~ spl0_48
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f446]) ).

fof(f15610,plain,
    ( ~ spl0_822
    | ~ spl0_22
    | spl0_819 ),
    inference(avatar_split_clause,[],[f15400,f15396,f296,f15607]) ).

fof(f15607,plain,
    ( spl0_822
  <=> function(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).

fof(f15400,plain,
    ( ~ function(composition_function)
    | ~ spl0_22
    | spl0_819 ),
    inference(resolution,[],[f15398,f297]) ).

fof(f15408,plain,
    ( spl0_821
    | ~ spl0_77
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2042,f2005,f615,f15406]) ).

fof(f15406,plain,
    ( spl0_821
  <=> ! [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_821])]) ).

fof(f2042,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X2,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_77
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f616]) ).

fof(f15404,plain,
    ( spl0_820
    | ~ spl0_77
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2014,f2001,f615,f15402]) ).

fof(f15402,plain,
    ( spl0_820
  <=> ! [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_820])]) ).

fof(f2014,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,X4)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
    | ~ spl0_77
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f616]) ).

fof(f15399,plain,
    ( spl0_818
    | ~ spl0_819
    | ~ spl0_84
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1884,f1875,f662,f15396,f15393]) ).

fof(f15393,plain,
    ( spl0_818
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f662,plain,
    ( spl0_84
  <=> ! [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_84])]) ).

fof(f1884,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
        | ~ member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_84
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f663]) ).

fof(f663,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_84 ),
    inference(avatar_component_clause,[],[f662]) ).

fof(f15391,plain,
    ( spl0_817
    | ~ spl0_48
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1692,f1667,f445,f15389]) ).

fof(f15389,plain,
    ( spl0_817
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f1692,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_48
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f446]) ).

fof(f15387,plain,
    ( spl0_816
    | ~ spl0_48
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1671,f1663,f445,f15385]) ).

fof(f15385,plain,
    ( spl0_816
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f1671,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 )
    | ~ spl0_48
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f446]) ).

fof(f15383,plain,
    ( spl0_815
    | ~ spl0_97
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1426,f1376,f733,f15381]) ).

fof(f15381,plain,
    ( spl0_815
  <=> ! [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_815])]) ).

fof(f1426,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,flip(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) )
    | ~ spl0_97
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f734]) ).

fof(f15377,plain,
    ( ~ spl0_814
    | ~ spl0_237
    | spl0_812 ),
    inference(avatar_split_clause,[],[f15369,f15361,f2324,f15374]) ).

fof(f15374,plain,
    ( spl0_814
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).

fof(f15361,plain,
    ( spl0_812
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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_812])]) ).

fof(f15369,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_237
    | spl0_812 ),
    inference(forward_demodulation,[],[f15362,f2326]) ).

fof(f15362,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
    | spl0_812 ),
    inference(avatar_component_clause,[],[f15361]) ).

fof(f15368,plain,
    ( spl0_533
    | ~ spl0_811
    | spl0_812
    | ~ spl0_813
    | ~ spl0_83
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1216,f1174,f652,f15365,f15361,f15357,f7419]) ).

fof(f7419,plain,
    ( spl0_533
  <=> null_class = domain_of(flip(cross_product(subset_relation,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f15365,plain,
    ( spl0_813
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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_813])]) ).

fof(f1216,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation)
    | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
    | ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_83
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f653]) ).

fof(f15350,plain,
    ( ~ spl0_810
    | ~ spl0_237
    | spl0_804 ),
    inference(avatar_split_clause,[],[f15325,f15316,f2324,f15347]) ).

fof(f15347,plain,
    ( spl0_810
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).

fof(f15316,plain,
    ( spl0_804
  <=> 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_804])]) ).

fof(f15325,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_237
    | spl0_804 ),
    inference(forward_demodulation,[],[f15317,f2326]) ).

fof(f15317,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | spl0_804 ),
    inference(avatar_component_clause,[],[f15316]) ).

fof(f15345,plain,
    ( spl0_808
    | ~ spl0_809
    | ~ spl0_39
    | ~ spl0_684 ),
    inference(avatar_split_clause,[],[f10908,f10885,f377,f15342,f15338]) ).

fof(f15338,plain,
    ( spl0_808
  <=> element_relation = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).

fof(f15342,plain,
    ( spl0_809
  <=> subclass(element_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).

fof(f10908,plain,
    ( ~ subclass(element_relation,successor_relation)
    | element_relation = successor_relation
    | ~ spl0_39
    | ~ spl0_684 ),
    inference(resolution,[],[f10887,f378]) ).

fof(f15336,plain,
    ( ~ spl0_807
    | ~ spl0_237
    | spl0_805 ),
    inference(avatar_split_clause,[],[f15324,f15320,f2324,f15333]) ).

fof(f15333,plain,
    ( spl0_807
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).

fof(f15320,plain,
    ( spl0_805
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(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_805])]) ).

fof(f15324,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(singleton_relation))),complement(compose(element_relation,complement(singleton_relation)))),universal_class)),universal_class))))))),element_relation)
    | ~ spl0_237
    | spl0_805 ),
    inference(forward_demodulation,[],[f15322,f2326]) ).

fof(f15322,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
    | spl0_805 ),
    inference(avatar_component_clause,[],[f15320]) ).

fof(f15331,plain,
    ( ~ spl0_806
    | ~ spl0_237
    | spl0_803 ),
    inference(avatar_split_clause,[],[f15326,f15312,f2324,f15328]) ).

fof(f15328,plain,
    ( spl0_806
  <=> member(complement(compose(element_relation,complement(singleton_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).

fof(f15312,plain,
    ( spl0_803
  <=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f15326,plain,
    ( ~ member(complement(compose(element_relation,complement(singleton_relation))),universal_class)
    | ~ spl0_237
    | spl0_803 ),
    inference(forward_demodulation,[],[f15314,f2326]) ).

fof(f15314,plain,
    ( ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | spl0_803 ),
    inference(avatar_component_clause,[],[f15312]) ).

fof(f15323,plain,
    ( spl0_527
    | ~ spl0_803
    | spl0_804
    | ~ spl0_805
    | ~ spl0_83
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1202,f1170,f652,f15320,f15316,f15312,f7385]) ).

fof(f7385,plain,
    ( spl0_527
  <=> null_class = complement(compose(element_relation,complement(identity_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f1202,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
    | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
    | ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
    | null_class = complement(compose(element_relation,complement(identity_relation)))
    | ~ spl0_83
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f653]) ).

fof(f15301,plain,
    ( spl0_802
    | ~ spl0_38
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1946,f1942,f373,f15299]) ).

fof(f15299,plain,
    ( spl0_802
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).

fof(f1946,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
        | ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
    | ~ spl0_38
    | ~ spl0_210 ),
    inference(resolution,[],[f1943,f374]) ).

fof(f15121,plain,
    ( spl0_801
    | ~ spl0_157
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1792,f1780,f1293,f15119]) ).

fof(f15119,plain,
    ( spl0_801
  <=> ! [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_801])]) ).

fof(f1293,plain,
    ( spl0_157
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f1780,plain,
    ( spl0_201
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f1792,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_157
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1294]) ).

fof(f1294,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_157 ),
    inference(avatar_component_clause,[],[f1293]) ).

fof(f1781,plain,
    ( ! [X2,X0,X1] :
        ( subclass(cross_product(X0,X1),X2)
        | not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))))) )
    | ~ spl0_201 ),
    inference(avatar_component_clause,[],[f1780]) ).

fof(f15117,plain,
    ( spl0_800
    | ~ spl0_156
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1791,f1780,f1289,f15115]) ).

fof(f15115,plain,
    ( spl0_800
  <=> ! [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_800])]) ).

fof(f1289,plain,
    ( spl0_156
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f1791,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_156
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1290]) ).

fof(f1290,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_156 ),
    inference(avatar_component_clause,[],[f1289]) ).

fof(f14857,plain,
    ( spl0_799
    | ~ spl0_793
    | ~ spl0_798 ),
    inference(avatar_split_clause,[],[f14853,f14850,f14711,f14855]) ).

fof(f14855,plain,
    ( spl0_799
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).

fof(f14711,plain,
    ( spl0_793
  <=> null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).

fof(f14850,plain,
    ( spl0_798
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).

fof(f14853,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(null_class,X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_793
    | ~ spl0_798 ),
    inference(forward_demodulation,[],[f14851,f14713]) ).

fof(f14713,plain,
    ( null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
    | ~ spl0_793 ),
    inference(avatar_component_clause,[],[f14711]) ).

fof(f14851,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_798 ),
    inference(avatar_component_clause,[],[f14850]) ).

fof(f14852,plain,
    ( spl0_798
    | ~ spl0_88
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1916,f1913,f680,f14850]) ).

fof(f1916,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_88
    | ~ spl0_207 ),
    inference(resolution,[],[f1914,f681]) ).

fof(f14848,plain,
    ( spl0_797
    | ~ spl0_143
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1703,f1667,f1166,f14846]) ).

fof(f14846,plain,
    ( spl0_797
  <=> ! [X0,X1] :
        ( null_class = intersection(regular(X0),X1)
        | ~ member(intersection(regular(X0),X1),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).

fof(f1703,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(regular(X0),X1)
        | ~ member(intersection(regular(X0),X1),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
        | null_class = X0 )
    | ~ spl0_143
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f1167]) ).

fof(f14844,plain,
    ( spl0_796
    | ~ spl0_143
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1682,f1663,f1166,f14842]) ).

fof(f14842,plain,
    ( spl0_796
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,regular(X1))
        | ~ member(intersection(X0,regular(X1)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).

fof(f1682,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,regular(X1))
        | ~ member(intersection(X0,regular(X1)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_143
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f1167]) ).

fof(f14811,plain,
    ( spl0_795
    | ~ spl0_400
    | ~ spl0_682 ),
    inference(avatar_split_clause,[],[f14497,f10626,f4303,f14808]) ).

fof(f14808,plain,
    ( spl0_795
  <=> null_class = intersection(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).

fof(f14497,plain,
    ( null_class = intersection(null_class,universal_class)
    | ~ spl0_400
    | ~ spl0_682 ),
    inference(superposition,[],[f10627,f4305]) ).

fof(f14717,plain,
    ( spl0_793
    | spl0_794
    | ~ spl0_40
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1949,f1942,f381,f14715,f14711]) ).

fof(f14715,plain,
    ( spl0_794
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).

fof(f1949,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(X1,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_210 ),
    inference(superposition,[],[f1943,f382]) ).

fof(f14709,plain,
    ( spl0_792
    | ~ spl0_40
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1846,f1815,f381,f14707]) ).

fof(f14707,plain,
    ( spl0_792
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).

fof(f1846,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_204 ),
    inference(superposition,[],[f1816,f382]) ).

fof(f14702,plain,
    ( spl0_790
    | ~ spl0_791
    | ~ spl0_40
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1812,f1800,f381,f14699,f14696]) ).

fof(f14696,plain,
    ( spl0_790
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).

fof(f14699,plain,
    ( spl0_791
  <=> inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).

fof(f1800,plain,
    ( spl0_202
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f1812,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f382]) ).

fof(f1801,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2)) )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f1800]) ).

fof(f14694,plain,
    ( spl0_789
    | ~ spl0_159
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1515,f1463,f1301,f14692]) ).

fof(f14692,plain,
    ( spl0_789
  <=> ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f1515,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) )
    | ~ spl0_159
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f1302]) ).

fof(f14646,plain,
    ( spl0_788
    | ~ spl0_49
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1653,f1646,f449,f14644]) ).

fof(f14644,plain,
    ( spl0_788
  <=> ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(complement(intersection(X0,X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f1653,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(complement(intersection(X0,X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) )
    | ~ spl0_49
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f450]) ).

fof(f14496,plain,
    ( spl0_787
    | ~ spl0_186
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1635,f1627,f1563,f14494]) ).

fof(f14494,plain,
    ( spl0_787
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f1635,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) )
    | ~ spl0_186
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f1564]) ).

fof(f14418,plain,
    ( spl0_786
    | ~ spl0_131
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1866,f1819,f1019,f14416]) ).

fof(f14416,plain,
    ( spl0_786
  <=> ! [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_786])]) ).

fof(f1866,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
        | subclass(X1,X2) )
    | ~ spl0_131
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f1020]) ).

fof(f14414,plain,
    ( spl0_785
    | ~ spl0_131
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1840,f1815,f1019,f14412]) ).

fof(f14412,plain,
    ( spl0_785
  <=> ! [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_785])]) ).

fof(f1840,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X1,X2) )
    | ~ spl0_131
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f1020]) ).

fof(f14410,plain,
    ( spl0_784
    | ~ spl0_115
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1796,f1780,f899,f14408]) ).

fof(f14408,plain,
    ( spl0_784
  <=> ! [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_784])]) ).

fof(f1796,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
        | function(cross_product(X0,X1))
        | ~ single_valued_class(cross_product(X0,X1)) )
    | ~ spl0_115
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f900]) ).

fof(f14406,plain,
    ( spl0_783
    | ~ spl0_94
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1075,f1019,f708,f14404]) ).

fof(f14404,plain,
    ( spl0_783
  <=> ! [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_783])]) ).

fof(f1075,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | subclass(X0,X4)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f709]) ).

fof(f14164,plain,
    ( spl0_782
    | ~ spl0_147
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1786,f1780,f1228,f14162]) ).

fof(f14162,plain,
    ( spl0_782
  <=> ! [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_782])]) ).

fof(f1228,plain,
    ( spl0_147
  <=> ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f1786,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_147
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1229]) ).

fof(f1229,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_147 ),
    inference(avatar_component_clause,[],[f1228]) ).

fof(f14160,plain,
    ( spl0_781
    | ~ spl0_159
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1439,f1376,f1301,f14158]) ).

fof(f14158,plain,
    ( spl0_781
  <=> ! [X0] :
        ( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).

fof(f1439,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
        | ~ member(X0,universal_class)
        | null_class = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) )
    | ~ spl0_159
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f1302]) ).

fof(f14156,plain,
    ( spl0_780
    | ~ spl0_79
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1139,f1094,f630,f14154]) ).

fof(f14154,plain,
    ( spl0_780
  <=> ! [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_780])]) ).

fof(f1139,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,cross_product(X1,X2)),X3)
        | not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) )
    | ~ spl0_79
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f631]) ).

fof(f14152,plain,
    ( spl0_779
    | ~ spl0_79
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1121,f1090,f630,f14150]) ).

fof(f14150,plain,
    ( spl0_779
  <=> ! [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_779])]) ).

fof(f1121,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(cross_product(X0,X1),X2),X3)
        | not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) )
    | ~ spl0_79
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f631]) ).

fof(f14089,plain,
    ( spl0_778
    | ~ spl0_38
    | ~ spl0_207 ),
    inference(avatar_split_clause,[],[f1917,f1913,f373,f14087]) ).

fof(f14087,plain,
    ( spl0_778
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f1917,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X2,X2),universal_class)
        | ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
    | ~ spl0_38
    | ~ spl0_207 ),
    inference(resolution,[],[f1914,f374]) ).

fof(f13787,plain,
    ( spl0_777
    | ~ spl0_109
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1865,f1819,f818,f13785]) ).

fof(f13785,plain,
    ( spl0_777
  <=> ! [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_777])]) ).

fof(f1865,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) )
    | ~ spl0_109
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f819]) ).

fof(f13783,plain,
    ( spl0_776
    | ~ spl0_70
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1848,f1819,f569,f13781]) ).

fof(f13781,plain,
    ( spl0_776
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f1848,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
    | ~ spl0_70
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f570]) ).

fof(f13779,plain,
    ( spl0_775
    | ~ spl0_109
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1839,f1815,f818,f13777]) ).

fof(f13777,plain,
    ( spl0_775
  <=> ! [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_775])]) ).

fof(f1839,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
    | ~ spl0_109
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f819]) ).

fof(f13775,plain,
    ( spl0_774
    | ~ spl0_70
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1822,f1815,f569,f13773]) ).

fof(f13773,plain,
    ( spl0_774
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f1822,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_70
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f570]) ).

fof(f13760,plain,
    ( spl0_773
    | ~ spl0_185
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1793,f1780,f1556,f13758]) ).

fof(f13758,plain,
    ( spl0_773
  <=> ! [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_773])]) ).

fof(f1556,plain,
    ( spl0_185
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f1793,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ member(X3,X0)
        | ~ member(X4,X1)
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) )
    | ~ spl0_185
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1557]) ).

fof(f1557,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(cross_product(X3,X1),X4)
        | ~ member(X2,X3)
        | ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f1556]) ).

fof(f13756,plain,
    ( spl0_772
    | ~ spl0_159
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1497,f1459,f1301,f13754]) ).

fof(f13754,plain,
    ( spl0_772
  <=> ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
        | ~ member(X1,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).

fof(f1497,plain,
    ( ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
        | ~ member(X1,universal_class)
        | null_class = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) )
    | ~ spl0_159
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f1302]) ).

fof(f13752,plain,
    ( spl0_771
    | ~ spl0_94
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f858,f818,f708,f13750]) ).

fof(f13750,plain,
    ( spl0_771
  <=> ! [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_771])]) ).

fof(f858,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f709]) ).

fof(f13664,plain,
    ( spl0_770
    | ~ spl0_117
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1863,f1819,f926,f13662]) ).

fof(f13662,plain,
    ( spl0_770
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f1863,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
        | null_class = X1 )
    | ~ spl0_117
    | ~ spl0_205 ),
    inference(resolution,[],[f1820,f927]) ).

fof(f13660,plain,
    ( spl0_769
    | ~ spl0_117
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1837,f1815,f926,f13658]) ).

fof(f13658,plain,
    ( spl0_769
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f1837,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
        | ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | null_class = X1 )
    | ~ spl0_117
    | ~ spl0_204 ),
    inference(resolution,[],[f1816,f927]) ).

fof(f13645,plain,
    ( spl0_768
    | ~ spl0_44
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1655,f1646,f425,f13643]) ).

fof(f13643,plain,
    ( spl0_768
  <=> ! [X0] :
        ( null_class = complement(complement(X0))
        | ~ member(complement(complement(X0)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).

fof(f1655,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | ~ member(complement(complement(X0)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) )
    | ~ spl0_44
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f426]) ).

fof(f13641,plain,
    ( spl0_767
    | ~ spl0_164
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1624,f1621,f1368,f13639]) ).

fof(f13639,plain,
    ( spl0_767
  <=> ! [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_767])]) ).

fof(f1368,plain,
    ( spl0_164
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f1621,plain,
    ( spl0_193
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f1624,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
        | not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 )
    | ~ spl0_164
    | ~ spl0_193 ),
    inference(resolution,[],[f1622,f1369]) ).

fof(f1369,plain,
    ( ! [X2,X0,X1] :
        ( subclass(unordered_pair(X0,X1),X2)
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0 )
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f1368]) ).

fof(f1622,plain,
    ( ! [X0] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | ~ inductive(X0)
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f1621]) ).

fof(f13637,plain,
    ( spl0_766
    | ~ spl0_94
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f991,f926,f708,f13635]) ).

fof(f13635,plain,
    ( spl0_766
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).

fof(f991,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
        | null_class = X0
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f709]) ).

fof(f13502,plain,
    ( spl0_765
    | ~ spl0_109
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2038,f2005,f818,f13500]) ).

fof(f13500,plain,
    ( spl0_765
  <=> ! [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_765])]) ).

fof(f2038,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_109
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f819]) ).

fof(f13498,plain,
    ( spl0_764
    | ~ spl0_109
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2010,f2001,f818,f13496]) ).

fof(f13496,plain,
    ( spl0_764
  <=> ! [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_764])]) ).

fof(f2010,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,X3) )
    | ~ spl0_109
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f819]) ).

fof(f13480,plain,
    ( spl0_763
    | ~ spl0_112
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1934,f1930,f830,f13478]) ).

fof(f13478,plain,
    ( spl0_763
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f1934,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_209 ),
    inference(resolution,[],[f1931,f831]) ).

fof(f13476,plain,
    ( spl0_762
    | ~ spl0_40
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1870,f1819,f381,f13474]) ).

fof(f13474,plain,
    ( spl0_762
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f1870,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_205 ),
    inference(superposition,[],[f1820,f382]) ).

fof(f13472,plain,
    ( spl0_761
    | ~ spl0_163
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1399,f1372,f1358,f13470]) ).

fof(f13470,plain,
    ( spl0_761
  <=> ! [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_761])]) ).

fof(f1399,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
        | subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
    | ~ spl0_163
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f1359]) ).

fof(f13441,plain,
    ( spl0_760
    | ~ spl0_38
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1895,f1875,f373,f13439]) ).

fof(f13439,plain,
    ( spl0_760
  <=> ! [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_760])]) ).

fof(f1895,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,X0)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ subclass(X0,X3)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) )
    | ~ spl0_38
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f374]) ).

fof(f13437,plain,
    ( spl0_759
    | ~ spl0_40
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1809,f1800,f381,f13435]) ).

fof(f13435,plain,
    ( spl0_759
  <=> ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).

fof(f1809,plain,
    ( ! [X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X1),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f382]) ).

fof(f13370,plain,
    ( spl0_758
    | spl0_629
    | ~ spl0_79
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1268,f1254,f630,f9626,f13368]) ).

fof(f13368,plain,
    ( spl0_758
  <=> ! [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_758])]) ).

fof(f1268,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) )
    | ~ spl0_79
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f631]) ).

fof(f13346,plain,
    ( spl0_757
    | ~ spl0_236
    | ~ spl0_237
    | ~ spl0_641 ),
    inference(avatar_split_clause,[],[f13045,f9800,f2324,f2318,f13343]) ).

fof(f13045,plain,
    ( member(regular(singleton_relation),universal_class)
    | ~ spl0_236
    | ~ spl0_237
    | ~ spl0_641 ),
    inference(forward_demodulation,[],[f12986,f2326]) ).

fof(f12986,plain,
    ( member(regular(identity_relation),universal_class)
    | ~ spl0_236
    | ~ spl0_641 ),
    inference(resolution,[],[f9801,f2320]) ).

fof(f13053,plain,
    ( spl0_756
    | ~ spl0_31
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1899,f1875,f336,f13051]) ).

fof(f13051,plain,
    ( spl0_756
  <=> ! [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_756])]) ).

fof(f336,plain,
    ( spl0_31
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f1899,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) )
    | ~ spl0_31
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f337]) ).

fof(f337,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f336]) ).

fof(f13049,plain,
    ( spl0_755
    | ~ spl0_32
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1898,f1875,f340,f13047]) ).

fof(f13047,plain,
    ( spl0_755
  <=> ! [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_755])]) ).

fof(f1898,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,intersection(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) )
    | ~ spl0_32
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f341]) ).

fof(f12974,plain,
    ( spl0_754
    | ~ spl0_88
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1888,f1875,f680,f12972]) ).

fof(f12972,plain,
    ( spl0_754
  <=> ! [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_754])]) ).

fof(f1888,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,compose(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
    | ~ spl0_88
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f681]) ).

fof(f12970,plain,
    ( spl0_753
    | ~ spl0_84
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1757,f1752,f662,f12968]) ).

fof(f12968,plain,
    ( spl0_753
  <=> ! [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_753])]) ).

fof(f1757,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_84
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f663]) ).

fof(f12966,plain,
    ( spl0_752
    | ~ spl0_164
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1750,f1718,f1368,f12964]) ).

fof(f12964,plain,
    ( spl0_752
  <=> ! [X2,X0,X1] :
        ( subclass(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f1750,plain,
    ( ! [X2,X0,X1] :
        ( subclass(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_164
    | ~ spl0_199 ),
    inference(superposition,[],[f1369,f1719]) ).

fof(f12962,plain,
    ( spl0_751
    | ~ spl0_90
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1732,f1718,f689,f12960]) ).

fof(f12960,plain,
    ( spl0_751
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f689,plain,
    ( spl0_90
  <=> ! [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_90])]) ).

fof(f1732,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_90
    | ~ spl0_199 ),
    inference(superposition,[],[f690,f1719]) ).

fof(f690,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_90 ),
    inference(avatar_component_clause,[],[f689]) ).

fof(f12958,plain,
    ( spl0_750
    | ~ spl0_83
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1188,f1166,f652,f12956]) ).

fof(f12956,plain,
    ( spl0_750
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
        | null_class = X0
        | ~ member(regular(X0),universal_class)
        | null_class = regular(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f1188,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
        | null_class = X0
        | ~ member(regular(X0),universal_class)
        | null_class = regular(X0) )
    | ~ spl0_83
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f653]) ).

fof(f12954,plain,
    ( spl0_749
    | ~ spl0_79
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1052,f1015,f630,f12952]) ).

fof(f12952,plain,
    ( spl0_749
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f1052,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,cross_product(X1,X2))
        | regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) )
    | ~ spl0_79
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f631]) ).

fof(f12950,plain,
    ( spl0_748
    | ~ spl0_79
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1036,f1011,f630,f12948]) ).

fof(f12948,plain,
    ( spl0_748
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f1036,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(cross_product(X0,X1),X2)
        | regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) )
    | ~ spl0_79
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f631]) ).

fof(f12588,plain,
    ( spl0_747
    | ~ spl0_9
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f2039,f2005,f241,f12586]) ).

fof(f12586,plain,
    ( spl0_747
  <=> ! [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_747])]) ).

fof(f2039,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_9
    | ~ spl0_213 ),
    inference(resolution,[],[f2006,f242]) ).

fof(f12584,plain,
    ( spl0_746
    | ~ spl0_9
    | ~ spl0_212 ),
    inference(avatar_split_clause,[],[f2011,f2001,f241,f12582]) ).

fof(f12582,plain,
    ( spl0_746
  <=> ! [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_746])]) ).

fof(f2011,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_9
    | ~ spl0_212 ),
    inference(resolution,[],[f2002,f242]) ).

fof(f12580,plain,
    ( spl0_745
    | ~ spl0_20
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1901,f1875,f288,f12578]) ).

fof(f12578,plain,
    ( spl0_745
  <=> ! [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_745])]) ).

fof(f1901,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,complement(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) )
    | ~ spl0_20
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f289]) ).

fof(f12576,plain,
    ( spl0_744
    | spl0_151
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1790,f1780,f1245,f12573]) ).

fof(f1245,plain,
    ( spl0_151
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f1790,plain,
    ( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)))))
    | spl0_151
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1247]) ).

fof(f1247,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | spl0_151 ),
    inference(avatar_component_clause,[],[f1245]) ).

fof(f12570,plain,
    ( spl0_743
    | ~ spl0_25
    | ~ spl0_148 ),
    inference(avatar_split_clause,[],[f12514,f1232,f309,f12567]) ).

fof(f12567,plain,
    ( spl0_743
  <=> subclass(application_function,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).

fof(f309,plain,
    ( spl0_25
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1232,plain,
    ( spl0_148
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f12514,plain,
    ( subclass(application_function,composition_function)
    | ~ spl0_25
    | ~ spl0_148 ),
    inference(superposition,[],[f311,f1234]) ).

fof(f1234,plain,
    ( composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_148 ),
    inference(avatar_component_clause,[],[f1232]) ).

fof(f311,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f309]) ).

fof(f12512,plain,
    ( spl0_742
    | spl0_149
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1789,f1780,f1236,f12509]) ).

fof(f1236,plain,
    ( spl0_149
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1789,plain,
    ( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)))))
    | spl0_149
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1238]) ).

fof(f1238,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | spl0_149 ),
    inference(avatar_component_clause,[],[f1236]) ).

fof(f12507,plain,
    ( spl0_741
    | ~ spl0_140
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1787,f1780,f1111,f12505]) ).

fof(f12505,plain,
    ( spl0_741
  <=> ! [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_741])]) ).

fof(f1111,plain,
    ( spl0_140
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f1787,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_140
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1112]) ).

fof(f1112,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_140 ),
    inference(avatar_component_clause,[],[f1111]) ).

fof(f12163,plain,
    ( spl0_740
    | ~ spl0_237
    | ~ spl0_732 ),
    inference(avatar_split_clause,[],[f12129,f12126,f2324,f12161]) ).

fof(f12161,plain,
    ( spl0_740
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
        | null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).

fof(f12126,plain,
    ( spl0_732
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f12129,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
        | null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_732 ),
    inference(forward_demodulation,[],[f12127,f2326]) ).

fof(f12127,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_732 ),
    inference(avatar_component_clause,[],[f12126]) ).

fof(f12159,plain,
    ( spl0_739
    | ~ spl0_237
    | ~ spl0_731 ),
    inference(avatar_split_clause,[],[f12124,f12121,f2324,f12157]) ).

fof(f12157,plain,
    ( spl0_739
  <=> ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).

fof(f12121,plain,
    ( spl0_731
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f12124,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | null_class = X0
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_731 ),
    inference(forward_demodulation,[],[f12122,f2326]) ).

fof(f12122,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_731 ),
    inference(avatar_component_clause,[],[f12121]) ).

fof(f12155,plain,
    ( spl0_738
    | ~ spl0_9
    | ~ spl0_208 ),
    inference(avatar_split_clause,[],[f1923,f1920,f241,f12153]) ).

fof(f12153,plain,
    ( spl0_738
  <=> ! [X0,X1] :
        ( unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).

fof(f1920,plain,
    ( spl0_208
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f1923,plain,
    ( ! [X0,X1] :
        ( unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_9
    | ~ spl0_208 ),
    inference(resolution,[],[f1921,f242]) ).

fof(f1921,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_208 ),
    inference(avatar_component_clause,[],[f1920]) ).

fof(f12151,plain,
    ( ~ spl0_737
    | ~ spl0_237
    | spl0_736 ),
    inference(avatar_split_clause,[],[f12146,f12142,f2324,f12148]) ).

fof(f12148,plain,
    ( spl0_737
  <=> subclass(composition_function,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).

fof(f12142,plain,
    ( spl0_736
  <=> subclass(composition_function,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).

fof(f12146,plain,
    ( ~ subclass(composition_function,singleton_relation)
    | ~ spl0_237
    | spl0_736 ),
    inference(forward_demodulation,[],[f12144,f2326]) ).

fof(f12144,plain,
    ( ~ subclass(composition_function,identity_relation)
    | spl0_736 ),
    inference(avatar_component_clause,[],[f12142]) ).

fof(f12145,plain,
    ( spl0_735
    | ~ spl0_736
    | ~ spl0_104
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1909,f1875,f768,f12142,f12139]) ).

fof(f12139,plain,
    ( spl0_735
  <=> ! [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_735])]) ).

fof(f1909,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,identity_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) )
    | ~ spl0_104
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f769]) ).

fof(f12137,plain,
    ( spl0_734
    | ~ spl0_161
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1748,f1718,f1323,f12135]) ).

fof(f12135,plain,
    ( spl0_734
  <=> ! [X0,X1] :
        ( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
        | null_class = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).

fof(f1323,plain,
    ( spl0_161
  <=> ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f1748,plain,
    ( ! [X0,X1] :
        ( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
        | null_class = regular(cross_product(X0,X1))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_161
    | ~ spl0_199 ),
    inference(superposition,[],[f1324,f1719]) ).

fof(f1324,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1323]) ).

fof(f12133,plain,
    ( spl0_733
    | ~ spl0_143
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1643,f1627,f1166,f12131]) ).

fof(f12131,plain,
    ( spl0_733
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f1643,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,regular(X1))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_143
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f1167]) ).

fof(f12128,plain,
    ( spl0_732
    | ~ spl0_145
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1640,f1627,f1174,f12126]) ).

fof(f1640,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation) )
    | ~ spl0_145
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f1175]) ).

fof(f12123,plain,
    ( spl0_731
    | ~ spl0_144
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1637,f1627,f1170,f12121]) ).

fof(f1637,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f1171]) ).

fof(f12085,plain,
    ( spl0_729
    | ~ spl0_730
    | ~ spl0_9
    | ~ spl0_400
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f6820,f6485,f4303,f241,f12082,f12079]) ).

fof(f12082,plain,
    ( spl0_730
  <=> subclass(domain_relation,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).

fof(f6820,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,null_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_9
    | ~ spl0_400
    | ~ spl0_489 ),
    inference(forward_demodulation,[],[f6797,f4305]) ).

fof(f6797,plain,
    ( ! [X0] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,complement(universal_class)) )
    | ~ spl0_9
    | ~ spl0_489 ),
    inference(resolution,[],[f6486,f242]) ).

fof(f12073,plain,
    ( spl0_728
    | ~ spl0_39
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1795,f1780,f377,f12071]) ).

fof(f12071,plain,
    ( spl0_728
  <=> ! [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_728])]) ).

fof(f1795,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | ~ subclass(X2,cross_product(X0,X1))
        | cross_product(X0,X1) = X2 )
    | ~ spl0_39
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f378]) ).

fof(f12069,plain,
    ( spl0_727
    | ~ spl0_88
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1761,f1752,f680,f12067]) ).

fof(f12067,plain,
    ( spl0_727
  <=> ! [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_727])]) ).

fof(f1761,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_88
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f681]) ).

fof(f12065,plain,
    ( spl0_726
    | ~ spl0_95
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f888,f830,f724,f12063]) ).

fof(f12063,plain,
    ( spl0_726
  <=> ! [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_726])]) ).

fof(f724,plain,
    ( spl0_95
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f888,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_95
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f725]) ).

fof(f725,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f724]) ).

fof(f11977,plain,
    ( spl0_725
    | ~ spl0_50
    | ~ spl0_204 ),
    inference(avatar_split_clause,[],[f1845,f1815,f453,f11975]) ).

fof(f11975,plain,
    ( spl0_725
  <=> ! [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_725])]) ).

fof(f1845,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_204 ),
    inference(superposition,[],[f1816,f454]) ).

fof(f11973,plain,
    ( spl0_724
    | ~ spl0_133
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1747,f1718,f1027,f11971]) ).

fof(f11971,plain,
    ( spl0_724
  <=> ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f1027,plain,
    ( spl0_133
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1747,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_133
    | ~ spl0_199 ),
    inference(superposition,[],[f1028,f1719]) ).

fof(f1028,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1027]) ).

fof(f11969,plain,
    ( spl0_723
    | ~ spl0_48
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1631,f1627,f445,f11967]) ).

fof(f11967,plain,
    ( spl0_723
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f1631,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,unordered_pair(X1,X2))
        | ~ member(X0,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 )
    | ~ spl0_48
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f446]) ).

fof(f11940,plain,
    ( spl0_722
    | ~ spl0_50
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1811,f1800,f453,f11938]) ).

fof(f11938,plain,
    ( spl0_722
  <=> ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).

fof(f1811,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_50
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f454]) ).

fof(f11936,plain,
    ( spl0_721
    | ~ spl0_50
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1808,f1800,f453,f11934]) ).

fof(f11934,plain,
    ( spl0_721
  <=> ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).

fof(f1808,plain,
    ( ! [X2,X0,X1] :
        ( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X2,X1)) )
    | ~ spl0_50
    | ~ spl0_202 ),
    inference(superposition,[],[f1801,f454]) ).

fof(f11932,plain,
    ( spl0_720
    | ~ spl0_88
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1731,f1718,f680,f11930]) ).

fof(f11930,plain,
    ( spl0_720
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
        | member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).

fof(f1731,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
        | member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_88
    | ~ spl0_199 ),
    inference(superposition,[],[f681,f1719]) ).

fof(f11904,plain,
    ( spl0_719
    | ~ spl0_77
    | ~ spl0_209 ),
    inference(avatar_split_clause,[],[f1940,f1930,f615,f11902]) ).

fof(f11902,plain,
    ( spl0_719
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f1940,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_209 ),
    inference(duplicate_literal_removal,[],[f1933]) ).

fof(f1933,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_209 ),
    inference(resolution,[],[f1931,f616]) ).

fof(f11900,plain,
    ( spl0_718
    | ~ spl0_139
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1783,f1780,f1107,f11898]) ).

fof(f11898,plain,
    ( spl0_718
  <=> ! [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_718])]) ).

fof(f1107,plain,
    ( spl0_139
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f1783,plain,
    ( ! [X0] :
        ( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_139
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f1108]) ).

fof(f1108,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1107]) ).

fof(f11896,plain,
    ( ~ spl0_716
    | spl0_717
    | ~ spl0_109
    | ~ spl0_365 ),
    inference(avatar_split_clause,[],[f3874,f3792,f818,f11894,f11890]) ).

fof(f11890,plain,
    ( spl0_716
  <=> subclass(universal_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).

fof(f3874,plain,
    ( ! [X0] :
        ( member(X0,universal_class)
        | ~ subclass(universal_class,subset_relation) )
    | ~ spl0_109
    | ~ spl0_365 ),
    inference(resolution,[],[f3793,f819]) ).

fof(f11878,plain,
    ( spl0_715
    | ~ spl0_30
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1742,f1718,f332,f11876]) ).

fof(f11876,plain,
    ( spl0_715
  <=> ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).

fof(f1742,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_30
    | ~ spl0_199 ),
    inference(superposition,[],[f333,f1719]) ).

fof(f11874,plain,
    ( ~ spl0_713
    | spl0_714
    | ~ spl0_166
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1575,f1563,f1376,f11872,f11868]) ).

fof(f11868,plain,
    ( spl0_713
  <=> 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_713])]) ).

fof(f11872,plain,
    ( spl0_714
  <=> ! [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_714])]) ).

fof(f1575,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class))
        | ~ subclass(domain_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,universal_class) )
    | ~ spl0_166
    | ~ spl0_186 ),
    inference(resolution,[],[f1564,f1377]) ).

fof(f11863,plain,
    ( spl0_712
    | ~ spl0_38
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1764,f1752,f373,f11861]) ).

fof(f11861,plain,
    ( spl0_712
  <=> ! [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_712])]) ).

fof(f1764,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),X3)
        | ~ operation(X2)
        | ~ subclass(X3,X4)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
    | ~ spl0_38
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f374]) ).

fof(f11857,plain,
    ( ~ spl0_711
    | ~ spl0_237
    | spl0_709 ),
    inference(avatar_split_clause,[],[f11852,f11844,f2324,f11854]) ).

fof(f11854,plain,
    ( spl0_711
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).

fof(f11844,plain,
    ( spl0_709
  <=> 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_709])]) ).

fof(f11852,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_237
    | spl0_709 ),
    inference(forward_demodulation,[],[f11846,f2326]) ).

fof(f11846,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
    | spl0_709 ),
    inference(avatar_component_clause,[],[f11844]) ).

fof(f11851,plain,
    ( ~ spl0_709
    | ~ spl0_710
    | spl0_431
    | ~ spl0_126
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1658,f1646,f966,f5542,f11848,f11844]) ).

fof(f11848,plain,
    ( spl0_710
  <=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).

fof(f5542,plain,
    ( spl0_431
  <=> null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f1658,plain,
    ( null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
    | ~ spl0_126
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f967]) ).

fof(f11842,plain,
    ( spl0_708
    | ~ spl0_4
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f3781,f3651,f220,f11840]) ).

fof(f11840,plain,
    ( spl0_708
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).

fof(f3651,plain,
    ( spl0_362
  <=> ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f3781,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_362 ),
    inference(resolution,[],[f3652,f221]) ).

fof(f3652,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f3651]) ).

fof(f11836,plain,
    ( ~ spl0_707
    | ~ spl0_237
    | spl0_704 ),
    inference(avatar_split_clause,[],[f11826,f11817,f2324,f11833]) ).

fof(f11833,plain,
    ( spl0_707
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).

fof(f11817,plain,
    ( spl0_704
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(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_704])]) ).

fof(f11826,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(singleton_relation)))),complement(complement(compose(element_relation,complement(singleton_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_237
    | spl0_704 ),
    inference(forward_demodulation,[],[f11819,f2326]) ).

fof(f11819,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | spl0_704 ),
    inference(avatar_component_clause,[],[f11817]) ).

fof(f11831,plain,
    ( ~ spl0_706
    | ~ spl0_237
    | spl0_705 ),
    inference(avatar_split_clause,[],[f11825,f11821,f2324,f11828]) ).

fof(f11828,plain,
    ( spl0_706
  <=> member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).

fof(f11821,plain,
    ( spl0_705
  <=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).

fof(f11825,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(singleton_relation)))),universal_class)
    | ~ spl0_237
    | spl0_705 ),
    inference(forward_demodulation,[],[f11823,f2326]) ).

fof(f11823,plain,
    ( ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | spl0_705 ),
    inference(avatar_component_clause,[],[f11821]) ).

fof(f11824,plain,
    ( ~ spl0_704
    | ~ spl0_705
    | spl0_427
    | ~ spl0_125
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1656,f1646,f962,f5520,f11821,f11817]) ).

fof(f5520,plain,
    ( spl0_427
  <=> null_class = complement(complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f1656,plain,
    ( null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
    | ~ spl0_125
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f963]) ).

fof(f11790,plain,
    ( spl0_703
    | ~ spl0_31
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1768,f1752,f336,f11788]) ).

fof(f11788,plain,
    ( spl0_703
  <=> ! [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_703])]) ).

fof(f1768,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
    | ~ spl0_31
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f337]) ).

fof(f11786,plain,
    ( spl0_702
    | ~ spl0_32
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1767,f1752,f340,f11784]) ).

fof(f11784,plain,
    ( spl0_702
  <=> ! [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_702])]) ).

fof(f1767,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),intersection(X3,X4))
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
    | ~ spl0_32
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f341]) ).

fof(f11748,plain,
    ( spl0_701
    | ~ spl0_237
    | ~ spl0_295
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f3716,f3551,f2840,f2324,f11745]) ).

fof(f11745,plain,
    ( spl0_701
  <=> null_class = intersection(singleton_relation,complement(subset_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f3716,plain,
    ( null_class = intersection(singleton_relation,complement(subset_relation))
    | ~ spl0_237
    | ~ spl0_295
    | ~ spl0_356 ),
    inference(forward_demodulation,[],[f3706,f2326]) ).

fof(f3706,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_295
    | ~ spl0_356 ),
    inference(duplicate_literal_removal,[],[f3702]) ).

fof(f3702,plain,
    ( null_class = intersection(identity_relation,complement(subset_relation))
    | null_class = intersection(identity_relation,complement(subset_relation))
    | ~ spl0_295
    | ~ spl0_356 ),
    inference(resolution,[],[f3552,f2841]) ).

fof(f11686,plain,
    ( spl0_700
    | ~ spl0_20
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1770,f1752,f288,f11684]) ).

fof(f11684,plain,
    ( spl0_700
  <=> ! [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_700])]) ).

fof(f1770,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),complement(X3))
        | ~ operation(X2)
        | ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
    | ~ spl0_20
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f289]) ).

fof(f11682,plain,
    ( spl0_699
    | ~ spl0_48
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1743,f1718,f445,f11680]) ).

fof(f11680,plain,
    ( spl0_699
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).

fof(f1743,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,regular(cross_product(X0,X1)))
        | unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
        | unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
        | cross_product(X0,X1) = null_class )
    | ~ spl0_48
    | ~ spl0_199 ),
    inference(superposition,[],[f446,f1719]) ).

fof(f11664,plain,
    ( spl0_698
    | ~ spl0_237
    | ~ spl0_696 ),
    inference(avatar_split_clause,[],[f11656,f11653,f2324,f11662]) ).

fof(f11662,plain,
    ( spl0_698
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f11653,plain,
    ( spl0_696
  <=> ! [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_696])]) ).

fof(f11656,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),singleton_relation)
        | ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ operation(X2)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_696 ),
    inference(forward_demodulation,[],[f11654,f2326]) ).

fof(f11654,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_696 ),
    inference(avatar_component_clause,[],[f11653]) ).

fof(f11660,plain,
    ( spl0_697
    | ~ spl0_103
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1778,f1752,f764,f11658]) ).

fof(f11658,plain,
    ( spl0_697
  <=> ! [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_697])]) ).

fof(f1778,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_103
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f765]) ).

fof(f11655,plain,
    ( spl0_696
    | ~ spl0_104
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1776,f1752,f768,f11653]) ).

fof(f1776,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_104
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f769]) ).

fof(f11651,plain,
    ( spl0_695
    | ~ spl0_127
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1745,f1718,f970,f11649]) ).

fof(f11649,plain,
    ( spl0_695
  <=> ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f970,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1745,plain,
    ( ! [X0,X1] :
        ( ~ inductive(regular(cross_product(X0,X1)))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
        | null_class = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_127
    | ~ spl0_199 ),
    inference(superposition,[],[f971,f1719]) ).

fof(f971,plain,
    ( ! [X0,X1] :
        ( ~ inductive(unordered_pair(X0,X1))
        | null_class = X1
        | null_class = X0 )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f970]) ).

fof(f11647,plain,
    ( spl0_694
    | ~ spl0_129
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f3711,f3551,f1011,f11645]) ).

fof(f3711,plain,
    ( ! [X0] : null_class = intersection(X0,complement(X0))
    | ~ spl0_129
    | ~ spl0_356 ),
    inference(duplicate_literal_removal,[],[f3689]) ).

fof(f3689,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,complement(X0))
        | null_class = intersection(X0,complement(X0)) )
    | ~ spl0_129
    | ~ spl0_356 ),
    inference(resolution,[],[f3552,f1012]) ).

fof(f11267,plain,
    ( spl0_693
    | ~ spl0_38
    | ~ spl0_198 ),
    inference(avatar_split_clause,[],[f1716,f1712,f373,f11265]) ).

fof(f11265,plain,
    ( spl0_693
  <=> ! [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_693])]) ).

fof(f1716,plain,
    ( ! [X0,X1] :
        ( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(successor_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) )
    | ~ spl0_38
    | ~ spl0_198 ),
    inference(resolution,[],[f1713,f374]) ).

fof(f11263,plain,
    ( spl0_692
    | ~ spl0_31
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1695,f1667,f336,f11261]) ).

fof(f11261,plain,
    ( spl0_692
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).

fof(f1695,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_31
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f337]) ).

fof(f11259,plain,
    ( spl0_691
    | ~ spl0_32
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1694,f1667,f340,f11257]) ).

fof(f11257,plain,
    ( spl0_691
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).

fof(f1694,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | ~ member(intersection(intersection(X0,X1),X2),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_32
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f341]) ).

fof(f11255,plain,
    ( spl0_690
    | ~ spl0_31
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1674,f1663,f336,f11253]) ).

fof(f11253,plain,
    ( spl0_690
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f1674,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_31
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f337]) ).

fof(f11251,plain,
    ( spl0_689
    | ~ spl0_296
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f3708,f3551,f2844,f11248]) ).

fof(f11248,plain,
    ( spl0_689
  <=> null_class = intersection(singleton_relation,complement(element_relation)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f3708,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_296
    | ~ spl0_356 ),
    inference(duplicate_literal_removal,[],[f3693]) ).

fof(f3693,plain,
    ( null_class = intersection(singleton_relation,complement(element_relation))
    | null_class = intersection(singleton_relation,complement(element_relation))
    | ~ spl0_296
    | ~ spl0_356 ),
    inference(resolution,[],[f3552,f2845]) ).

fof(f11246,plain,
    ( spl0_688
    | ~ spl0_32
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1673,f1663,f340,f11244]) ).

fof(f11244,plain,
    ( spl0_688
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f1673,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | ~ member(intersection(X0,intersection(X1,X2)),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) )
    | ~ spl0_32
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f341]) ).

fof(f11242,plain,
    ( spl0_687
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1415,f1372,f569,f453,f11240]) ).

fof(f11240,plain,
    ( spl0_687
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).

fof(f1415,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_165 ),
    inference(forward_demodulation,[],[f1402,f454]) ).

fof(f1402,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
        | subclass(X0,intersection(X1,domain_of(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class),X2) )
    | ~ spl0_70
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f570]) ).

fof(f11016,plain,
    ( spl0_686
    | spl0_123
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1788,f1780,f953,f11013]) ).

fof(f953,plain,
    ( spl0_123
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1788,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)))))
    | spl0_123
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f955]) ).

fof(f955,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | spl0_123 ),
    inference(avatar_component_clause,[],[f953]) ).

fof(f11011,plain,
    ( spl0_685
    | spl0_121
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1785,f1780,f944,f11008]) ).

fof(f944,plain,
    ( spl0_121
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f1785,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)))))
    | spl0_121
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f946]) ).

fof(f946,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | spl0_121 ),
    inference(avatar_component_clause,[],[f944]) ).

fof(f10889,plain,
    ( spl0_291
    | ~ spl0_14
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f10721,f930,f263,f2764]) ).

fof(f2764,plain,
    ( spl0_291
  <=> subclass(domain_relation,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f930,plain,
    ( spl0_118
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f10721,plain,
    ( subclass(domain_relation,element_relation)
    | ~ spl0_14
    | ~ spl0_118 ),
    inference(superposition,[],[f265,f932]) ).

fof(f932,plain,
    ( element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f930]) ).

fof(f10888,plain,
    ( spl0_684
    | ~ spl0_11
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f10720,f930,f250,f10885]) ).

fof(f10720,plain,
    ( subclass(successor_relation,element_relation)
    | ~ spl0_11
    | ~ spl0_118 ),
    inference(superposition,[],[f252,f932]) ).

fof(f10718,plain,
    ( spl0_683
    | spl0_119
    | ~ spl0_201 ),
    inference(avatar_split_clause,[],[f1784,f1780,f934,f10715]) ).

fof(f934,plain,
    ( spl0_119
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1784,plain,
    ( not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
    | spl0_119
    | ~ spl0_201 ),
    inference(resolution,[],[f1781,f936]) ).

fof(f936,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | spl0_119 ),
    inference(avatar_component_clause,[],[f934]) ).

fof(f10628,plain,
    ( spl0_682
    | ~ spl0_130
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3682,f3547,f1015,f10626]) ).

fof(f3682,plain,
    ( ! [X0] : null_class = intersection(complement(X0),X0)
    | ~ spl0_130
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3658]) ).

fof(f3658,plain,
    ( ! [X0] :
        ( null_class = intersection(complement(X0),X0)
        | null_class = intersection(complement(X0),X0) )
    | ~ spl0_130
    | ~ spl0_355 ),
    inference(resolution,[],[f3548,f1016]) ).

fof(f10541,plain,
    ( spl0_681
    | ~ spl0_153
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1319,f1301,f1254,f10539]) ).

fof(f10539,plain,
    ( spl0_681
  <=> ! [X0] :
        ( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).

fof(f1319,plain,
    ( ! [X0] :
        ( null_class = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
        | ~ member(X0,universal_class) )
    | ~ spl0_153
    | ~ spl0_159 ),
    inference(resolution,[],[f1302,f1255]) ).

fof(f10537,plain,
    ( spl0_680
    | ~ spl0_97
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f849,f818,f733,f10535]) ).

fof(f849,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,flip(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
    | ~ spl0_97
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f734]) ).

fof(f10533,plain,
    ( spl0_679
    | ~ spl0_96
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f848,f818,f729,f10531]) ).

fof(f848,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,rotate(X0))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
    | ~ spl0_96
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f730]) ).

fof(f10500,plain,
    ( spl0_677
    | ~ spl0_678
    | ~ spl0_78
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1887,f1875,f626,f10497,f10494]) ).

fof(f10494,plain,
    ( spl0_677
  <=> ! [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_677])]) ).

fof(f10497,plain,
    ( spl0_678
  <=> subclass(composition_function,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).

fof(f626,plain,
    ( spl0_78
  <=> ! [X0,X1] :
        ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f1887,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
    | ~ spl0_78
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f627]) ).

fof(f627,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f626]) ).

fof(f10492,plain,
    ( spl0_676
    | ~ spl0_78
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1760,f1752,f626,f10490]) ).

fof(f10490,plain,
    ( spl0_676
  <=> ! [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_676])]) ).

fof(f1760,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),successor_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) )
    | ~ spl0_78
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f627]) ).

fof(f10488,plain,
    ( spl0_675
    | ~ spl0_143
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1517,f1463,f1166,f10486]) ).

fof(f10486,plain,
    ( spl0_675
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f1517,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),null_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
        | null_class = X0 )
    | ~ spl0_143
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f1167]) ).

fof(f10484,plain,
    ( spl0_674
    | ~ spl0_303
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3679,f3547,f2956,f10481]) ).

fof(f10481,plain,
    ( spl0_674
  <=> null_class = intersection(complement(element_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f3679,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_303
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3662]) ).

fof(f3662,plain,
    ( null_class = intersection(complement(element_relation),singleton_relation)
    | null_class = intersection(complement(element_relation),singleton_relation)
    | ~ spl0_303
    | ~ spl0_355 ),
    inference(resolution,[],[f3548,f2957]) ).

fof(f10479,plain,
    ( spl0_673
    | ~ spl0_436
    | ~ spl0_144
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1511,f1463,f1170,f5566,f10477]) ).

fof(f10477,plain,
    ( spl0_673
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f5566,plain,
    ( spl0_436
  <=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f1511,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),element_relation)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f1171]) ).

fof(f10379,plain,
    ( spl0_672
    | ~ spl0_132
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1746,f1718,f1023,f10377]) ).

fof(f10377,plain,
    ( spl0_672
  <=> ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f1023,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1746,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(regular(cross_product(X0,X1)),X2)
        | member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_132
    | ~ spl0_199 ),
    inference(superposition,[],[f1024,f1719]) ).

fof(f1024,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1023]) ).

fof(f10375,plain,
    ( spl0_671
    | ~ spl0_78
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1727,f1718,f626,f10373]) ).

fof(f10373,plain,
    ( spl0_671
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),successor_relation)
        | second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f1727,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),successor_relation)
        | second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_78
    | ~ spl0_199 ),
    inference(superposition,[],[f627,f1719]) ).

fof(f10371,plain,
    ( spl0_670
    | ~ spl0_20
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1697,f1667,f288,f10369]) ).

fof(f10369,plain,
    ( spl0_670
  <=> ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f1697,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(intersection(complement(X0),X1),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_20
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f289]) ).

fof(f10367,plain,
    ( spl0_669
    | ~ spl0_20
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1676,f1663,f288,f10365]) ).

fof(f10365,plain,
    ( spl0_669
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f1676,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(intersection(X0,complement(X1)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) )
    | ~ spl0_20
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f289]) ).

fof(f10360,plain,
    ( ~ spl0_667
    | ~ spl0_668
    | spl0_347
    | ~ spl0_112
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1652,f1646,f830,f3509,f10357,f10353]) ).

fof(f10353,plain,
    ( spl0_667
  <=> 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_667])]) ).

fof(f10357,plain,
    ( spl0_668
  <=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f1652,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
    | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_112
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f831]) ).

fof(f10048,plain,
    ( spl0_666
    | ~ spl0_314
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f3677,f3547,f3139,f10045]) ).

fof(f10045,plain,
    ( spl0_666
  <=> null_class = intersection(complement(subset_relation),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f3677,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_314
    | ~ spl0_355 ),
    inference(duplicate_literal_removal,[],[f3671]) ).

fof(f3671,plain,
    ( null_class = intersection(complement(subset_relation),singleton_relation)
    | null_class = intersection(complement(subset_relation),singleton_relation)
    | ~ spl0_314
    | ~ spl0_355 ),
    inference(resolution,[],[f3548,f3140]) ).

fof(f10021,plain,
    ( spl0_665
    | ~ spl0_177
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1739,f1718,f1484,f10019]) ).

fof(f10019,plain,
    ( spl0_665
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f1739,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | ~ member(second(regular(cross_product(X0,X1))),universal_class)
        | ~ member(first(regular(cross_product(X0,X1))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_177
    | ~ spl0_199 ),
    inference(superposition,[],[f1485,f1719]) ).

fof(f10017,plain,
    ( spl0_664
    | ~ spl0_114
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1699,f1667,f895,f10015]) ).

fof(f10015,plain,
    ( spl0_664
  <=> ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f895,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f1699,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | ~ member(intersection(null_class,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(null_class,X0),intersection(null_class,X0)),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f896]) ).

fof(f896,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_114 ),
    inference(avatar_component_clause,[],[f895]) ).

fof(f10013,plain,
    ( spl0_663
    | ~ spl0_38
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1691,f1667,f373,f10011]) ).

fof(f10011,plain,
    ( spl0_663
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f1691,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
    | ~ spl0_38
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f374]) ).

fof(f10009,plain,
    ( spl0_662
    | ~ spl0_114
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1678,f1663,f895,f10007]) ).

fof(f10007,plain,
    ( spl0_662
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f1678,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | ~ member(intersection(X0,null_class),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,null_class),intersection(X0,null_class)),universal_class)),universal_class))))))),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f896]) ).

fof(f10005,plain,
    ( spl0_661
    | ~ spl0_38
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1670,f1663,f373,f10003]) ).

fof(f10003,plain,
    ( spl0_661
  <=> ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f1670,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ member(intersection(X0,X1),universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
    | ~ spl0_38
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f374]) ).

fof(f10001,plain,
    ( spl0_660
    | ~ spl0_124
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1659,f1646,f958,f9999]) ).

fof(f9999,plain,
    ( spl0_660
  <=> ! [X0] :
        ( null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f1659,plain,
    ( ! [X0] :
        ( null_class = complement(regular(X0))
        | ~ member(complement(regular(X0)),universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),null_class)
        | null_class = X0 )
    | ~ spl0_124
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f959]) ).

fof(f9997,plain,
    ( spl0_659
    | ~ spl0_48
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1506,f1463,f445,f9995]) ).

fof(f9995,plain,
    ( spl0_659
  <=> ! [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_659])]) ).

fof(f1506,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
        | complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 )
    | ~ spl0_48
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f446]) ).

fof(f9993,plain,
    ( spl0_658
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1499,f1459,f1166,f9991]) ).

fof(f9991,plain,
    ( spl0_658
  <=> ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f1499,plain,
    ( ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,regular(X1))
        | ~ member(X2,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),null_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
        | null_class = X1 )
    | ~ spl0_143
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f1167]) ).

fof(f9989,plain,
    ( ~ spl0_436
    | spl0_657
    | ~ spl0_144
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1493,f1459,f1170,f9987,f5566]) ).

fof(f9987,plain,
    ( spl0_657
  <=> ! [X0,X1] :
        ( ~ function(X0)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation)
        | ~ member(X1,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f1493,plain,
    ( ! [X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),element_relation)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f1171]) ).

fof(f9985,plain,
    ( spl0_656
    | ~ spl0_28
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f3150,f3118,f324,f9983]) ).

fof(f9983,plain,
    ( spl0_656
  <=> ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f3150,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_313 ),
    inference(duplicate_literal_removal,[],[f3142]) ).

fof(f3142,plain,
    ( ! [X0] :
        ( subclass(X0,subset_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,subset_relation) )
    | ~ spl0_28
    | ~ spl0_313 ),
    inference(resolution,[],[f3119,f325]) ).

fof(f9981,plain,
    ( spl0_655
    | ~ spl0_143
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1441,f1376,f1166,f9979]) ).

fof(f9979,plain,
    ( spl0_655
  <=> ! [X0,X1] :
        ( ~ subclass(domain_relation,regular(X0))
        | ~ member(X1,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f1441,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,regular(X0))
        | ~ member(X1,universal_class)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),null_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
        | null_class = X0 )
    | ~ spl0_143
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f1167]) ).

fof(f9976,plain,
    ( spl0_653
    | ~ spl0_654
    | ~ spl0_145
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1438,f1376,f1174,f9973,f9970]) ).

fof(f9970,plain,
    ( spl0_653
  <=> ! [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_653])]) ).

fof(f9973,plain,
    ( spl0_654
  <=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f1438,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation) )
    | ~ spl0_145
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f1175]) ).

fof(f9968,plain,
    ( ~ spl0_652
    | ~ spl0_237
    | spl0_651 ),
    inference(avatar_split_clause,[],[f9963,f9959,f2324,f9965]) ).

fof(f9965,plain,
    ( spl0_652
  <=> subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f9959,plain,
    ( spl0_651
  <=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f9963,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_237
    | spl0_651 ),
    inference(forward_demodulation,[],[f9961,f2326]) ).

fof(f9961,plain,
    ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
    | spl0_651 ),
    inference(avatar_component_clause,[],[f9959]) ).

fof(f9962,plain,
    ( spl0_650
    | ~ spl0_651
    | ~ spl0_144
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1435,f1376,f1170,f9959,f9956]) ).

fof(f9956,plain,
    ( spl0_650
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),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_650])]) ).

fof(f1435,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f1171]) ).

fof(f9954,plain,
    ( spl0_649
    | ~ spl0_79
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1070,f1019,f630,f9952]) ).

fof(f9952,plain,
    ( spl0_649
  <=> ! [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_649])]) ).

fof(f1070,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) )
    | ~ spl0_79
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f631]) ).

fof(f9948,plain,
    ( spl0_648
    | ~ spl0_86
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1730,f1718,f671,f9946]) ).

fof(f9946,plain,
    ( spl0_648
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f671,plain,
    ( spl0_86
  <=> ! [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_86])]) ).

fof(f1730,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_86
    | ~ spl0_199 ),
    inference(superposition,[],[f672,f1719]) ).

fof(f672,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_86 ),
    inference(avatar_component_clause,[],[f671]) ).

fof(f9934,plain,
    ( spl0_647
    | ~ spl0_28
    | ~ spl0_305 ),
    inference(avatar_split_clause,[],[f3129,f2966,f324,f9932]) ).

fof(f9932,plain,
    ( spl0_647
  <=> ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f3129,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation) )
    | ~ spl0_28
    | ~ spl0_305 ),
    inference(duplicate_literal_removal,[],[f3121]) ).

fof(f3121,plain,
    ( ! [X0] :
        ( subclass(X0,element_relation)
        | ~ subclass(X0,singleton_relation)
        | subclass(X0,element_relation) )
    | ~ spl0_28
    | ~ spl0_305 ),
    inference(resolution,[],[f2967,f325]) ).

fof(f9822,plain,
    ( spl0_646
    | ~ spl0_72
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1889,f1875,f584,f9820]) ).

fof(f9820,plain,
    ( spl0_646
  <=> ! [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_646])]) ).

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

fof(f1889,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(composition_function,compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) )
    | ~ spl0_72
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f585]) ).

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

fof(f9818,plain,
    ( spl0_645
    | ~ spl0_29
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1741,f1718,f328,f9816]) ).

fof(f9816,plain,
    ( spl0_645
  <=> ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f1741,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
        | ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_29
    | ~ spl0_199 ),
    inference(superposition,[],[f329,f1719]) ).

fof(f9814,plain,
    ( spl0_644
    | ~ spl0_48
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1488,f1459,f445,f9812]) ).

fof(f9812,plain,
    ( spl0_644
  <=> ! [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_644])]) ).

fof(f1488,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,unordered_pair(X1,X2))
        | ~ member(X3,universal_class)
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
        | domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 )
    | ~ spl0_48
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f446]) ).

fof(f9810,plain,
    ( spl0_643
    | ~ spl0_48
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1430,f1376,f445,f9808]) ).

fof(f9808,plain,
    ( spl0_643
  <=> ! [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_643])]) ).

fof(f1430,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
        | unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 )
    | ~ spl0_48
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f446]) ).

fof(f9806,plain,
    ( spl0_642
    | ~ spl0_49
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1398,f1372,f449,f9804]) ).

fof(f9804,plain,
    ( spl0_642
  <=> ! [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_642])]) ).

fof(f1398,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
        | subclass(X0,intersection(X1,intersection(X2,X3)))
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
        | ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) )
    | ~ spl0_49
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f450]) ).

fof(f9802,plain,
    ( spl0_641
    | ~ spl0_4
    | ~ spl0_293 ),
    inference(avatar_split_clause,[],[f2982,f2832,f220,f9800]) ).

fof(f2832,plain,
    ( spl0_293
  <=> ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f2982,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_293 ),
    inference(resolution,[],[f2833,f221]) ).

fof(f2833,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),X1)
        | ~ member(X0,subset_relation)
        | member(X0,X1) )
    | ~ spl0_293 ),
    inference(avatar_component_clause,[],[f2832]) ).

fof(f9798,plain,
    ( spl0_640
    | ~ spl0_116
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1365,f1358,f922,f9796]) ).

fof(f9796,plain,
    ( spl0_640
  <=> ! [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_640])]) ).

fof(f922,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1365,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
        | subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
    | ~ spl0_116
    | ~ spl0_163 ),
    inference(resolution,[],[f1359,f923]) ).

fof(f923,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(X0),X1),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f922]) ).

fof(f9757,plain,
    ( spl0_639
    | ~ spl0_237
    | ~ spl0_634 ),
    inference(avatar_split_clause,[],[f9728,f9723,f2324,f9755]) ).

fof(f9755,plain,
    ( spl0_639
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f9723,plain,
    ( spl0_634
  <=> ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f9728,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0) )
    | ~ spl0_237
    | ~ spl0_634 ),
    inference(forward_demodulation,[],[f9727,f2326]) ).

fof(f9727,plain,
    ( ! [X0] :
        ( ~ member(intersection(singleton_relation,X0),universal_class)
        | null_class = intersection(singleton_relation,X0)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_634 ),
    inference(forward_demodulation,[],[f9726,f2326]) ).

fof(f9726,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_634 ),
    inference(forward_demodulation,[],[f9724,f2326]) ).

fof(f9724,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_634 ),
    inference(avatar_component_clause,[],[f9723]) ).

fof(f9744,plain,
    ( spl0_638
    | ~ spl0_237
    | ~ spl0_632 ),
    inference(avatar_split_clause,[],[f9717,f9712,f2324,f9742]) ).

fof(f9742,plain,
    ( spl0_638
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f9712,plain,
    ( spl0_632
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f9717,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),subset_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_237
    | ~ spl0_632 ),
    inference(forward_demodulation,[],[f9716,f2326]) ).

fof(f9716,plain,
    ( ! [X0] :
        ( ~ member(intersection(X0,singleton_relation),universal_class)
        | null_class = intersection(X0,singleton_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_632 ),
    inference(forward_demodulation,[],[f9715,f2326]) ).

fof(f9715,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_632 ),
    inference(forward_demodulation,[],[f9713,f2326]) ).

fof(f9713,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_632 ),
    inference(avatar_component_clause,[],[f9712]) ).

fof(f9740,plain,
    ( spl0_637
    | ~ spl0_67
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1883,f1875,f557,f9738]) ).

fof(f9738,plain,
    ( spl0_637
  <=> ! [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_637])]) ).

fof(f1883,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) )
    | ~ spl0_67
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f558]) ).

fof(f9736,plain,
    ( spl0_636
    | ~ spl0_103
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1704,f1667,f764,f9734]) ).

fof(f9734,plain,
    ( spl0_636
  <=> ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).

fof(f1704,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | ~ member(intersection(singleton_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_103
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f765]) ).

fof(f9732,plain,
    ( spl0_635
    | ~ spl0_104
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2904,f2324,f768,f9730]) ).

fof(f9730,plain,
    ( spl0_635
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f2904,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,subset_relation) )
    | ~ spl0_104
    | ~ spl0_237 ),
    inference(superposition,[],[f769,f2326]) ).

fof(f9725,plain,
    ( spl0_634
    | ~ spl0_104
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1702,f1667,f768,f9723]) ).

fof(f1702,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | ~ member(intersection(identity_relation,X0),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_104
    | ~ spl0_197 ),
    inference(resolution,[],[f1668,f769]) ).

fof(f9721,plain,
    ( spl0_633
    | ~ spl0_103
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1683,f1663,f764,f9719]) ).

fof(f9719,plain,
    ( spl0_633
  <=> ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f1683,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | ~ member(intersection(X0,singleton_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_103
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f765]) ).

fof(f9714,plain,
    ( spl0_632
    | ~ spl0_104
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1681,f1663,f768,f9712]) ).

fof(f1681,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | ~ member(intersection(X0,identity_relation),universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_104
    | ~ spl0_196 ),
    inference(resolution,[],[f1664,f769]) ).

fof(f9707,plain,
    ( spl0_630
    | ~ spl0_631
    | ~ spl0_113
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1366,f1358,f891,f9704,f9700]) ).

fof(f9704,plain,
    ( spl0_631
  <=> 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_631])]) ).

fof(f1366,plain,
    ( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
    | null_class = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_113
    | ~ spl0_163 ),
    inference(resolution,[],[f1359,f892]) ).

fof(f9628,plain,
    ( spl0_628
    | spl0_629
    | ~ spl0_79
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f854,f818,f630,f9626,f9623]) ).

fof(f854,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) )
    | ~ spl0_79
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f631]) ).

fof(f9509,plain,
    ( spl0_626
    | ~ spl0_627
    | ~ spl0_64
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1890,f1875,f540,f9506,f9503]) ).

fof(f9503,plain,
    ( spl0_626
  <=> ! [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_626])]) ).

fof(f9506,plain,
    ( spl0_627
  <=> subclass(composition_function,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f540,plain,
    ( spl0_64
  <=> ! [X0,X1] :
        ( domain_of(X0) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f1890,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,domain_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
    | ~ spl0_64
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f541]) ).

fof(f541,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f540]) ).

fof(f9501,plain,
    ( spl0_625
    | ~ spl0_88
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1422,f1376,f680,f9499]) ).

fof(f9499,plain,
    ( spl0_625
  <=> ! [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_625])]) ).

fof(f1422,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_88
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f681]) ).

fof(f9497,plain,
    ( spl0_624
    | ~ spl0_28
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1364,f1358,f324,f9495]) ).

fof(f9495,plain,
    ( spl0_624
  <=> ! [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_624])]) ).

fof(f1364,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
        | subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_28
    | ~ spl0_163 ),
    inference(resolution,[],[f1359,f325]) ).

fof(f9383,plain,
    ( spl0_623
    | ~ spl0_237
    | ~ spl0_618 ),
    inference(avatar_split_clause,[],[f9355,f9352,f2324,f9381]) ).

fof(f9381,plain,
    ( spl0_623
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f9352,plain,
    ( spl0_618
  <=> ! [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_618])]) ).

fof(f9355,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))) )
    | ~ spl0_237
    | ~ spl0_618 ),
    inference(forward_demodulation,[],[f9353,f2326]) ).

fof(f9353,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_618 ),
    inference(avatar_component_clause,[],[f9352]) ).

fof(f9379,plain,
    ( spl0_622
    | ~ spl0_237
    | ~ spl0_617 ),
    inference(avatar_split_clause,[],[f9350,f9345,f2324,f9377]) ).

fof(f9377,plain,
    ( spl0_622
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f9345,plain,
    ( spl0_617
  <=> ! [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_617])]) ).

fof(f9350,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1) )
    | ~ spl0_237
    | ~ spl0_617 ),
    inference(forward_demodulation,[],[f9349,f2326]) ).

fof(f9349,plain,
    ( ! [X0,X1] :
        ( subclass(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_617 ),
    inference(forward_demodulation,[],[f9348,f2326]) ).

fof(f9348,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(singleton_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_617 ),
    inference(forward_demodulation,[],[f9346,f2326]) ).

fof(f9346,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_617 ),
    inference(avatar_component_clause,[],[f9345]) ).

fof(f9367,plain,
    ( spl0_620
    | ~ spl0_621
    | ~ spl0_61
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1885,f1875,f527,f9364,f9361]) ).

fof(f9361,plain,
    ( spl0_620
  <=> ! [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_620])]) ).

fof(f9364,plain,
    ( spl0_621
  <=> subclass(composition_function,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f527,plain,
    ( spl0_61
  <=> ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f1885,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
    | ~ spl0_61
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f528]) ).

fof(f528,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | member(X0,X1) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f527]) ).

fof(f9359,plain,
    ( spl0_619
    | ~ spl0_38
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1630,f1627,f373,f9357]) ).

fof(f9357,plain,
    ( spl0_619
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f1630,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(X1,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_38
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f374]) ).

fof(f9354,plain,
    ( spl0_618
    | ~ spl0_126
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1403,f1372,f966,f9352]) ).

fof(f1403,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
        | subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
        | ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
    | ~ spl0_126
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f967]) ).

fof(f9347,plain,
    ( spl0_617
    | ~ spl0_125
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1401,f1372,f962,f9345]) ).

fof(f1401,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
        | subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
        | ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
    | ~ spl0_125
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f963]) ).

fof(f9342,plain,
    ( spl0_616
    | ~ spl0_136
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1221,f1174,f1094,f9340]) ).

fof(f9340,plain,
    ( spl0_616
  <=> ! [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_616])]) ).

fof(f1221,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
        | member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
        | subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) )
    | ~ spl0_136
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f1095]) ).

fof(f9337,plain,
    ( spl0_615
    | ~ spl0_135
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1214,f1174,f1090,f9335]) ).

fof(f9335,plain,
    ( spl0_615
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
        | member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
        | subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f1214,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
        | member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
        | subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) )
    | ~ spl0_135
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f1091]) ).

fof(f9330,plain,
    ( spl0_614
    | ~ spl0_136
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1207,f1170,f1094,f9328]) ).

fof(f9328,plain,
    ( spl0_614
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
        | subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f1207,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
        | member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
        | subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) )
    | ~ spl0_136
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f1095]) ).

fof(f9323,plain,
    ( spl0_613
    | ~ spl0_135
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1200,f1170,f1090,f9321]) ).

fof(f9321,plain,
    ( spl0_613
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
        | subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f1200,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
        | member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
        | subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) )
    | ~ spl0_135
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f1091]) ).

fof(f9319,plain,
    ( spl0_612
    | ~ spl0_87
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f889,f830,f675,f9317]) ).

fof(f9317,plain,
    ( spl0_612
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f675,plain,
    ( spl0_87
  <=> ! [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_87])]) ).

fof(f889,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_87
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f676]) ).

fof(f676,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_87 ),
    inference(avatar_component_clause,[],[f675]) ).

fof(f9313,plain,
    ( spl0_611
    | ~ spl0_55
    | ~ spl0_492 ),
    inference(avatar_split_clause,[],[f8774,f6497,f478,f9310]) ).

fof(f9310,plain,
    ( spl0_611
  <=> universal_class = intersection(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f8774,plain,
    ( universal_class = intersection(universal_class,universal_class)
    | ~ spl0_55
    | ~ spl0_492 ),
    inference(resolution,[],[f6498,f479]) ).

fof(f9201,plain,
    ( spl0_610
    | ~ spl0_85
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1729,f1718,f667,f9199]) ).

fof(f9199,plain,
    ( spl0_610
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f667,plain,
    ( spl0_85
  <=> ! [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_85])]) ).

fof(f1729,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
        | member(first(regular(cross_product(X0,X1))),domain_of(X2))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_85
    | ~ spl0_199 ),
    inference(superposition,[],[f668,f1719]) ).

fof(f668,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_85 ),
    inference(avatar_component_clause,[],[f667]) ).

fof(f9197,plain,
    ( spl0_609
    | ~ spl0_84
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1728,f1718,f662,f9195]) ).

fof(f9195,plain,
    ( spl0_609
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f1728,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
        | member(regular(cross_product(X0,X1)),element_relation)
        | ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_84
    | ~ spl0_199 ),
    inference(superposition,[],[f663,f1719]) ).

fof(f9193,plain,
    ( spl0_608
    | ~ spl0_31
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1634,f1627,f336,f9191]) ).

fof(f9191,plain,
    ( spl0_608
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f1634,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_31
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f337]) ).

fof(f9189,plain,
    ( spl0_607
    | ~ spl0_32
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1633,f1627,f340,f9187]) ).

fof(f9187,plain,
    ( spl0_607
  <=> ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f1633,plain,
    ( ! [X2,X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,intersection(X1,X2))
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
    | ~ spl0_32
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f341]) ).

fof(f9184,plain,
    ( spl0_606
    | ~ spl0_229
    | ~ spl0_492 ),
    inference(avatar_split_clause,[],[f8773,f6497,f2272,f9181]) ).

fof(f9181,plain,
    ( spl0_606
  <=> member(null_class,intersection(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f8773,plain,
    ( member(null_class,intersection(universal_class,universal_class))
    | ~ spl0_229
    | ~ spl0_492 ),
    inference(resolution,[],[f6498,f2273]) ).

fof(f9179,plain,
    ( spl0_605
    | ~ spl0_131
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1581,f1563,f1019,f9177]) ).

fof(f9177,plain,
    ( spl0_605
  <=> ! [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_605])]) ).

fof(f1581,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),subset_relation)
        | ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_186 ),
    inference(resolution,[],[f1564,f1020]) ).

fof(f9175,plain,
    ( spl0_604
    | ~ spl0_44
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1400,f1372,f425,f9173]) ).

fof(f9173,plain,
    ( spl0_604
  <=> ! [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_604])]) ).

fof(f1400,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
        | subclass(X0,intersection(X1,complement(X2)))
        | member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) )
    | ~ spl0_44
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f426]) ).

fof(f9171,plain,
    ( spl0_603
    | ~ spl0_79
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f986,f926,f630,f9169]) ).

fof(f9169,plain,
    ( spl0_603
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | null_class = X0
        | regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f986,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,cross_product(X1,X2))
        | null_class = X0
        | regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) )
    | ~ spl0_79
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f631]) ).

fof(f9122,plain,
    ( ~ spl0_602
    | ~ spl0_237
    | spl0_601 ),
    inference(avatar_split_clause,[],[f9117,f9113,f2324,f9119]) ).

fof(f9119,plain,
    ( spl0_602
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f9113,plain,
    ( spl0_601
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f9117,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_237
    | spl0_601 ),
    inference(forward_demodulation,[],[f9114,f2326]) ).

fof(f9114,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | spl0_601 ),
    inference(avatar_component_clause,[],[f9113]) ).

fof(f9116,plain,
    ( ~ spl0_554
    | spl0_235
    | spl0_601
    | ~ spl0_43
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1710,f1667,f394,f9113,f2314,f8190]) ).

fof(f8190,plain,
    ( spl0_554
  <=> member(identity_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f2314,plain,
    ( spl0_235
  <=> null_class = identity_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f1710,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ member(identity_relation,universal_class)
    | ~ spl0_43
    | ~ spl0_197 ),
    inference(superposition,[],[f1668,f396]) ).

fof(f9111,plain,
    ( spl0_600
    | ~ spl0_20
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1636,f1627,f288,f9109]) ).

fof(f9109,plain,
    ( spl0_600
  <=> ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f1636,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | ~ subclass(X0,complement(X1))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_20
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f289]) ).

fof(f9106,plain,
    ( spl0_599
    | ~ spl0_130
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1220,f1174,f1015,f9104]) ).

fof(f9104,plain,
    ( spl0_599
  <=> ! [X0] :
        ( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
        | member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f1220,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
        | member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
        | null_class = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_130
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f1016]) ).

fof(f9093,plain,
    ( spl0_598
    | ~ spl0_129
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1218,f1174,f1011,f9091]) ).

fof(f9091,plain,
    ( spl0_598
  <=> ! [X0] :
        ( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
        | member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f1218,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
        | member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
        | null_class = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_129
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f1012]) ).

fof(f9086,plain,
    ( spl0_597
    | ~ spl0_130
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1206,f1170,f1015,f9084]) ).

fof(f9084,plain,
    ( spl0_597
  <=> ! [X0] :
        ( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
        | member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
        | null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f1206,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
        | member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
        | null_class = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_130
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f1016]) ).

fof(f9079,plain,
    ( spl0_596
    | ~ spl0_129
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1204,f1170,f1011,f9077]) ).

fof(f9077,plain,
    ( spl0_596
  <=> ! [X0] :
        ( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
        | member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
        | null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f1204,plain,
    ( ! [X0] :
        ( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
        | member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
        | null_class = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_129
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f1012]) ).

fof(f9075,plain,
    ( spl0_595
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f982,f922,f569,f453,f9073]) ).

fof(f9073,plain,
    ( spl0_595
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
        | subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f982,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
        | subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_116 ),
    inference(forward_demodulation,[],[f981,f454]) ).

fof(f981,plain,
    ( ! [X0,X1] :
        ( subclass(complement(domain_of(X0)),X1)
        | ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class),X0) )
    | ~ spl0_70
    | ~ spl0_116 ),
    inference(resolution,[],[f923,f570]) ).

fof(f9052,plain,
    ( spl0_594
    | ~ spl0_237
    | ~ spl0_591 ),
    inference(avatar_split_clause,[],[f8977,f8974,f2324,f9050]) ).

fof(f9050,plain,
    ( spl0_594
  <=> ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f8974,plain,
    ( spl0_591
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f8977,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_237
    | ~ spl0_591 ),
    inference(forward_demodulation,[],[f8975,f2326]) ).

fof(f8975,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_591 ),
    inference(avatar_component_clause,[],[f8974]) ).

fof(f8985,plain,
    ( spl0_593
    | ~ spl0_72
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1762,f1752,f584,f8983]) ).

fof(f8983,plain,
    ( spl0_593
  <=> ! [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_593])]) ).

fof(f1762,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),compose_class(X3))
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) )
    | ~ spl0_72
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f585]) ).

fof(f8981,plain,
    ( spl0_592
    | ~ spl0_103
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1644,f1627,f764,f8979]) ).

fof(f8979,plain,
    ( spl0_592
  <=> ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f1644,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,singleton_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) )
    | ~ spl0_103
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f765]) ).

fof(f8976,plain,
    ( spl0_591
    | ~ spl0_104
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1642,f1627,f768,f8974]) ).

fof(f1642,plain,
    ( ! [X0] :
        ( null_class = X0
        | ~ subclass(X0,identity_relation)
        | ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
    | ~ spl0_104
    | ~ spl0_194 ),
    inference(resolution,[],[f1628,f769]) ).

fof(f8972,plain,
    ( spl0_590
    | ~ spl0_117
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1578,f1563,f926,f8970]) ).

fof(f8970,plain,
    ( spl0_590
  <=> ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f1578,plain,
    ( ! [X0] :
        ( member(regular(X0),subset_relation)
        | ~ member(regular(X0),cross_product(universal_class,universal_class))
        | ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_186 ),
    inference(resolution,[],[f1564,f927]) ).

fof(f8968,plain,
    ( spl0_589
    | ~ spl0_88
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f839,f818,f680,f8966]) ).

fof(f839,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_88
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f681]) ).

fof(f8834,plain,
    ( spl0_588
    | ~ spl0_77
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1726,f1718,f615,f8832]) ).

fof(f8832,plain,
    ( spl0_588
  <=> ! [X0,X3,X2,X1] :
        ( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),X3)
        | ~ member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f1726,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | ~ member(second(regular(cross_product(X0,X1))),X3)
        | ~ member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_77
    | ~ spl0_199 ),
    inference(superposition,[],[f616,f1719]) ).

fof(f8827,plain,
    ( ~ spl0_586
    | spl0_276
    | spl0_587
    | ~ spl0_76
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1708,f1667,f610,f8824,f2551,f8820]) ).

fof(f8820,plain,
    ( spl0_586
  <=> member(subset_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f8824,plain,
    ( spl0_587
  <=> 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_587])]) ).

fof(f1708,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ member(subset_relation,universal_class)
    | ~ spl0_76
    | ~ spl0_197 ),
    inference(superposition,[],[f1668,f612]) ).

fof(f8818,plain,
    ( spl0_585
    | ~ spl0_153
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1650,f1646,f1254,f8816]) ).

fof(f8816,plain,
    ( spl0_585
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(complement(X0),universal_class)
        | ~ subclass(universal_class,X0)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f1650,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(complement(X0),universal_class)
        | ~ subclass(universal_class,X0)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class) )
    | ~ spl0_153
    | ~ spl0_195 ),
    inference(resolution,[],[f1647,f1255]) ).

fof(f8814,plain,
    ( spl0_584
    | ~ spl0_38
    | ~ spl0_187 ),
    inference(avatar_split_clause,[],[f1589,f1585,f373,f8812]) ).

fof(f8812,plain,
    ( spl0_584
  <=> ! [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_584])]) ).

fof(f1589,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(compose(X0,X1),universal_class)
        | ~ member(X1,universal_class)
        | ~ subclass(compose_class(X0),X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) )
    | ~ spl0_38
    | ~ spl0_187 ),
    inference(resolution,[],[f1586,f374]) ).

fof(f8810,plain,
    ( ~ spl0_582
    | spl0_583
    | ~ spl0_109
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1580,f1563,f818,f8808,f8804]) ).

fof(f8804,plain,
    ( spl0_582
  <=> 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_582])]) ).

fof(f8808,plain,
    ( spl0_583
  <=> ! [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_583])]) ).

fof(f1580,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(X0,X1),subset_relation)
        | ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class))
        | ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_109
    | ~ spl0_186 ),
    inference(resolution,[],[f1564,f819]) ).

fof(f8802,plain,
    ( spl0_581
    | ~ spl0_76
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1408,f1372,f610,f8800]) ).

fof(f8800,plain,
    ( spl0_581
  <=> ! [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_581])]) ).

fof(f1408,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
        | subclass(X0,subset_relation) )
    | ~ spl0_76
    | ~ spl0_165 ),
    inference(superposition,[],[f1373,f612]) ).

fof(f8798,plain,
    ( spl0_580
    | ~ spl0_131
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1321,f1301,f1019,f8796]) ).

fof(f8796,plain,
    ( spl0_580
  <=> ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f1321,plain,
    ( ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_159 ),
    inference(resolution,[],[f1302,f1020]) ).

fof(f8672,plain,
    ( spl0_579
    | ~ spl0_64
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1763,f1752,f540,f8670]) ).

fof(f8670,plain,
    ( spl0_579
  <=> ! [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_579])]) ).

fof(f1763,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),domain_relation)
        | ~ operation(X2)
        | not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) )
    | ~ spl0_64
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f541]) ).

fof(f8668,plain,
    ( spl0_578
    | ~ spl0_115
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1392,f1368,f899,f8666]) ).

fof(f8666,plain,
    ( spl0_578
  <=> ! [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_578])]) ).

fof(f1392,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
        | not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
        | function(unordered_pair(X0,X1))
        | ~ single_valued_class(unordered_pair(X0,X1)) )
    | ~ spl0_115
    | ~ spl0_164 ),
    inference(resolution,[],[f1369,f900]) ).

fof(f8664,plain,
    ( spl0_577
    | ~ spl0_143
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1277,f1254,f1166,f8662]) ).

fof(f8662,plain,
    ( spl0_577
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f1277,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,regular(X0))
        | ~ member(X1,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),null_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
        | null_class = X0 )
    | ~ spl0_143
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f1167]) ).

fof(f8660,plain,
    ( spl0_576
    | ~ spl0_436
    | ~ spl0_144
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1272,f1254,f1170,f5566,f8658]) ).

fof(f8658,plain,
    ( spl0_576
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f1272,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X0,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),element_relation)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),singleton_relation) )
    | ~ spl0_144
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f1171]) ).

fof(f8656,plain,
    ( spl0_575
    | ~ spl0_76
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1263,f1250,f610,f8654]) ).

fof(f8654,plain,
    ( spl0_575
  <=> ! [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_575])]) ).

fof(f1250,plain,
    ( spl0_152
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f1263,plain,
    ( ! [X0,X1] :
        ( ~ subclass(subset_relation,X0)
        | ~ member(X1,cross_product(universal_class,universal_class))
        | ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | member(X1,X0) )
    | ~ spl0_76
    | ~ spl0_152 ),
    inference(superposition,[],[f1251,f612]) ).

fof(f1251,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(intersection(X2,X1),X3)
        | ~ member(X0,X2)
        | ~ member(X0,X1)
        | member(X0,X3) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1250]) ).

fof(f8644,plain,
    ( spl0_574
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f906,f891,f569,f453,f8642]) ).

fof(f8642,plain,
    ( spl0_574
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f906,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
        | null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_113 ),
    inference(forward_demodulation,[],[f905,f454]) ).

fof(f905,plain,
    ( ! [X0] :
        ( null_class = complement(domain_of(X0))
        | ~ member(regular(complement(domain_of(X0))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class),X0) )
    | ~ spl0_70
    | ~ spl0_113 ),
    inference(resolution,[],[f892,f570]) ).

fof(f8295,plain,
    ( spl0_573
    | ~ spl0_61
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1758,f1752,f527,f8293]) ).

fof(f8293,plain,
    ( spl0_573
  <=> ! [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_573])]) ).

fof(f1758,plain,
    ( ! [X2,X0,X1] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),element_relation)
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
    | ~ spl0_61
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f528]) ).

fof(f8291,plain,
    ( spl0_572
    | ~ spl0_72
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1725,f1718,f584,f8289]) ).

fof(f8289,plain,
    ( spl0_572
  <=> ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f1725,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
        | second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_72
    | ~ spl0_199 ),
    inference(superposition,[],[f585,f1719]) ).

fof(f8287,plain,
    ( spl0_571
    | ~ spl0_135
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1618,f1591,f1090,f8285]) ).

fof(f8285,plain,
    ( spl0_571
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f1591,plain,
    ( spl0_188
  <=> ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f1618,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0)) )
    | ~ spl0_135
    | ~ spl0_188 ),
    inference(duplicate_literal_removal,[],[f1613]) ).

fof(f1613,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X1),domain_of(X0)),not_subclass_element(intersection(universal_class,X1),domain_of(X0))),universal_class))
        | subclass(intersection(universal_class,X1),domain_of(X0))
        | subclass(intersection(universal_class,X1),domain_of(X0)) )
    | ~ spl0_135
    | ~ spl0_188 ),
    inference(resolution,[],[f1592,f1091]) ).

fof(f1592,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_188 ),
    inference(avatar_component_clause,[],[f1591]) ).

fof(f8283,plain,
    ( spl0_570
    | ~ spl0_136
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1617,f1591,f1094,f8281]) ).

fof(f8281,plain,
    ( spl0_570
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f1617,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0)) )
    | ~ spl0_136
    | ~ spl0_188 ),
    inference(duplicate_literal_removal,[],[f1614]) ).

fof(f1614,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(intersection(X1,universal_class),domain_of(X0)),not_subclass_element(intersection(X1,universal_class),domain_of(X0))),universal_class))
        | subclass(intersection(X1,universal_class),domain_of(X0))
        | subclass(intersection(X1,universal_class),domain_of(X0)) )
    | ~ spl0_136
    | ~ spl0_188 ),
    inference(resolution,[],[f1592,f1095]) ).

fof(f8279,plain,
    ( spl0_569
    | ~ spl0_63
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1444,f1380,f535,f8277]) ).

fof(f8277,plain,
    ( spl0_569
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | ~ inductive(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f535,plain,
    ( spl0_63
  <=> ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1380,plain,
    ( spl0_167
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1444,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | ~ inductive(X1) )
    | ~ spl0_63
    | ~ spl0_167 ),
    inference(resolution,[],[f1381,f536]) ).

fof(f536,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f535]) ).

fof(f1381,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_of(X1),X2)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,X2) )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1380]) ).

fof(f8265,plain,
    ( spl0_568
    | ~ spl0_14
    | ~ spl0_84
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1418,f1376,f662,f263,f8263]) ).

fof(f1418,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_84
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f663]) ).

fof(f8255,plain,
    ( spl0_567
    | ~ spl0_124
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1404,f1372,f958,f8253]) ).

fof(f8253,plain,
    ( spl0_567
  <=> ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
        | subclass(X0,intersection(X1,regular(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f1404,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
        | subclass(X0,intersection(X1,regular(X2)))
        | ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),null_class)
        | null_class = X2 )
    | ~ spl0_124
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f959]) ).

fof(f8251,plain,
    ( spl0_566
    | ~ spl0_112
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1397,f1372,f830,f8249]) ).

fof(f8249,plain,
    ( spl0_566
  <=> ! [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_566])]) ).

fof(f1397,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
        | subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
        | ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) )
    | ~ spl0_112
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f831]) ).

fof(f8246,plain,
    ( spl0_565
    | ~ spl0_27
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1213,f1174,f320,f8244]) ).

fof(f8244,plain,
    ( spl0_565
  <=> ! [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_565])]) ).

fof(f1213,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
        | member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
        | subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
    | ~ spl0_27
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f321]) ).

fof(f8239,plain,
    ( spl0_564
    | ~ spl0_27
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1199,f1170,f320,f8237]) ).

fof(f8237,plain,
    ( spl0_564
  <=> ! [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_564])]) ).

fof(f1199,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
        | member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
        | subclass(complement(compose(element_relation,complement(identity_relation))),X0) )
    | ~ spl0_27
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f321]) ).

fof(f8235,plain,
    ( spl0_563
    | ~ spl0_136
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1193,f1166,f1094,f8233]) ).

fof(f8233,plain,
    ( spl0_563
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | null_class = X1
        | subclass(intersection(X0,regular(X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f1193,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,regular(X1)),X2),null_class)
        | ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
        | null_class = X1
        | subclass(intersection(X0,regular(X1)),X2) )
    | ~ spl0_136
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f1095]) ).

fof(f8231,plain,
    ( spl0_562
    | ~ spl0_135
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1186,f1166,f1090,f8229]) ).

fof(f8229,plain,
    ( spl0_562
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | null_class = X0
        | subclass(intersection(regular(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f1186,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(regular(X0),X1),X2),null_class)
        | ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
        | null_class = X0
        | subclass(intersection(regular(X0),X1),X2) )
    | ~ spl0_135
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f1091]) ).

fof(f8227,plain,
    ( spl0_561
    | ~ spl0_48
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1138,f1094,f445,f8225]) ).

fof(f8225,plain,
    ( spl0_561
  <=> ! [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_561])]) ).

fof(f1138,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
        | not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 )
    | ~ spl0_48
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f446]) ).

fof(f8223,plain,
    ( spl0_560
    | ~ spl0_48
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1120,f1090,f445,f8221]) ).

fof(f8221,plain,
    ( spl0_560
  <=> ! [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_560])]) ).

fof(f1120,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(unordered_pair(X0,X1),X2),X3)
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
        | not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 )
    | ~ spl0_48
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f446]) ).

fof(f8219,plain,
    ( spl0_559
    | ~ spl0_84
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f885,f830,f662,f8217]) ).

fof(f8217,plain,
    ( spl0_559
  <=> ! [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_559])]) ).

fof(f885,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_84
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f663]) ).

fof(f8215,plain,
    ( ~ spl0_2
    | ~ spl0_557
    | spl0_558
    | ~ spl0_63
    | ~ spl0_111 ),
    inference(avatar_split_clause,[],[f879,f826,f535,f8212,f8208,f210]) ).

fof(f210,plain,
    ( spl0_2
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f8208,plain,
    ( spl0_557
  <=> 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_557])]) ).

fof(f8212,plain,
    ( spl0_558
  <=> 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_558])]) ).

fof(f879,plain,
    ( omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))
    | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))))
    | ~ inductive(omega)
    | ~ spl0_63
    | ~ spl0_111 ),
    inference(resolution,[],[f827,f536]) ).

fof(f8204,plain,
    ( ~ spl0_556
    | ~ spl0_237
    | spl0_555 ),
    inference(avatar_split_clause,[],[f8198,f8194,f2324,f8201]) ).

fof(f8201,plain,
    ( spl0_556
  <=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f8194,plain,
    ( spl0_555
  <=> 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_555])]) ).

fof(f8198,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ spl0_237
    | spl0_555 ),
    inference(forward_demodulation,[],[f8195,f2326]) ).

fof(f8195,plain,
    ( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | spl0_555 ),
    inference(avatar_component_clause,[],[f8194]) ).

fof(f8197,plain,
    ( spl0_235
    | ~ spl0_554
    | spl0_555
    | ~ spl0_83
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f783,f768,f652,f8194,f8190,f2314]) ).

fof(f783,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
    | ~ member(identity_relation,universal_class)
    | null_class = identity_relation
    | ~ spl0_83
    | ~ spl0_104 ),
    inference(resolution,[],[f769,f653]) ).

fof(f8186,plain,
    ( spl0_232
    | ~ spl0_552
    | spl0_553
    | ~ spl0_83
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f779,f764,f652,f8183,f8179,f2289]) ).

fof(f8179,plain,
    ( spl0_552
  <=> member(singleton_relation,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f8183,plain,
    ( spl0_553
  <=> 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_553])]) ).

fof(f779,plain,
    ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation)
    | ~ member(singleton_relation,universal_class)
    | null_class = singleton_relation
    | ~ spl0_83
    | ~ spl0_103 ),
    inference(resolution,[],[f765,f653]) ).

fof(f8160,plain,
    ( spl0_551
    | ~ spl0_67
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1756,f1752,f557,f8158]) ).

fof(f8158,plain,
    ( spl0_551
  <=> ! [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_551])]) ).

fof(f1756,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism2(X0,X1,X2),X4) )
    | ~ spl0_67
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f558]) ).

fof(f8156,plain,
    ( spl0_550
    | ~ spl0_68
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1755,f1752,f561,f8154]) ).

fof(f8154,plain,
    ( spl0_550
  <=> ! [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_550])]) ).

fof(f1755,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ compatible(X0,X1,X2)
        | homomorphism(X0,X1,X2)
        | ~ operation(X1)
        | ~ subclass(domain_of(X1),cross_product(X3,X4))
        | ~ operation(X2)
        | member(not_homomorphism1(X0,X1,X2),X3) )
    | ~ spl0_68
    | ~ spl0_200 ),
    inference(resolution,[],[f1753,f562]) ).

fof(f8152,plain,
    ( spl0_549
    | ~ spl0_39
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1390,f1368,f377,f8150]) ).

fof(f8150,plain,
    ( spl0_549
  <=> ! [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_549])]) ).

fof(f1390,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | ~ subclass(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = X2 )
    | ~ spl0_39
    | ~ spl0_164 ),
    inference(resolution,[],[f1369,f378]) ).

fof(f8148,plain,
    ( spl0_548
    | ~ spl0_109
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1320,f1301,f818,f8146]) ).

fof(f8146,plain,
    ( spl0_548
  <=> ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f1320,plain,
    ( ! [X0,X1] :
        ( null_class = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)
        | ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)))) )
    | ~ spl0_109
    | ~ spl0_159 ),
    inference(resolution,[],[f1302,f819]) ).

fof(f8144,plain,
    ( spl0_547
    | ~ spl0_48
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1267,f1254,f445,f8142]) ).

fof(f8142,plain,
    ( spl0_547
  <=> ! [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_547])]) ).

fof(f1267,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | ~ member(X2,universal_class)
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 )
    | ~ spl0_48
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f446]) ).

fof(f8136,plain,
    ( ~ spl0_545
    | spl0_546
    | ~ spl0_115
    | ~ spl0_453 ),
    inference(avatar_split_clause,[],[f7473,f5932,f899,f8133,f8129]) ).

fof(f8129,plain,
    ( spl0_545
  <=> single_valued_class(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f8133,plain,
    ( spl0_546
  <=> function(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f5932,plain,
    ( spl0_453
  <=> subclass(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f7473,plain,
    ( function(singleton_relation)
    | ~ single_valued_class(singleton_relation)
    | ~ spl0_115
    | ~ spl0_453 ),
    inference(resolution,[],[f5934,f900]) ).

fof(f5934,plain,
    ( subclass(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_453 ),
    inference(avatar_component_clause,[],[f5932]) ).

fof(f7472,plain,
    ( spl0_544
    | ~ spl0_64
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1722,f1718,f540,f7470]) ).

fof(f7470,plain,
    ( spl0_544
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_relation)
        | second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f1722,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),domain_relation)
        | second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_64
    | ~ spl0_199 ),
    inference(superposition,[],[f541,f1719]) ).

fof(f7468,plain,
    ( spl0_543
    | ~ spl0_22
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1561,f1556,f296,f7466]) ).

fof(f7466,plain,
    ( spl0_543
  <=> ! [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_543])]) ).

fof(f1561,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ function(cross_product(X1,X3)) )
    | ~ spl0_22
    | ~ spl0_185 ),
    inference(resolution,[],[f1557,f297]) ).

fof(f7464,plain,
    ( spl0_542
    | ~ spl0_38
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1520,f1484,f373,f7462]) ).

fof(f7462,plain,
    ( spl0_542
  <=> ! [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_542])]) ).

fof(f1520,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class)
        | ~ subclass(element_relation,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
    | ~ spl0_38
    | ~ spl0_177 ),
    inference(resolution,[],[f1485,f374]) ).

fof(f7460,plain,
    ( spl0_541
    | ~ spl0_38
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1505,f1463,f373,f7458]) ).

fof(f7458,plain,
    ( spl0_541
  <=> ! [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_541])]) ).

fof(f1505,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) )
    | ~ spl0_38
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f374]) ).

fof(f7456,plain,
    ( spl0_540
    | ~ spl0_38
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1487,f1459,f373,f7454]) ).

fof(f7454,plain,
    ( spl0_540
  <=> ! [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_540])]) ).

fof(f1487,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,X1)
        | ~ member(X2,universal_class)
        | ~ subclass(X1,X3)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) )
    | ~ spl0_38
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f374]) ).

fof(f7452,plain,
    ( spl0_539
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1443,f1380,f505,f7450]) ).

fof(f7450,plain,
    ( spl0_539
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,domain_of(domain_of(X1)))
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f505,plain,
    ( spl0_57
  <=> ! [X8] :
        ( ~ operation(X8)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f1443,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
        | ~ member(X0,universal_class)
        | member(X0,domain_of(domain_of(X1)))
        | ~ operation(X1) )
    | ~ spl0_57
    | ~ spl0_167 ),
    inference(resolution,[],[f1381,f506]) ).

fof(f506,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f505]) ).

fof(f7448,plain,
    ( spl0_538
    | ~ spl0_111
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1391,f1368,f826,f7446]) ).

fof(f7446,plain,
    ( spl0_538
  <=> ! [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_538])]) ).

fof(f1391,plain,
    ( ! [X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),omega) = X1
        | not_subclass_element(unordered_pair(X0,X1),omega) = X0
        | unordered_pair(X0,X1) = omega
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_111
    | ~ spl0_164 ),
    inference(resolution,[],[f1369,f827]) ).

fof(f7444,plain,
    ( spl0_537
    | ~ spl0_117
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1318,f1301,f926,f7442]) ).

fof(f7442,plain,
    ( spl0_537
  <=> ! [X0] :
        ( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f1318,plain,
    ( ! [X0] :
        ( null_class = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
        | ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_159 ),
    inference(resolution,[],[f1302,f927]) ).

fof(f7439,plain,
    ( ~ spl0_536
    | ~ spl0_237
    | spl0_534 ),
    inference(avatar_split_clause,[],[f7431,f7423,f2324,f7436]) ).

fof(f7436,plain,
    ( spl0_536
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f7423,plain,
    ( spl0_534
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f7431,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
    | ~ spl0_237
    | spl0_534 ),
    inference(forward_demodulation,[],[f7424,f2326]) ).

fof(f7424,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | spl0_534 ),
    inference(avatar_component_clause,[],[f7423]) ).

fof(f7430,plain,
    ( spl0_533
    | spl0_534
    | ~ spl0_535
    | ~ spl0_23
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1217,f1174,f300,f7427,f7423,f7419]) ).

fof(f7427,plain,
    ( spl0_535
  <=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f1217,plain,
    ( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
    | member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
    | null_class = domain_of(flip(cross_product(subset_relation,universal_class)))
    | ~ spl0_23
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f301]) ).

fof(f7414,plain,
    ( ~ spl0_532
    | ~ spl0_237
    | spl0_528 ),
    inference(avatar_split_clause,[],[f7398,f7389,f2324,f7411]) ).

fof(f7411,plain,
    ( spl0_532
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f7389,plain,
    ( spl0_528
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f7398,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
    | ~ spl0_237
    | spl0_528 ),
    inference(forward_demodulation,[],[f7390,f2326]) ).

fof(f7390,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | spl0_528 ),
    inference(avatar_component_clause,[],[f7389]) ).

fof(f7409,plain,
    ( ~ spl0_531
    | ~ spl0_237
    | spl0_529 ),
    inference(avatar_split_clause,[],[f7397,f7393,f2324,f7406]) ).

fof(f7406,plain,
    ( spl0_531
  <=> member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f7393,plain,
    ( spl0_529
  <=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f7397,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(singleton_relation)))),element_relation)
    | ~ spl0_237
    | spl0_529 ),
    inference(forward_demodulation,[],[f7395,f2326]) ).

fof(f7395,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | spl0_529 ),
    inference(avatar_component_clause,[],[f7393]) ).

fof(f7404,plain,
    ( ~ spl0_530
    | ~ spl0_237
    | spl0_527 ),
    inference(avatar_split_clause,[],[f7399,f7385,f2324,f7401]) ).

fof(f7401,plain,
    ( spl0_530
  <=> null_class = complement(compose(element_relation,complement(singleton_relation))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f7399,plain,
    ( null_class != complement(compose(element_relation,complement(singleton_relation)))
    | ~ spl0_237
    | spl0_527 ),
    inference(forward_demodulation,[],[f7386,f2326]) ).

fof(f7386,plain,
    ( null_class != complement(compose(element_relation,complement(identity_relation)))
    | spl0_527 ),
    inference(avatar_component_clause,[],[f7385]) ).

fof(f7396,plain,
    ( spl0_527
    | spl0_528
    | ~ spl0_529
    | ~ spl0_23
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1203,f1170,f300,f7393,f7389,f7385]) ).

fof(f1203,plain,
    ( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
    | member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
    | null_class = complement(compose(element_relation,complement(identity_relation)))
    | ~ spl0_23
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f301]) ).

fof(f7383,plain,
    ( spl0_526
    | ~ spl0_130
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1192,f1166,f1015,f7381]) ).

fof(f7381,plain,
    ( spl0_526
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),null_class)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | null_class = X1
        | null_class = intersection(X0,regular(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f1192,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,regular(X1))),null_class)
        | ~ member(regular(intersection(X0,regular(X1))),X1)
        | null_class = X1
        | null_class = intersection(X0,regular(X1)) )
    | ~ spl0_130
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f1016]) ).

fof(f7379,plain,
    ( spl0_525
    | ~ spl0_129
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1190,f1166,f1011,f7377]) ).

fof(f7377,plain,
    ( spl0_525
  <=> ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),null_class)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | null_class = X0
        | null_class = intersection(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f1190,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(regular(X0),X1)),null_class)
        | ~ member(regular(intersection(regular(X0),X1)),X0)
        | null_class = X0
        | null_class = intersection(regular(X0),X1) )
    | ~ spl0_129
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f1012]) ).

fof(f7375,plain,
    ( spl0_524
    | ~ spl0_48
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1051,f1015,f445,f7373]) ).

fof(f7373,plain,
    ( spl0_524
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | regular(intersection(X0,unordered_pair(X1,X2))) = X1
        | regular(intersection(X0,unordered_pair(X1,X2))) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f1051,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,unordered_pair(X1,X2))
        | regular(intersection(X0,unordered_pair(X1,X2))) = X1
        | regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
    | ~ spl0_48
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f446]) ).

fof(f7371,plain,
    ( spl0_523
    | ~ spl0_48
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1035,f1011,f445,f7369]) ).

fof(f7369,plain,
    ( spl0_523
  <=> ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f1035,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X2)
        | regular(intersection(unordered_pair(X0,X1),X2)) = X0
        | regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
    | ~ spl0_48
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f446]) ).

fof(f7299,plain,
    ( ~ spl0_521
    | spl0_522
    | ~ spl0_115
    | ~ spl0_442 ),
    inference(avatar_split_clause,[],[f7068,f5592,f899,f7296,f7292]) ).

fof(f7292,plain,
    ( spl0_521
  <=> single_valued_class(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f7296,plain,
    ( spl0_522
  <=> function(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f5592,plain,
    ( spl0_442
  <=> subclass(subset_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f7068,plain,
    ( function(subset_relation)
    | ~ single_valued_class(subset_relation)
    | ~ spl0_115
    | ~ spl0_442 ),
    inference(resolution,[],[f5594,f900]) ).

fof(f5594,plain,
    ( subclass(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_442 ),
    inference(avatar_component_clause,[],[f5592]) ).

fof(f7093,plain,
    ( spl0_520
    | ~ spl0_61
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1721,f1718,f527,f7091]) ).

fof(f7091,plain,
    ( spl0_520
  <=> ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f1721,plain,
    ( ! [X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),element_relation)
        | member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_61
    | ~ spl0_199 ),
    inference(superposition,[],[f528,f1719]) ).

fof(f7089,plain,
    ( spl0_519
    | ~ spl0_131
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1616,f1591,f1019,f7087]) ).

fof(f7087,plain,
    ( spl0_519
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f1616,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class) )
    | ~ spl0_131
    | ~ spl0_188 ),
    inference(duplicate_literal_removal,[],[f1615]) ).

fof(f1615,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(X1,domain_of(X0)),not_subclass_element(X1,domain_of(X0))),universal_class))
        | subclass(X1,domain_of(X0))
        | ~ subclass(X1,universal_class)
        | subclass(X1,domain_of(X0)) )
    | ~ spl0_131
    | ~ spl0_188 ),
    inference(resolution,[],[f1592,f1020]) ).

fof(f7085,plain,
    ( ~ spl0_518
    | ~ spl0_183
    | spl0_192
    | ~ spl0_12
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1570,f1563,f255,f1608,f1545,f7082]) ).

fof(f7082,plain,
    ( spl0_518
  <=> inductive(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f1545,plain,
    ( spl0_183
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f1608,plain,
    ( spl0_192
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f1570,plain,
    ( member(null_class,subset_relation)
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_12
    | ~ spl0_186 ),
    inference(resolution,[],[f1564,f256]) ).

fof(f7080,plain,
    ( spl0_517
    | ~ spl0_31
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1509,f1463,f336,f7078]) ).

fof(f7078,plain,
    ( spl0_517
  <=> ! [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_517])]) ).

fof(f1509,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) )
    | ~ spl0_31
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f337]) ).

fof(f7076,plain,
    ( spl0_516
    | ~ spl0_32
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1508,f1463,f340,f7074]) ).

fof(f7074,plain,
    ( spl0_516
  <=> ! [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_516])]) ).

fof(f1508,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) )
    | ~ spl0_32
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f341]) ).

fof(f7067,plain,
    ( spl0_515
    | ~ spl0_31
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1491,f1459,f336,f7065]) ).

fof(f7065,plain,
    ( spl0_515
  <=> ! [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_515])]) ).

fof(f1491,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) )
    | ~ spl0_31
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f337]) ).

fof(f7063,plain,
    ( spl0_514
    | ~ spl0_32
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1490,f1459,f340,f7061]) ).

fof(f7061,plain,
    ( spl0_514
  <=> ! [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_514])]) ).

fof(f1490,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,intersection(X1,X2))
        | ~ member(X3,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) )
    | ~ spl0_32
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f341]) ).

fof(f7059,plain,
    ( spl0_513
    | ~ spl0_38
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1429,f1376,f373,f7057]) ).

fof(f7057,plain,
    ( spl0_513
  <=> ! [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_513])]) ).

fof(f1429,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) )
    | ~ spl0_38
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f374]) ).

fof(f7055,plain,
    ( spl0_512
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1353,f1323,f1166,f7053]) ).

fof(f7053,plain,
    ( spl0_512
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f1353,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1332]) ).

fof(f1332,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X1)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(superposition,[],[f1167,f1324]) ).

fof(f7051,plain,
    ( spl0_511
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1348,f1323,f1166,f7049]) ).

fof(f7049,plain,
    ( spl0_511
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).

fof(f1348,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1337]) ).

fof(f1337,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | member(X2,null_class)
        | ~ member(X2,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_143
    | ~ spl0_161 ),
    inference(superposition,[],[f1167,f1324]) ).

fof(f7047,plain,
    ( spl0_510
    | ~ spl0_49
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f979,f922,f449,f7045]) ).

fof(f7045,plain,
    ( spl0_510
  <=> ! [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_510])]) ).

fof(f979,plain,
    ( ! [X2,X0,X1] :
        ( subclass(complement(intersection(X0,X1)),X2)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
        | ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) )
    | ~ spl0_49
    | ~ spl0_116 ),
    inference(resolution,[],[f923,f450]) ).

fof(f6923,plain,
    ( spl0_509
    | ~ spl0_28
    | ~ spl0_338 ),
    inference(avatar_split_clause,[],[f3475,f3352,f324,f6921]) ).

fof(f6921,plain,
    ( spl0_509
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).

fof(f3475,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),subset_relation)
    | ~ spl0_28
    | ~ spl0_338 ),
    inference(duplicate_literal_removal,[],[f3462]) ).

fof(f3462,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),subset_relation)
        | subclass(intersection(X0,singleton_relation),subset_relation) )
    | ~ spl0_28
    | ~ spl0_338 ),
    inference(resolution,[],[f3353,f325]) ).

fof(f6895,plain,
    ( spl0_508
    | ~ spl0_237
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f6859,f6856,f2324,f6893]) ).

fof(f6893,plain,
    ( spl0_508
  <=> ! [X0] :
        ( member(X0,singleton_relation)
        | null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f6856,plain,
    ( spl0_499
  <=> ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f6859,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_237
    | ~ spl0_499 ),
    inference(forward_demodulation,[],[f6857,f2326]) ).

fof(f6857,plain,
    ( ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_499 ),
    inference(avatar_component_clause,[],[f6856]) ).

fof(f6891,plain,
    ( spl0_507
    | ~ spl0_68
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1882,f1875,f561,f6889]) ).

fof(f6889,plain,
    ( spl0_507
  <=> ! [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_507])]) ).

fof(f1882,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(composition_function,cross_product(X0,X1))
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f562]) ).

fof(f6887,plain,
    ( spl0_506
    | ~ spl0_20
    | ~ spl0_172 ),
    inference(avatar_split_clause,[],[f1510,f1463,f288,f6885]) ).

fof(f6885,plain,
    ( spl0_506
  <=> ! [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_506])]) ).

fof(f1510,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) )
    | ~ spl0_20
    | ~ spl0_172 ),
    inference(resolution,[],[f1464,f289]) ).

fof(f6883,plain,
    ( spl0_505
    | ~ spl0_20
    | ~ spl0_171 ),
    inference(avatar_split_clause,[],[f1492,f1459,f288,f6881]) ).

fof(f6881,plain,
    ( spl0_505
  <=> ! [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_505])]) ).

fof(f1492,plain,
    ( ! [X2,X0,X1] :
        ( ~ function(X0)
        | ~ subclass(universal_class,complement(X1))
        | ~ member(X2,universal_class)
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) )
    | ~ spl0_20
    | ~ spl0_171 ),
    inference(resolution,[],[f1460,f289]) ).

fof(f6879,plain,
    ( spl0_504
    | ~ spl0_31
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1433,f1376,f336,f6877]) ).

fof(f6877,plain,
    ( spl0_504
  <=> ! [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_504])]) ).

fof(f1433,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) )
    | ~ spl0_31
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f337]) ).

fof(f6875,plain,
    ( spl0_503
    | ~ spl0_32
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1432,f1376,f340,f6873]) ).

fof(f6873,plain,
    ( spl0_503
  <=> ! [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_503])]) ).

fof(f1432,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) )
    | ~ spl0_32
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f341]) ).

fof(f6871,plain,
    ( spl0_502
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f3436,f3330,f324,f6869]) ).

fof(f6869,plain,
    ( spl0_502
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f3436,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),subset_relation)
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(duplicate_literal_removal,[],[f3423]) ).

fof(f3423,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),subset_relation)
        | subclass(intersection(singleton_relation,X0),subset_relation) )
    | ~ spl0_28
    | ~ spl0_335 ),
    inference(resolution,[],[f3331,f325]) ).

fof(f6867,plain,
    ( spl0_501
    | ~ spl0_110
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1389,f1368,f822,f6865]) ).

fof(f6865,plain,
    ( spl0_501
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(null_class,X2)
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).

fof(f822,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1389,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(null_class,X2)
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_110
    | ~ spl0_164 ),
    inference(resolution,[],[f1369,f823]) ).

fof(f823,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f822]) ).

fof(f6863,plain,
    ( spl0_500
    | ~ spl0_38
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1363,f1358,f373,f6861]) ).

fof(f6861,plain,
    ( spl0_500
  <=> ! [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_500])]) ).

fof(f1363,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_163 ),
    inference(resolution,[],[f1359,f374]) ).

fof(f6858,plain,
    ( spl0_499
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1224,f1174,f569,f453,f6856]) ).

fof(f1224,plain,
    ( ! [X0] :
        ( null_class = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_50
    | ~ spl0_70
    | ~ spl0_145 ),
    inference(forward_demodulation,[],[f1211,f454]) ).

fof(f1211,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,identity_relation)
        | ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),flip(cross_product(subset_relation,universal_class))) )
    | ~ spl0_70
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f570]) ).

fof(f6740,plain,
    ( spl0_498
    | ~ spl0_237
    | ~ spl0_246
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3411,f3231,f2381,f2324,f6737]) ).

fof(f3411,plain,
    ( subclass(singleton_relation,intersection(subset_relation,singleton_relation))
    | ~ spl0_237
    | ~ spl0_246
    | ~ spl0_330 ),
    inference(forward_demodulation,[],[f3396,f2326]) ).

fof(f3396,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_246
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3387]) ).

fof(f3387,plain,
    ( subclass(identity_relation,intersection(subset_relation,identity_relation))
    | subclass(identity_relation,intersection(subset_relation,identity_relation))
    | ~ spl0_246
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f2382]) ).

fof(f6647,plain,
    ( spl0_497
    | ~ spl0_237
    | ~ spl0_485 ),
    inference(avatar_split_clause,[],[f6471,f6468,f2324,f6645]) ).

fof(f6645,plain,
    ( spl0_497
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),singleton_relation)
        | ~ member(not_subclass_element(X0,X1),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f6468,plain,
    ( spl0_485
  <=> ! [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_485])]) ).

fof(f6471,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),singleton_relation)
        | ~ member(not_subclass_element(X0,X1),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_237
    | ~ spl0_485 ),
    inference(forward_demodulation,[],[f6469,f2326]) ).

fof(f6469,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_485 ),
    inference(avatar_component_clause,[],[f6468]) ).

fof(f6643,plain,
    ( spl0_496
    | ~ spl0_237
    | ~ spl0_484 ),
    inference(avatar_split_clause,[],[f6466,f6463,f2324,f6641]) ).

fof(f6641,plain,
    ( spl0_496
  <=> ! [X0,X1] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f6463,plain,
    ( spl0_484
  <=> ! [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_484])]) ).

fof(f6466,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | subclass(X0,X1) )
    | ~ spl0_237
    | ~ spl0_484 ),
    inference(forward_demodulation,[],[f6464,f2326]) ).

fof(f6464,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_484 ),
    inference(avatar_component_clause,[],[f6463]) ).

fof(f6511,plain,
    ( spl0_494
    | ~ spl0_495
    | ~ spl0_85
    | ~ spl0_206 ),
    inference(avatar_split_clause,[],[f1879,f1875,f667,f6508,f6505]) ).

fof(f6505,plain,
    ( spl0_494
  <=> ! [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_494])]) ).

fof(f6508,plain,
    ( spl0_495
  <=> subclass(composition_function,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f1879,plain,
    ( ! [X0,X1] :
        ( ~ subclass(composition_function,application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(X1,domain_of(X0)) )
    | ~ spl0_85
    | ~ spl0_206 ),
    inference(resolution,[],[f1876,f668]) ).

fof(f6503,plain,
    ( spl0_493
    | ~ spl0_68
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1724,f1718,f561,f6501]) ).

fof(f1724,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(first(regular(cross_product(X0,X1))),X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_68
    | ~ spl0_199 ),
    inference(superposition,[],[f562,f1719]) ).

fof(f6499,plain,
    ( spl0_492
    | ~ spl0_27
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3405,f3231,f320,f6497]) ).

fof(f3405,plain,
    ( ! [X0] : subclass(X0,intersection(X0,X0))
    | ~ spl0_27
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3370]) ).

fof(f3370,plain,
    ( ! [X0] :
        ( subclass(X0,intersection(X0,X0))
        | subclass(X0,intersection(X0,X0)) )
    | ~ spl0_27
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f321]) ).

fof(f6495,plain,
    ( spl0_491
    | ~ spl0_67
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1723,f1718,f557,f6493]) ).

fof(f1723,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
        | member(second(regular(cross_product(X0,X1))),X3)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_67
    | ~ spl0_199 ),
    inference(superposition,[],[f558,f1719]) ).

fof(f6491,plain,
    ( spl0_490
    | ~ spl0_22
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1447,f1380,f296,f6489]) ).

fof(f6489,plain,
    ( spl0_490
  <=> ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f1447,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ member(X0,universal_class)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(domain_of(X1)) )
    | ~ spl0_22
    | ~ spl0_167 ),
    inference(resolution,[],[f1381,f297]) ).

fof(f6487,plain,
    ( spl0_489
    | ~ spl0_20
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1434,f1376,f288,f6485]) ).

fof(f1434,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) )
    | ~ spl0_20
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f289]) ).

fof(f6483,plain,
    ( spl0_488
    | ~ spl0_132
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1388,f1368,f1023,f6481]) ).

fof(f6481,plain,
    ( spl0_488
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f1388,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_132
    | ~ spl0_164 ),
    inference(resolution,[],[f1369,f1024]) ).

fof(f6479,plain,
    ( spl0_487
    | ~ spl0_133
    | ~ spl0_164 ),
    inference(avatar_split_clause,[],[f1387,f1368,f1027,f6477]) ).

fof(f6477,plain,
    ( spl0_487
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).

fof(f1387,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_133
    | ~ spl0_164 ),
    inference(resolution,[],[f1369,f1028]) ).

fof(f6475,plain,
    ( spl0_486
    | ~ spl0_38
    | ~ spl0_162 ),
    inference(avatar_split_clause,[],[f1354,f1327,f373,f6473]) ).

fof(f6473,plain,
    ( spl0_486
  <=> ! [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_486])]) ).

fof(f1327,plain,
    ( spl0_162
  <=> ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f1354,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) )
    | ~ spl0_38
    | ~ spl0_162 ),
    inference(resolution,[],[f1328,f374]) ).

fof(f1328,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1327]) ).

fof(f6470,plain,
    ( spl0_485
    | ~ spl0_131
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1223,f1174,f1019,f6468]) ).

fof(f1223,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),subset_relation)
        | member(not_subclass_element(X0,X1),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f1020]) ).

fof(f6465,plain,
    ( spl0_484
    | ~ spl0_131
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1209,f1170,f1019,f6463]) ).

fof(f1209,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),element_relation)
        | member(not_subclass_element(X0,X1),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f1020]) ).

fof(f6461,plain,
    ( spl0_483
    | ~ spl0_131
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1195,f1166,f1019,f6459]) ).

fof(f6459,plain,
    ( spl0_483
  <=> ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | ~ member(not_subclass_element(X0,X1),X2)
        | null_class = X2
        | ~ subclass(X0,regular(X2))
        | subclass(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f1195,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(X0,X1),null_class)
        | ~ member(not_subclass_element(X0,X1),X2)
        | null_class = X2
        | ~ subclass(X0,regular(X2))
        | subclass(X0,X1) )
    | ~ spl0_131
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f1020]) ).

fof(f6457,plain,
    ( spl0_482
    | ~ spl0_76
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1150,f1094,f610,f6455]) ).

fof(f6455,plain,
    ( spl0_482
  <=> ! [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_482])]) ).

fof(f1150,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | subclass(subset_relation,X0) )
    | ~ spl0_76
    | ~ spl0_136 ),
    inference(superposition,[],[f1095,f612]) ).

fof(f6453,plain,
    ( spl0_481
    | ~ spl0_245
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f3400,f3231,f2377,f6450]) ).

fof(f3400,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_245
    | ~ spl0_330 ),
    inference(duplicate_literal_removal,[],[f3376]) ).

fof(f3376,plain,
    ( subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | subclass(singleton_relation,intersection(element_relation,singleton_relation))
    | ~ spl0_245
    | ~ spl0_330 ),
    inference(resolution,[],[f3232,f2378]) ).

fof(f6448,plain,
    ( spl0_480
    | ~ spl0_49
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f903,f891,f449,f6446]) ).

fof(f6446,plain,
    ( spl0_480
  <=> ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f903,plain,
    ( ! [X0,X1] :
        ( complement(intersection(X0,X1)) = null_class
        | ~ member(regular(complement(intersection(X0,X1))),X1)
        | ~ member(regular(complement(intersection(X0,X1))),X0) )
    | ~ spl0_49
    | ~ spl0_113 ),
    inference(resolution,[],[f892,f450]) ).

fof(f6289,plain,
    ( spl0_479
    | ~ spl0_27
    | ~ spl0_188 ),
    inference(avatar_split_clause,[],[f1619,f1591,f320,f6287]) ).

fof(f6287,plain,
    ( spl0_479
  <=> ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).

fof(f1619,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0)) )
    | ~ spl0_27
    | ~ spl0_188 ),
    inference(duplicate_literal_removal,[],[f1612]) ).

fof(f1612,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
        | subclass(universal_class,domain_of(X0))
        | subclass(universal_class,domain_of(X0)) )
    | ~ spl0_27
    | ~ spl0_188 ),
    inference(resolution,[],[f1592,f321]) ).

fof(f6285,plain,
    ( spl0_478
    | ~ spl0_49
    | ~ spl0_186 ),
    inference(avatar_split_clause,[],[f1583,f1563,f449,f6283]) ).

fof(f6283,plain,
    ( spl0_478
  <=> ! [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_478])]) ).

fof(f1583,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_49
    | ~ spl0_186 ),
    inference(duplicate_literal_removal,[],[f1567]) ).

fof(f1567,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_49
    | ~ spl0_186 ),
    inference(resolution,[],[f1564,f450]) ).

fof(f6281,plain,
    ( spl0_477
    | ~ spl0_28
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f3369,f3214,f324,f6279]) ).

fof(f6279,plain,
    ( spl0_477
  <=> ! [X0] : subclass(intersection(X0,singleton_relation),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f3369,plain,
    ( ! [X0] : subclass(intersection(X0,singleton_relation),element_relation)
    | ~ spl0_28
    | ~ spl0_327 ),
    inference(duplicate_literal_removal,[],[f3360]) ).

fof(f3360,plain,
    ( ! [X0] :
        ( subclass(intersection(X0,singleton_relation),element_relation)
        | subclass(intersection(X0,singleton_relation),element_relation) )
    | ~ spl0_28
    | ~ spl0_327 ),
    inference(resolution,[],[f3215,f325]) ).

fof(f6277,plain,
    ( ~ spl0_476
    | ~ spl0_237
    | spl0_475 ),
    inference(avatar_split_clause,[],[f6272,f6268,f2324,f6274]) ).

fof(f6274,plain,
    ( spl0_476
  <=> subclass(domain_relation,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f6268,plain,
    ( spl0_475
  <=> subclass(domain_relation,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f6272,plain,
    ( ~ subclass(domain_relation,singleton_relation)
    | ~ spl0_237
    | spl0_475 ),
    inference(forward_demodulation,[],[f6270,f2326]) ).

fof(f6270,plain,
    ( ~ subclass(domain_relation,identity_relation)
    | spl0_475 ),
    inference(avatar_component_clause,[],[f6268]) ).

fof(f6271,plain,
    ( spl0_474
    | ~ spl0_475
    | ~ spl0_104
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1440,f1376,f768,f6268,f6265]) ).

fof(f6265,plain,
    ( spl0_474
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f1440,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_104
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f769]) ).

fof(f6263,plain,
    ( spl0_473
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1351,f1323,f926,f6261]) ).

fof(f6261,plain,
    ( spl0_473
  <=> ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f1351,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1334]) ).

fof(f1334,plain,
    ( ! [X2,X0,X1] :
        ( member(X1,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(superposition,[],[f927,f1324]) ).

fof(f6259,plain,
    ( spl0_472
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1346,f1323,f926,f6257]) ).

fof(f6257,plain,
    ( spl0_472
  <=> ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f1346,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1339]) ).

fof(f1339,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X2)
        | ~ subclass(unordered_pair(X0,X1),X2)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_117
    | ~ spl0_161 ),
    inference(superposition,[],[f927,f1324]) ).

fof(f6255,plain,
    ( spl0_471
    | ~ spl0_27
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1185,f1166,f320,f6253]) ).

fof(f6253,plain,
    ( spl0_471
  <=> ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),null_class)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | null_class = X0
        | subclass(regular(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f1185,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(regular(X0),X1),null_class)
        | ~ member(not_subclass_element(regular(X0),X1),X0)
        | null_class = X0
        | subclass(regular(X0),X1) )
    | ~ spl0_27
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f321]) ).

fof(f6243,plain,
    ( spl0_276
    | spl0_470
    | ~ spl0_76
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1063,f1015,f610,f6240,f2551]) ).

fof(f1063,plain,
    ( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | null_class = subset_relation
    | ~ spl0_76
    | ~ spl0_130 ),
    inference(superposition,[],[f1016,f612]) ).

fof(f6238,plain,
    ( spl0_469
    | ~ spl0_44
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f980,f922,f425,f6236]) ).

fof(f6236,plain,
    ( spl0_469
  <=> ! [X0,X1] :
        ( subclass(complement(complement(X0)),X1)
        | member(not_subclass_element(complement(complement(X0)),X1),X0)
        | ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f980,plain,
    ( ! [X0,X1] :
        ( subclass(complement(complement(X0)),X1)
        | member(not_subclass_element(complement(complement(X0)),X1),X0)
        | ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) )
    | ~ spl0_44
    | ~ spl0_116 ),
    inference(resolution,[],[f923,f426]) ).

fof(f6234,plain,
    ( spl0_468
    | ~ spl0_79
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f882,f830,f630,f6232]) ).

fof(f6232,plain,
    ( spl0_468
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f882,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
    | ~ spl0_79
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f631]) ).

fof(f6229,plain,
    ( spl0_466
    | ~ spl0_467
    | ~ spl0_84
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f835,f818,f662,f6226,f6223]) ).

fof(f6223,plain,
    ( spl0_466
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f6226,plain,
    ( spl0_467
  <=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f835,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_84
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f663]) ).

fof(f6071,plain,
    ( spl0_465
    | ~ spl0_237
    | ~ spl0_458 ),
    inference(avatar_split_clause,[],[f5958,f5955,f2324,f6069]) ).

fof(f6069,plain,
    ( spl0_465
  <=> ! [X0] :
        ( member(regular(X0),singleton_relation)
        | ~ member(regular(X0),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).

fof(f5955,plain,
    ( spl0_458
  <=> ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f5958,plain,
    ( ! [X0] :
        ( member(regular(X0),singleton_relation)
        | ~ member(regular(X0),subset_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_237
    | ~ spl0_458 ),
    inference(forward_demodulation,[],[f5956,f2326]) ).

fof(f5956,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_458 ),
    inference(avatar_component_clause,[],[f5955]) ).

fof(f6067,plain,
    ( spl0_464
    | ~ spl0_237
    | ~ spl0_457 ),
    inference(avatar_split_clause,[],[f5953,f5950,f2324,f6065]) ).

fof(f6065,plain,
    ( spl0_464
  <=> ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f5950,plain,
    ( spl0_457
  <=> ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f5953,plain,
    ( ! [X0] :
        ( ~ subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | null_class = X0 )
    | ~ spl0_237
    | ~ spl0_457 ),
    inference(forward_demodulation,[],[f5951,f2326]) ).

fof(f5951,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 )
    | ~ spl0_457 ),
    inference(avatar_component_clause,[],[f5950]) ).

fof(f5987,plain,
    ( spl0_463
    | ~ spl0_28
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f3342,f3188,f324,f5985]) ).

fof(f5985,plain,
    ( spl0_463
  <=> ! [X0] : subclass(intersection(singleton_relation,X0),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f3342,plain,
    ( ! [X0] : subclass(intersection(singleton_relation,X0),element_relation)
    | ~ spl0_28
    | ~ spl0_322 ),
    inference(duplicate_literal_removal,[],[f3333]) ).

fof(f3333,plain,
    ( ! [X0] :
        ( subclass(intersection(singleton_relation,X0),element_relation)
        | subclass(intersection(singleton_relation,X0),element_relation) )
    | ~ spl0_28
    | ~ spl0_322 ),
    inference(resolution,[],[f3189,f325]) ).

fof(f5974,plain,
    ( spl0_462
    | ~ spl0_237
    | ~ spl0_454 ),
    inference(avatar_split_clause,[],[f5940,f5937,f2324,f5972]) ).

fof(f5972,plain,
    ( spl0_462
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f5937,plain,
    ( spl0_454
  <=> ! [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_454])]) ).

fof(f5940,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),singleton_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
    | ~ spl0_237
    | ~ spl0_454 ),
    inference(forward_demodulation,[],[f5938,f2326]) ).

fof(f5938,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_454 ),
    inference(avatar_component_clause,[],[f5937]) ).

fof(f5970,plain,
    ( spl0_461
    | ~ spl0_237
    | ~ spl0_452 ),
    inference(avatar_split_clause,[],[f5930,f5926,f2324,f5968]) ).

fof(f5968,plain,
    ( spl0_461
  <=> ! [X0] :
        ( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
        | ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f5926,plain,
    ( spl0_452
  <=> ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f5930,plain,
    ( ! [X0] :
        ( subclass(complement(complement(compose(element_relation,complement(singleton_relation)))),X0)
        | ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f5929,f2326]) ).

fof(f5929,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(singleton_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_237
    | ~ spl0_452 ),
    inference(forward_demodulation,[],[f5927,f2326]) ).

fof(f5927,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_452 ),
    inference(avatar_component_clause,[],[f5926]) ).

fof(f5966,plain,
    ( spl0_460
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1350,f1323,f381,f5964]) ).

fof(f5964,plain,
    ( spl0_460
  <=> ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f1350,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1335]) ).

fof(f1335,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X1)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(superposition,[],[f382,f1324]) ).

fof(f5962,plain,
    ( spl0_459
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1345,f1323,f381,f5960]) ).

fof(f5960,plain,
    ( spl0_459
  <=> ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f1345,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1340]) ).

fof(f1340,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(unordered_pair(X0,X1),X0)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_40
    | ~ spl0_161 ),
    inference(superposition,[],[f382,f1324]) ).

fof(f5957,plain,
    ( spl0_458
    | ~ spl0_117
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1219,f1174,f926,f5955]) ).

fof(f1219,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),subset_relation)
        | member(regular(X0),identity_relation)
        | ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f927]) ).

fof(f5952,plain,
    ( spl0_457
    | ~ spl0_117
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1205,f1170,f926,f5950]) ).

fof(f1205,plain,
    ( ! [X0] :
        ( ~ member(regular(X0),element_relation)
        | member(regular(X0),singleton_relation)
        | ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f927]) ).

fof(f5948,plain,
    ( spl0_456
    | ~ spl0_117
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1191,f1166,f926,f5946]) ).

fof(f1191,plain,
    ( ! [X0,X1] :
        ( member(regular(X0),null_class)
        | ~ member(regular(X0),X1)
        | null_class = X1
        | ~ subclass(X0,regular(X1))
        | null_class = X0 )
    | ~ spl0_117
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f927]) ).

fof(f5944,plain,
    ( spl0_455
    | ~ spl0_48
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1069,f1019,f445,f5942]) ).

fof(f5942,plain,
    ( spl0_455
  <=> ! [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_455])]) ).

fof(f1069,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | subclass(X0,X3)
        | not_subclass_element(X0,X3) = X1
        | not_subclass_element(X0,X3) = X2 )
    | ~ spl0_48
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f446]) ).

fof(f5939,plain,
    ( spl0_454
    | ~ spl0_116
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1006,f966,f922,f5937]) ).

fof(f1006,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
        | subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
    | ~ spl0_116
    | ~ spl0_126 ),
    inference(resolution,[],[f967,f923]) ).

fof(f5935,plain,
    ( spl0_453
    | ~ spl0_237
    | ~ spl0_246
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f3258,f3158,f2381,f2324,f5932]) ).

fof(f3258,plain,
    ( subclass(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_237
    | ~ spl0_246
    | ~ spl0_315 ),
    inference(forward_demodulation,[],[f3257,f2326]) ).

fof(f3257,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_246
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f3246]) ).

fof(f3246,plain,
    ( subclass(identity_relation,cross_product(universal_class,universal_class))
    | subclass(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_246
    | ~ spl0_315 ),
    inference(resolution,[],[f3159,f2382]) ).

fof(f5928,plain,
    ( spl0_452
    | ~ spl0_116
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1002,f962,f922,f5926]) ).

fof(f1002,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
        | subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
    | ~ spl0_116
    | ~ spl0_125 ),
    inference(resolution,[],[f963,f923]) ).

fof(f5867,plain,
    ( spl0_451
    | ~ spl0_237
    | ~ spl0_447 ),
    inference(avatar_split_clause,[],[f5619,f5614,f2324,f5865]) ).

fof(f5865,plain,
    ( spl0_451
  <=> ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f5614,plain,
    ( spl0_447
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).

fof(f5619,plain,
    ( ! [X0] :
        ( subclass(X0,singleton_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation) )
    | ~ spl0_237
    | ~ spl0_447 ),
    inference(forward_demodulation,[],[f5618,f2326]) ).

fof(f5618,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | subclass(X0,identity_relation) )
    | ~ spl0_237
    | ~ spl0_447 ),
    inference(forward_demodulation,[],[f5617,f2326]) ).

fof(f5617,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_237
    | ~ spl0_447 ),
    inference(forward_demodulation,[],[f5615,f2326]) ).

fof(f5615,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_447 ),
    inference(avatar_component_clause,[],[f5614]) ).

fof(f5863,plain,
    ( spl0_450
    | ~ spl0_237
    | ~ spl0_446 ),
    inference(avatar_split_clause,[],[f5612,f5609,f2324,f5861]) ).

fof(f5861,plain,
    ( spl0_450
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f5609,plain,
    ( spl0_446
  <=> ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).

fof(f5612,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | subclass(X0,singleton_relation) )
    | ~ spl0_237
    | ~ spl0_446 ),
    inference(forward_demodulation,[],[f5610,f2326]) ).

fof(f5610,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_446 ),
    inference(avatar_component_clause,[],[f5609]) ).

fof(f5692,plain,
    ( spl0_183
    | ~ spl0_6
    | ~ spl0_267 ),
    inference(avatar_split_clause,[],[f2529,f2497,f229,f1545]) ).

fof(f2497,plain,
    ( spl0_267
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f2529,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_6
    | ~ spl0_267 ),
    inference(resolution,[],[f2498,f230]) ).

fof(f2498,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_267 ),
    inference(avatar_component_clause,[],[f2497]) ).

fof(f5627,plain,
    ( spl0_448
    | ~ spl0_449
    | ~ spl0_78
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1421,f1376,f626,f5624,f5621]) ).

fof(f5621,plain,
    ( spl0_448
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f5624,plain,
    ( spl0_449
  <=> subclass(domain_relation,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f1421,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,successor_relation)
        | ~ member(X0,universal_class)
        | domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
    | ~ spl0_78
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f627]) ).

fof(f5616,plain,
    ( spl0_447
    | ~ spl0_43
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1410,f1372,f394,f5614]) ).

fof(f1410,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
        | ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(X0,identity_relation) )
    | ~ spl0_43
    | ~ spl0_165 ),
    inference(superposition,[],[f1373,f396]) ).

fof(f5611,plain,
    ( spl0_446
    | ~ spl0_41
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1409,f1372,f385,f5609]) ).

fof(f1409,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
        | ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
        | subclass(X0,singleton_relation) )
    | ~ spl0_41
    | ~ spl0_165 ),
    inference(superposition,[],[f1373,f387]) ).

fof(f5607,plain,
    ( spl0_445
    | ~ spl0_40
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1405,f1372,f381,f5605]) ).

fof(f5605,plain,
    ( spl0_445
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),regular(X0))
        | ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f1405,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X1,null_class),regular(X0))
        | ~ member(not_subclass_element(X1,null_class),X0)
        | subclass(X1,null_class)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_165 ),
    inference(superposition,[],[f1373,f382]) ).

fof(f5603,plain,
    ( spl0_444
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1352,f1323,f958,f5601]) ).

fof(f5601,plain,
    ( spl0_444
  <=> ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f1352,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1333]) ).

fof(f1333,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X1)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(superposition,[],[f959,f1324]) ).

fof(f5599,plain,
    ( spl0_443
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1347,f1323,f958,f5597]) ).

fof(f5597,plain,
    ( spl0_443
  <=> ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f1347,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1338]) ).

fof(f1338,plain,
    ( ! [X2,X0,X1] :
        ( member(X2,X0)
        | ~ member(X2,null_class)
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_124
    | ~ spl0_161 ),
    inference(superposition,[],[f959,f1324]) ).

fof(f5595,plain,
    ( spl0_442
    | ~ spl0_76
    | ~ spl0_224 ),
    inference(avatar_split_clause,[],[f2245,f2230,f610,f5592]) ).

fof(f2245,plain,
    ( subclass(subset_relation,cross_product(universal_class,universal_class))
    | ~ spl0_76
    | ~ spl0_224 ),
    inference(superposition,[],[f2231,f612]) ).

fof(f5590,plain,
    ( spl0_441
    | ~ spl0_38
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1266,f1254,f373,f5588]) ).

fof(f5588,plain,
    ( spl0_441
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f1266,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ member(X1,universal_class)
        | ~ subclass(X0,X2)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
    | ~ spl0_38
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f374]) ).

fof(f5586,plain,
    ( ~ spl0_439
    | spl0_440
    | ~ spl0_109
    | ~ spl0_145 ),
    inference(avatar_split_clause,[],[f1222,f1174,f818,f5584,f5580]) ).

fof(f5580,plain,
    ( spl0_439
  <=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).

fof(f5584,plain,
    ( spl0_440
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f1222,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),subset_relation)
        | member(unordered_pair(X0,X1),identity_relation)
        | ~ subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_109
    | ~ spl0_145 ),
    inference(resolution,[],[f1175,f819]) ).

fof(f5578,plain,
    ( ~ spl0_438
    | ~ spl0_237
    | spl0_436 ),
    inference(avatar_split_clause,[],[f5573,f5566,f2324,f5575]) ).

fof(f5575,plain,
    ( spl0_438
  <=> subclass(universal_class,complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f5573,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_237
    | spl0_436 ),
    inference(forward_demodulation,[],[f5568,f2326]) ).

fof(f5568,plain,
    ( ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation))))
    | spl0_436 ),
    inference(avatar_component_clause,[],[f5566]) ).

fof(f5572,plain,
    ( ~ spl0_436
    | spl0_437
    | ~ spl0_109
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1208,f1170,f818,f5570,f5566]) ).

fof(f5570,plain,
    ( spl0_437
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f1208,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),element_relation)
        | member(unordered_pair(X0,X1),singleton_relation)
        | ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_109
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f819]) ).

fof(f5564,plain,
    ( spl0_435
    | ~ spl0_109
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1194,f1166,f818,f5562]) ).

fof(f1194,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(X0,X1),null_class)
        | ~ member(unordered_pair(X0,X1),X2)
        | null_class = X2
        | ~ subclass(universal_class,regular(X2)) )
    | ~ spl0_109
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f819]) ).

fof(f5560,plain,
    ( spl0_434
    | ~ spl0_23
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1189,f1166,f300,f5558]) ).

fof(f5558,plain,
    ( spl0_434
  <=> ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f1189,plain,
    ( ! [X0] :
        ( member(regular(regular(X0)),null_class)
        | ~ member(regular(regular(X0)),X0)
        | null_class = X0
        | null_class = regular(X0) )
    | ~ spl0_23
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f301]) ).

fof(f5555,plain,
    ( ~ spl0_433
    | ~ spl0_237
    | spl0_432 ),
    inference(avatar_split_clause,[],[f5550,f5546,f2324,f5552]) ).

fof(f5552,plain,
    ( spl0_433
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f5546,plain,
    ( spl0_432
  <=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f5550,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),singleton_relation)
    | ~ spl0_237
    | spl0_432 ),
    inference(forward_demodulation,[],[f5548,f2326]) ).

fof(f5548,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | spl0_432 ),
    inference(avatar_component_clause,[],[f5546]) ).

fof(f5549,plain,
    ( spl0_431
    | ~ spl0_432
    | ~ spl0_113
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1008,f966,f891,f5546,f5542]) ).

fof(f1008,plain,
    ( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
    | null_class = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_113
    | ~ spl0_126 ),
    inference(resolution,[],[f967,f892]) ).

fof(f5539,plain,
    ( ~ spl0_430
    | ~ spl0_237
    | spl0_428 ),
    inference(avatar_split_clause,[],[f5528,f5524,f2324,f5536]) ).

fof(f5536,plain,
    ( spl0_430
  <=> member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f5524,plain,
    ( spl0_428
  <=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).

fof(f5528,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(singleton_relation))))),singleton_relation)
    | ~ spl0_237
    | spl0_428 ),
    inference(forward_demodulation,[],[f5526,f2326]) ).

fof(f5526,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | spl0_428 ),
    inference(avatar_component_clause,[],[f5524]) ).

fof(f5534,plain,
    ( ~ spl0_429
    | ~ spl0_237
    | spl0_427 ),
    inference(avatar_split_clause,[],[f5529,f5520,f2324,f5531]) ).

fof(f5531,plain,
    ( spl0_429
  <=> null_class = complement(complement(compose(element_relation,complement(singleton_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f5529,plain,
    ( null_class != complement(complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_237
    | spl0_427 ),
    inference(forward_demodulation,[],[f5521,f2326]) ).

fof(f5521,plain,
    ( null_class != complement(complement(compose(element_relation,complement(identity_relation))))
    | spl0_427 ),
    inference(avatar_component_clause,[],[f5520]) ).

fof(f5527,plain,
    ( spl0_427
    | ~ spl0_428
    | ~ spl0_113
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1003,f962,f891,f5524,f5520]) ).

fof(f1003,plain,
    ( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
    | null_class = complement(complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_113
    | ~ spl0_125 ),
    inference(resolution,[],[f963,f892]) ).

fof(f5518,plain,
    ( spl0_426
    | ~ spl0_44
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f904,f891,f425,f5516]) ).

fof(f5516,plain,
    ( spl0_426
  <=> ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f904,plain,
    ( ! [X0] :
        ( null_class = complement(complement(X0))
        | member(regular(complement(complement(X0))),X0)
        | ~ member(regular(complement(complement(X0))),universal_class) )
    | ~ spl0_44
    | ~ spl0_113 ),
    inference(resolution,[],[f892,f426]) ).

fof(f5206,plain,
    ( spl0_425
    | ~ spl0_237
    | ~ spl0_413 ),
    inference(avatar_split_clause,[],[f4863,f4860,f2324,f5204]) ).

fof(f5204,plain,
    ( spl0_425
  <=> ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f4860,plain,
    ( spl0_413
  <=> ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f4863,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_237
    | ~ spl0_413 ),
    inference(forward_demodulation,[],[f4861,f2326]) ).

fof(f4861,plain,
    ( ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_413 ),
    inference(avatar_component_clause,[],[f4860]) ).

fof(f5202,plain,
    ( spl0_424
    | ~ spl0_237
    | ~ spl0_412 ),
    inference(avatar_split_clause,[],[f4858,f4855,f2324,f5200]) ).

fof(f5200,plain,
    ( spl0_424
  <=> ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f4855,plain,
    ( spl0_412
  <=> ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f4858,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,complement(compose(element_relation,complement(singleton_relation))))
        | ~ subclass(singleton_relation,X0)
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_237
    | ~ spl0_412 ),
    inference(forward_demodulation,[],[f4856,f2326]) ).

fof(f4856,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_412 ),
    inference(avatar_component_clause,[],[f4855]) ).

fof(f5198,plain,
    ( ~ spl0_422
    | spl0_423
    | ~ spl0_115
    | ~ spl0_349 ),
    inference(avatar_split_clause,[],[f3899,f3521,f899,f5195,f5191]) ).

fof(f5191,plain,
    ( spl0_422
  <=> single_valued_class(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).

fof(f5195,plain,
    ( spl0_423
  <=> function(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).

fof(f3899,plain,
    ( function(null_class)
    | ~ single_valued_class(null_class)
    | ~ spl0_115
    | ~ spl0_349 ),
    inference(resolution,[],[f3522,f900]) ).

fof(f4908,plain,
    ( spl0_421
    | ~ spl0_237
    | ~ spl0_406 ),
    inference(avatar_split_clause,[],[f4810,f4807,f2324,f4906]) ).

fof(f4807,plain,
    ( spl0_406
  <=> ! [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_406])]) ).

fof(f4810,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),singleton_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_237
    | ~ spl0_406 ),
    inference(forward_demodulation,[],[f4808,f2326]) ).

fof(f4808,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_406 ),
    inference(avatar_component_clause,[],[f4807]) ).

fof(f4904,plain,
    ( spl0_420
    | ~ spl0_237
    | ~ spl0_405 ),
    inference(avatar_split_clause,[],[f4805,f4801,f2324,f4902]) ).

fof(f4801,plain,
    ( spl0_405
  <=> ! [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_405])]) ).

fof(f4805,plain,
    ( ! [X0] :
        ( subclass(X0,complement(compose(element_relation,complement(singleton_relation))))
        | ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation) )
    | ~ spl0_237
    | ~ spl0_405 ),
    inference(forward_demodulation,[],[f4804,f2326]) ).

fof(f4804,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(singleton_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_237
    | ~ spl0_405 ),
    inference(forward_demodulation,[],[f4802,f2326]) ).

fof(f4802,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_405 ),
    inference(avatar_component_clause,[],[f4801]) ).

fof(f4891,plain,
    ( spl0_419
    | ~ spl0_135
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1413,f1372,f1090,f4889]) ).

fof(f1413,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_135
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1394]) ).

fof(f1394,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X0))
        | subclass(intersection(X0,X1),intersection(X2,X0)) )
    | ~ spl0_135
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f1091]) ).

fof(f4887,plain,
    ( spl0_418
    | ~ spl0_136
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1412,f1372,f1094,f4885]) ).

fof(f1412,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_136
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1395]) ).

fof(f1395,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
        | subclass(intersection(X0,X1),intersection(X2,X1))
        | subclass(intersection(X0,X1),intersection(X2,X1)) )
    | ~ spl0_136
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f1095]) ).

fof(f4879,plain,
    ( spl0_417
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1349,f1323,f300,f4877]) ).

fof(f4877,plain,
    ( spl0_417
  <=> ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f1349,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0 )
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1336]) ).

fof(f1336,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(superposition,[],[f301,f1324]) ).

fof(f4875,plain,
    ( spl0_416
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1344,f1323,f300,f4873]) ).

fof(f4873,plain,
    ( spl0_416
  <=> ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f1344,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1 )
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(duplicate_literal_removal,[],[f1341]) ).

fof(f1341,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | unordered_pair(X0,X1) = null_class
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_161 ),
    inference(superposition,[],[f301,f1324]) ).

fof(f4871,plain,
    ( spl0_415
    | ~ spl0_31
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1270,f1254,f336,f4869]) ).

fof(f4869,plain,
    ( spl0_415
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f1270,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) )
    | ~ spl0_31
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f337]) ).

fof(f4867,plain,
    ( spl0_414
    | ~ spl0_32
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1269,f1254,f340,f4865]) ).

fof(f4865,plain,
    ( spl0_414
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).

fof(f1269,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) )
    | ~ spl0_32
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f341]) ).

fof(f4862,plain,
    ( spl0_413
    | ~ spl0_43
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1265,f1250,f394,f4860]) ).

fof(f1265,plain,
    ( ! [X0,X1] :
        ( ~ subclass(identity_relation,X0)
        | ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
        | ~ member(X1,subset_relation)
        | member(X1,X0) )
    | ~ spl0_43
    | ~ spl0_152 ),
    inference(superposition,[],[f1251,f396]) ).

fof(f4857,plain,
    ( spl0_412
    | ~ spl0_41
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1264,f1250,f385,f4855]) ).

fof(f1264,plain,
    ( ! [X0,X1] :
        ( ~ subclass(singleton_relation,X0)
        | ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
        | ~ member(X1,element_relation)
        | member(X1,X0) )
    | ~ spl0_41
    | ~ spl0_152 ),
    inference(superposition,[],[f1251,f387]) ).

fof(f4853,plain,
    ( spl0_411
    | ~ spl0_40
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1260,f1250,f381,f4851]) ).

fof(f4851,plain,
    ( spl0_411
  <=> ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f1260,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(null_class,X1)
        | ~ member(X2,X0)
        | ~ member(X2,regular(X0))
        | member(X2,X1)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_152 ),
    inference(superposition,[],[f1251,f382]) ).

fof(f4849,plain,
    ( spl0_410
    | ~ spl0_31
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1141,f1094,f336,f4847]) ).

fof(f1141,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
    | ~ spl0_31
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f337]) ).

fof(f4845,plain,
    ( spl0_409
    | ~ spl0_32
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1140,f1094,f340,f4843]) ).

fof(f1140,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,intersection(X1,X2)),X3)
        | member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
    | ~ spl0_32
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f341]) ).

fof(f4841,plain,
    ( spl0_408
    | ~ spl0_31
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1123,f1090,f336,f4839]) ).

fof(f1123,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
    | ~ spl0_31
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f337]) ).

fof(f4814,plain,
    ( spl0_407
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1122,f1090,f340,f4812]) ).

fof(f1122,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(intersection(X0,X1),X2),X3)
        | member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
    | ~ spl0_32
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f341]) ).

fof(f4809,plain,
    ( spl0_406
    | ~ spl0_28
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1005,f966,f324,f4807]) ).

fof(f1005,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
        | subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_28
    | ~ spl0_126 ),
    inference(resolution,[],[f967,f325]) ).

fof(f4803,plain,
    ( spl0_405
    | ~ spl0_28
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1001,f962,f324,f4801]) ).

fof(f1001,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
        | subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_28
    | ~ spl0_125 ),
    inference(resolution,[],[f963,f325]) ).

fof(f4799,plain,
    ( spl0_404
    | ~ spl0_48
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f985,f926,f445,f4797]) ).

fof(f4797,plain,
    ( spl0_404
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f985,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,unordered_pair(X1,X2))
        | null_class = X0
        | regular(X0) = X1
        | regular(X0) = X2 )
    | ~ spl0_48
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f446]) ).

fof(f4681,plain,
    ( spl0_403
    | ~ spl0_237
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f4284,f4281,f2324,f4679]) ).

fof(f4679,plain,
    ( spl0_403
  <=> ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).

fof(f4281,plain,
    ( spl0_395
  <=> ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f4284,plain,
    ( ! [X0] :
        ( member(X0,compose(element_relation,complement(singleton_relation)))
        | ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_237
    | ~ spl0_395 ),
    inference(forward_demodulation,[],[f4282,f2326]) ).

fof(f4282,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_395 ),
    inference(avatar_component_clause,[],[f4281]) ).

fof(f4634,plain,
    ( spl0_402
    | ~ spl0_236
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2910,f2324,f2318,f4631]) ).

fof(f2910,plain,
    ( member(regular(singleton_relation),subset_relation)
    | ~ spl0_236
    | ~ spl0_237 ),
    inference(superposition,[],[f2320,f2326]) ).

fof(f4310,plain,
    ( spl0_401
    | ~ spl0_131
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1411,f1372,f1019,f4308]) ).

fof(f1411,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2) )
    | ~ spl0_131
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1396]) ).

fof(f1396,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2))
        | ~ subclass(X0,X2)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_131
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f1020]) ).

fof(f4306,plain,
    ( spl0_400
    | ~ spl0_4
    | ~ spl0_265 ),
    inference(avatar_split_clause,[],[f2507,f2475,f220,f4303]) ).

fof(f2507,plain,
    ( null_class = complement(universal_class)
    | ~ spl0_4
    | ~ spl0_265 ),
    inference(resolution,[],[f2476,f221]) ).

fof(f4301,plain,
    ( ~ spl0_398
    | spl0_399
    | ~ spl0_12
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1317,f1301,f255,f4298,f4294]) ).

fof(f4294,plain,
    ( spl0_398
  <=> inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f4298,plain,
    ( spl0_399
  <=> null_class = cross_product(unordered_pair(null_class,null_class),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f1317,plain,
    ( null_class = cross_product(unordered_pair(null_class,null_class),universal_class)
    | ~ inductive(domain_of(regular(cross_product(unordered_pair(null_class,null_class),universal_class))))
    | ~ spl0_12
    | ~ spl0_159 ),
    inference(resolution,[],[f1302,f256]) ).

fof(f4292,plain,
    ( spl0_397
    | ~ spl0_20
    | ~ spl0_153 ),
    inference(avatar_split_clause,[],[f1271,f1254,f288,f4290]) ).

fof(f4290,plain,
    ( spl0_397
  <=> ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f1271,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(X1,universal_class)
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) )
    | ~ spl0_20
    | ~ spl0_153 ),
    inference(resolution,[],[f1255,f289]) ).

fof(f4288,plain,
    ( spl0_396
    | ~ spl0_22
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1259,f1250,f296,f4286]) ).

fof(f4286,plain,
    ( spl0_396
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f1259,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(intersection(X1,X2)) )
    | ~ spl0_22
    | ~ spl0_152 ),
    inference(resolution,[],[f1251,f297]) ).

fof(f4283,plain,
    ( spl0_395
    | ~ spl0_44
    | ~ spl0_144 ),
    inference(avatar_split_clause,[],[f1198,f1170,f425,f4281]) ).

fof(f1198,plain,
    ( ! [X0] :
        ( ~ member(X0,element_relation)
        | member(X0,singleton_relation)
        | member(X0,compose(element_relation,complement(identity_relation)))
        | ~ member(X0,universal_class) )
    | ~ spl0_44
    | ~ spl0_144 ),
    inference(resolution,[],[f1171,f426]) ).

fof(f4279,plain,
    ( spl0_394
    | ~ spl0_114
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1143,f1094,f895,f4277]) ).

fof(f1143,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,null_class),X1)
        | member(not_subclass_element(intersection(X0,null_class),X1),X2)
        | null_class = X2 )
    | ~ spl0_114
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f896]) ).

fof(f4275,plain,
    ( spl0_393
    | ~ spl0_38
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1137,f1094,f373,f4273]) ).

fof(f1137,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_38
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f374]) ).

fof(f4271,plain,
    ( spl0_392
    | ~ spl0_114
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1125,f1090,f895,f4269]) ).

fof(f1125,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(null_class,X0),X1)
        | member(not_subclass_element(intersection(null_class,X0),X1),X2)
        | null_class = X2 )
    | ~ spl0_114
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f896]) ).

fof(f4267,plain,
    ( spl0_391
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1119,f1090,f373,f4265]) ).

fof(f1119,plain,
    ( ! [X2,X3,X0,X1] :
        ( subclass(intersection(X0,X1),X2)
        | ~ subclass(X0,X3)
        | member(not_subclass_element(intersection(X0,X1),X2),X3) )
    | ~ spl0_38
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f374]) ).

fof(f4259,plain,
    ( spl0_390
    | ~ spl0_31
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1054,f1015,f336,f4257]) ).

fof(f1054,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X1) )
    | ~ spl0_31
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f337]) ).

fof(f4255,plain,
    ( spl0_389
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1053,f1015,f340,f4253]) ).

fof(f1053,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(X0,intersection(X1,X2))
        | member(regular(intersection(X0,intersection(X1,X2))),X2) )
    | ~ spl0_32
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f341]) ).

fof(f4251,plain,
    ( spl0_388
    | ~ spl0_31
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1038,f1011,f336,f4249]) ).

fof(f1038,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X0) )
    | ~ spl0_31
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f337]) ).

fof(f4247,plain,
    ( spl0_387
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1037,f1011,f340,f4245]) ).

fof(f1037,plain,
    ( ! [X2,X0,X1] :
        ( null_class = intersection(intersection(X0,X1),X2)
        | member(regular(intersection(intersection(X0,X1),X2)),X1) )
    | ~ spl0_32
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f341]) ).

fof(f4243,plain,
    ( spl0_386
    | ~ spl0_116
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f997,f958,f922,f4241]) ).

fof(f4241,plain,
    ( spl0_386
  <=> ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).

fof(f997,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(complement(regular(X0)),X1),null_class)
        | null_class = X0
        | subclass(complement(regular(X0)),X1) )
    | ~ spl0_116
    | ~ spl0_124 ),
    inference(resolution,[],[f959,f923]) ).

fof(f4239,plain,
    ( spl0_385
    | ~ spl0_48
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f853,f818,f445,f4237]) ).

fof(f4237,plain,
    ( spl0_385
  <=> ! [X0,X3,X2,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).

fof(f853,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,unordered_pair(X0,X1))
        | unordered_pair(X2,X3) = X0
        | unordered_pair(X2,X3) = X1 )
    | ~ spl0_48
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f446]) ).

fof(f3871,plain,
    ( spl0_384
    | ~ spl0_109
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1744,f1718,f818,f3869]) ).

fof(f3869,plain,
    ( spl0_384
  <=> ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f1744,plain,
    ( ! [X2,X0,X1] :
        ( member(regular(cross_product(X0,X1)),X2)
        | ~ subclass(universal_class,X2)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_109
    | ~ spl0_199 ),
    inference(superposition,[],[f819,f1719]) ).

fof(f3867,plain,
    ( spl0_383
    | ~ spl0_32
    | ~ spl0_163 ),
    inference(avatar_split_clause,[],[f1361,f1358,f340,f3865]) ).

fof(f1361,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
    | ~ spl0_32
    | ~ spl0_163 ),
    inference(resolution,[],[f1359,f341]) ).

fof(f3863,plain,
    ( spl0_382
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1343,f1323,f3861]) ).

fof(f3861,plain,
    ( spl0_382
  <=> ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f1343,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_161 ),
    inference(equality_factoring,[],[f1324]) ).

fof(f3859,plain,
    ( spl0_381
    | ~ spl0_161 ),
    inference(avatar_split_clause,[],[f1342,f1323,f3857]) ).

fof(f1342,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | regular(unordered_pair(X0,X1)) = X0
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_161 ),
    inference(equality_factoring,[],[f1324]) ).

fof(f3855,plain,
    ( spl0_380
    | ~ spl0_135
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1314,f1297,f1090,f3853]) ).

fof(f3853,plain,
    ( spl0_380
  <=> ! [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_380])]) ).

fof(f1297,plain,
    ( spl0_158
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1314,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_135
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1309]) ).

fof(f1309,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
        | subclass(intersection(universal_class,X0),complement(X1))
        | subclass(intersection(universal_class,X0),complement(X1)) )
    | ~ spl0_135
    | ~ spl0_158 ),
    inference(resolution,[],[f1298,f1091]) ).

fof(f1298,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1)) )
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1297]) ).

fof(f3851,plain,
    ( spl0_379
    | ~ spl0_136
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1313,f1297,f1094,f3849]) ).

fof(f3849,plain,
    ( spl0_379
  <=> ! [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_379])]) ).

fof(f1313,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_136
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1310]) ).

fof(f1310,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
        | subclass(intersection(X0,universal_class),complement(X1))
        | subclass(intersection(X0,universal_class),complement(X1)) )
    | ~ spl0_136
    | ~ spl0_158 ),
    inference(resolution,[],[f1298,f1095]) ).

fof(f3847,plain,
    ( spl0_378
    | ~ spl0_22
    | ~ spl0_142 ),
    inference(avatar_split_clause,[],[f1183,f1162,f296,f3845]) ).

fof(f3845,plain,
    ( spl0_378
  <=> ! [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_378])]) ).

fof(f1162,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f1183,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,cross_product(universal_class,universal_class))
        | ~ function(complement(X1)) )
    | ~ spl0_22
    | ~ spl0_142 ),
    inference(resolution,[],[f1163,f297]) ).

fof(f1163,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(complement(X1),X2)
        | ~ member(X0,universal_class)
        | member(X0,X1)
        | member(X0,X2) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1162]) ).

fof(f3843,plain,
    ( spl0_377
    | ~ spl0_20
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1142,f1094,f288,f3841]) ).

fof(f1142,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(X0,complement(X1)),X2)
        | ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
    | ~ spl0_20
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f289]) ).

fof(f3839,plain,
    ( spl0_376
    | ~ spl0_20
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1124,f1090,f288,f3837]) ).

fof(f1124,plain,
    ( ! [X2,X0,X1] :
        ( subclass(intersection(complement(X0),X1),X2)
        | ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
    | ~ spl0_20
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f289]) ).

fof(f3835,plain,
    ( spl0_375
    | ~ spl0_114
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1074,f1019,f895,f3833]) ).

fof(f3833,plain,
    ( spl0_375
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f1074,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,null_class)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X2)
        | null_class = X2 )
    | ~ spl0_114
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f896]) ).

fof(f3831,plain,
    ( spl0_374
    | ~ spl0_38
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1068,f1019,f373,f3829]) ).

fof(f1068,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,X1)
        | subclass(X0,X2)
        | ~ subclass(X1,X3)
        | member(not_subclass_element(X0,X2),X3) )
    | ~ spl0_38
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f374]) ).

fof(f3827,plain,
    ( spl0_373
    | ~ spl0_114
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1056,f1015,f895,f3825]) ).

fof(f3825,plain,
    ( spl0_373
  <=> ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f1056,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,null_class)
        | member(regular(intersection(X0,null_class)),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f896]) ).

fof(f3823,plain,
    ( spl0_372
    | ~ spl0_38
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1050,f1015,f373,f3821]) ).

fof(f1050,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X1,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_38
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f374]) ).

fof(f3819,plain,
    ( spl0_371
    | ~ spl0_114
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1040,f1011,f895,f3817]) ).

fof(f3817,plain,
    ( spl0_371
  <=> ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f1040,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(null_class,X0)
        | member(regular(intersection(null_class,X0)),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f896]) ).

fof(f3815,plain,
    ( spl0_370
    | ~ spl0_38
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1034,f1011,f373,f3813]) ).

fof(f1034,plain,
    ( ! [X2,X0,X1] :
        ( intersection(X0,X1) = null_class
        | ~ subclass(X0,X2)
        | member(regular(intersection(X0,X1)),X2) )
    | ~ spl0_38
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f374]) ).

fof(f3811,plain,
    ( spl0_369
    | ~ spl0_237
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f3264,f3260,f2324,f3808]) ).

fof(f3260,plain,
    ( spl0_334
  <=> subclass(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f3264,plain,
    ( subclass(singleton_relation,subset_relation)
    | ~ spl0_237
    | ~ spl0_334 ),
    inference(forward_demodulation,[],[f3262,f2326]) ).

fof(f3262,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f3260]) ).

fof(f3806,plain,
    ( spl0_368
    | ~ spl0_113
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f998,f958,f891,f3804]) ).

fof(f3804,plain,
    ( spl0_368
  <=> ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f998,plain,
    ( ! [X0] :
        ( ~ member(regular(complement(regular(X0))),null_class)
        | null_class = X0
        | null_class = complement(regular(X0)) )
    | ~ spl0_113
    | ~ spl0_124 ),
    inference(resolution,[],[f959,f892]) ).

fof(f3802,plain,
    ( spl0_367
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(avatar_split_clause,[],[f978,f922,f830,f3800]) ).

fof(f978,plain,
    ( ! [X0] :
        ( subclass(complement(cross_product(universal_class,universal_class)),X0)
        | ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) )
    | ~ spl0_112
    | ~ spl0_116 ),
    inference(resolution,[],[f923,f831]) ).

fof(f3798,plain,
    ( spl0_366
    | ~ spl0_67
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f887,f830,f557,f3796]) ).

fof(f887,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X1,universal_class) )
    | ~ spl0_67
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f558]) ).

fof(f3794,plain,
    ( spl0_365
    | ~ spl0_68
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f886,f830,f561,f3792]) ).

fof(f886,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
        | member(X0,universal_class) )
    | ~ spl0_68
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f562]) ).

fof(f3790,plain,
    ( spl0_364
    | ~ spl0_57
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f865,f822,f505,f3788]) ).

fof(f3788,plain,
    ( spl0_364
  <=> ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f865,plain,
    ( ! [X0] :
        ( member(null_class,domain_of(domain_of(X0)))
        | ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | ~ operation(X0) )
    | ~ spl0_57
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f506]) ).

fof(f3657,plain,
    ( spl0_363
    | ~ spl0_237
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f3545,f3542,f2324,f3655]) ).

fof(f3542,plain,
    ( spl0_354
  <=> ! [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_354])]) ).

fof(f3545,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_237
    | ~ spl0_354 ),
    inference(forward_demodulation,[],[f3543,f2326]) ).

fof(f3543,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_354 ),
    inference(avatar_component_clause,[],[f3542]) ).

fof(f3653,plain,
    ( spl0_362
    | ~ spl0_237
    | ~ spl0_353 ),
    inference(avatar_split_clause,[],[f3540,f3537,f2324,f3651]) ).

fof(f3537,plain,
    ( spl0_353
  <=> ! [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_353])]) ).

fof(f3540,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(compose(element_relation,complement(singleton_relation))),X1)
        | ~ member(X0,singleton_relation)
        | member(X0,X1) )
    | ~ spl0_237
    | ~ spl0_353 ),
    inference(forward_demodulation,[],[f3538,f2326]) ).

fof(f3538,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_353 ),
    inference(avatar_component_clause,[],[f3537]) ).

fof(f3574,plain,
    ( spl0_361
    | ~ spl0_72
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1423,f1376,f584,f3572]) ).

fof(f3572,plain,
    ( spl0_361
  <=> ! [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_361])]) ).

fof(f1423,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_relation,compose_class(X0))
        | ~ member(X1,universal_class)
        | compose(X0,X1) = domain_of(X1) )
    | ~ spl0_72
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f585]) ).

fof(f3570,plain,
    ( ~ spl0_360
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_265
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2604,f2517,f2475,f241,f220,f3567]) ).

fof(f3567,plain,
    ( spl0_360
  <=> subclass(universal_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f2604,plain,
    ( ~ subclass(universal_class,null_class)
    | ~ spl0_4
    | ~ spl0_9
    | ~ spl0_265
    | ~ spl0_270 ),
    inference(forward_demodulation,[],[f2583,f2507]) ).

fof(f2583,plain,
    ( ~ subclass(universal_class,complement(universal_class))
    | ~ spl0_9
    | ~ spl0_270 ),
    inference(resolution,[],[f2518,f242]) ).

fof(f3565,plain,
    ( spl0_359
    | ~ spl0_131
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1312,f1297,f1019,f3563]) ).

fof(f1312,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class) )
    | ~ spl0_131
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1311]) ).

fof(f1311,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | subclass(X0,complement(X1))
        | ~ subclass(X0,universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_131
    | ~ spl0_158 ),
    inference(resolution,[],[f1298,f1020]) ).

fof(f3561,plain,
    ( spl0_358
    | ~ spl0_31
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1072,f1019,f336,f3559]) ).

fof(f1072,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X1) )
    | ~ spl0_31
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f337]) ).

fof(f3557,plain,
    ( spl0_357
    | ~ spl0_32
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1071,f1019,f340,f3555]) ).

fof(f1071,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | subclass(X0,X3)
        | member(not_subclass_element(X0,X3),X2) )
    | ~ spl0_32
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f341]) ).

fof(f3553,plain,
    ( spl0_356
    | ~ spl0_20
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1055,f1015,f288,f3551]) ).

fof(f1055,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X0,complement(X1))
        | ~ member(regular(intersection(X0,complement(X1))),X1) )
    | ~ spl0_20
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f289]) ).

fof(f3549,plain,
    ( spl0_355
    | ~ spl0_20
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1039,f1011,f288,f3547]) ).

fof(f1039,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(complement(X0),X1)
        | ~ member(regular(intersection(complement(X0),X1)),X0) )
    | ~ spl0_20
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f289]) ).

fof(f3544,plain,
    ( spl0_354
    | ~ spl0_38
    | ~ spl0_126 ),
    inference(avatar_split_clause,[],[f1004,f966,f373,f3542]) ).

fof(f1004,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,identity_relation)
        | ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_126 ),
    inference(resolution,[],[f967,f374]) ).

fof(f3539,plain,
    ( spl0_353
    | ~ spl0_38
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f1000,f962,f373,f3537]) ).

fof(f1000,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,singleton_relation)
        | ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_125 ),
    inference(resolution,[],[f963,f374]) ).

fof(f3535,plain,
    ( spl0_352
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f996,f958,f324,f3533]) ).

fof(f996,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,regular(X1)),null_class)
        | null_class = X1
        | subclass(X0,regular(X1)) )
    | ~ spl0_28
    | ~ spl0_124 ),
    inference(resolution,[],[f959,f325]) ).

fof(f3531,plain,
    ( spl0_351
    | ~ spl0_38
    | ~ spl0_124 ),
    inference(avatar_split_clause,[],[f995,f958,f373,f3529]) ).

fof(f3529,plain,
    ( spl0_351
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f995,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,null_class)
        | null_class = X1
        | ~ subclass(regular(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_124 ),
    inference(resolution,[],[f959,f374]) ).

fof(f3527,plain,
    ( spl0_350
    | ~ spl0_114
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f990,f926,f895,f3525]) ).

fof(f3525,plain,
    ( spl0_350
  <=> ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f990,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,null_class)
        | null_class = X0
        | member(regular(X0),X1)
        | null_class = X1 )
    | ~ spl0_114
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f896]) ).

fof(f3523,plain,
    ( spl0_349
    | ~ spl0_4
    | ~ spl0_265
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f2511,f2479,f2475,f220,f3521]) ).

fof(f2479,plain,
    ( spl0_266
  <=> ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f2511,plain,
    ( ! [X0] : subclass(null_class,X0)
    | ~ spl0_4
    | ~ spl0_265
    | ~ spl0_266 ),
    inference(forward_demodulation,[],[f2509,f2507]) ).

fof(f2509,plain,
    ( ! [X0] : subclass(complement(universal_class),X0)
    | ~ spl0_4
    | ~ spl0_266 ),
    inference(resolution,[],[f2480,f221]) ).

fof(f2480,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f2479]) ).

fof(f3519,plain,
    ( spl0_348
    | ~ spl0_38
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f984,f926,f373,f3517]) ).

fof(f984,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | null_class = X0
        | ~ subclass(X1,X2)
        | member(regular(X0),X2) )
    | ~ spl0_38
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f374]) ).

fof(f3512,plain,
    ( ~ spl0_346
    | spl0_347
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(avatar_split_clause,[],[f902,f891,f830,f3509,f3505]) ).

fof(f902,plain,
    ( null_class = complement(cross_product(universal_class,universal_class))
    | ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
    | ~ spl0_112
    | ~ spl0_113 ),
    inference(resolution,[],[f892,f831]) ).

fof(f3503,plain,
    ( spl0_345
    | spl0_343
    | ~ spl0_51
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f873,f822,f457,f3488,f3501]) ).

fof(f3501,plain,
    ( spl0_345
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).

fof(f3488,plain,
    ( spl0_343
  <=> member(null_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f873,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f458]) ).

fof(f3497,plain,
    ( spl0_344
    | ~ spl0_237
    | ~ spl0_343 ),
    inference(avatar_split_clause,[],[f3492,f3488,f2324,f3494]) ).

fof(f3494,plain,
    ( spl0_344
  <=> member(null_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).

fof(f3492,plain,
    ( member(null_class,singleton_relation)
    | ~ spl0_237
    | ~ spl0_343 ),
    inference(forward_demodulation,[],[f3490,f2326]) ).

fof(f3490,plain,
    ( member(null_class,identity_relation)
    | ~ spl0_343 ),
    inference(avatar_component_clause,[],[f3488]) ).

fof(f3491,plain,
    ( spl0_342
    | spl0_343
    | ~ spl0_52
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f872,f822,f461,f3488,f3485]) ).

fof(f3485,plain,
    ( spl0_342
  <=> ! [X0] :
        ( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f872,plain,
    ( ! [X0] :
        ( member(null_class,identity_relation)
        | ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f462]) ).

fof(f3483,plain,
    ( spl0_340
    | ~ spl0_341
    | ~ spl0_78
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f838,f818,f626,f3480,f3477]) ).

fof(f3477,plain,
    ( spl0_340
  <=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f3480,plain,
    ( spl0_341
  <=> subclass(universal_class,successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f838,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,successor_relation)
        | complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
    | ~ spl0_78
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f627]) ).

fof(f3359,plain,
    ( ~ spl0_339
    | ~ spl0_112
    | spl0_231 ),
    inference(avatar_split_clause,[],[f2287,f2283,f830,f3356]) ).

fof(f3356,plain,
    ( spl0_339
  <=> member(omega,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f2283,plain,
    ( spl0_231
  <=> member(omega,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f2287,plain,
    ( ~ member(omega,subset_relation)
    | ~ spl0_112
    | spl0_231 ),
    inference(resolution,[],[f2284,f831]) ).

fof(f2284,plain,
    ( ~ member(omega,cross_product(universal_class,universal_class))
    | spl0_231 ),
    inference(avatar_component_clause,[],[f2283]) ).

fof(f3354,plain,
    ( spl0_338
    | ~ spl0_237
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f3212,f3208,f2324,f3352]) ).

fof(f3208,plain,
    ( spl0_326
  <=> ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f3212,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(X0,singleton_relation),X1),subset_relation)
        | subclass(intersection(X0,singleton_relation),X1) )
    | ~ spl0_237
    | ~ spl0_326 ),
    inference(forward_demodulation,[],[f3211,f2326]) ).

fof(f3211,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_237
    | ~ spl0_326 ),
    inference(forward_demodulation,[],[f3209,f2326]) ).

fof(f3209,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_326 ),
    inference(avatar_component_clause,[],[f3208]) ).

fof(f3350,plain,
    ( spl0_337
    | ~ spl0_237
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f3201,f3197,f2324,f3348]) ).

fof(f3197,plain,
    ( spl0_324
  <=> ! [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_324])]) ).

fof(f3201,plain,
    ( ! [X0] :
        ( subclass(singleton_relation,X0)
        | member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_237
    | ~ spl0_324 ),
    inference(forward_demodulation,[],[f3200,f2326]) ).

fof(f3200,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_237
    | ~ spl0_324 ),
    inference(forward_demodulation,[],[f3198,f2326]) ).

fof(f3198,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_324 ),
    inference(avatar_component_clause,[],[f3197]) ).

fof(f3346,plain,
    ( spl0_336
    | ~ spl0_237
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f3195,f3192,f2324,f3344]) ).

fof(f3192,plain,
    ( spl0_323
  <=> ! [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_323])]) ).

fof(f3195,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(singleton_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_237
    | ~ spl0_323 ),
    inference(forward_demodulation,[],[f3193,f2326]) ).

fof(f3193,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f3192]) ).

fof(f3332,plain,
    ( spl0_335
    | ~ spl0_237
    | ~ spl0_321 ),
    inference(avatar_split_clause,[],[f3186,f3182,f2324,f3330]) ).

fof(f3182,plain,
    ( spl0_321
  <=> ! [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_321])]) ).

fof(f3186,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(intersection(singleton_relation,X0),X1),subset_relation)
        | subclass(intersection(singleton_relation,X0),X1) )
    | ~ spl0_237
    | ~ spl0_321 ),
    inference(forward_demodulation,[],[f3185,f2326]) ).

fof(f3185,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_237
    | ~ spl0_321 ),
    inference(forward_demodulation,[],[f3183,f2326]) ).

fof(f3183,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_321 ),
    inference(avatar_component_clause,[],[f3182]) ).

fof(f3263,plain,
    ( spl0_334
    | ~ spl0_43
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2258,f2234,f394,f3260]) ).

fof(f2258,plain,
    ( subclass(identity_relation,subset_relation)
    | ~ spl0_43
    | ~ spl0_225 ),
    inference(superposition,[],[f2235,f396]) ).

fof(f3245,plain,
    ( spl0_333
    | ~ spl0_6
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1449,f1384,f229,f3243]) ).

fof(f3243,plain,
    ( spl0_333
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f1384,plain,
    ( spl0_168
  <=> ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f1449,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
    | ~ spl0_6
    | ~ spl0_168 ),
    inference(resolution,[],[f1385,f230]) ).

fof(f1385,plain,
    ( ! [X0,X1] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1)))
        | ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,X1) )
    | ~ spl0_168 ),
    inference(avatar_component_clause,[],[f1384]) ).

fof(f3241,plain,
    ( spl0_332
    | ~ spl0_57
    | ~ spl0_168 ),
    inference(avatar_split_clause,[],[f1448,f1384,f505,f3239]) ).

fof(f3239,plain,
    ( spl0_332
  <=> ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f1448,plain,
    ( ! [X0] :
        ( ~ function(domain_of(X0))
        | compatible(domain_of(X0),X0,domain_of(X0))
        | ~ operation(domain_of(X0)) )
    | ~ spl0_57
    | ~ spl0_168 ),
    inference(resolution,[],[f1385,f506]) ).

fof(f3237,plain,
    ( spl0_331
    | ~ spl0_67
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1417,f1376,f557,f3235]) ).

fof(f1417,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(domain_of(X2),X1) )
    | ~ spl0_67
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f558]) ).

fof(f3233,plain,
    ( spl0_330
    | ~ spl0_27
    | ~ spl0_165 ),
    inference(avatar_split_clause,[],[f1414,f1372,f320,f3231]) ).

fof(f1414,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_27
    | ~ spl0_165 ),
    inference(duplicate_literal_removal,[],[f1393]) ).

fof(f1393,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
        | subclass(X0,intersection(X1,X0))
        | subclass(X0,intersection(X1,X0)) )
    | ~ spl0_27
    | ~ spl0_165 ),
    inference(resolution,[],[f1373,f321]) ).

fof(f3224,plain,
    ( spl0_328
    | spl0_329
    | ~ spl0_12
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1187,f1166,f255,f3221,f3218]) ).

fof(f3218,plain,
    ( spl0_328
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f3221,plain,
    ( spl0_329
  <=> member(null_class,null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f1187,plain,
    ( ! [X0] :
        ( member(null_class,null_class)
        | ~ member(null_class,X0)
        | null_class = X0
        | ~ inductive(regular(X0)) )
    | ~ spl0_12
    | ~ spl0_143 ),
    inference(resolution,[],[f1167,f256]) ).

fof(f3216,plain,
    ( spl0_327
    | ~ spl0_103
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1146,f1094,f764,f3214]) ).

fof(f1146,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,singleton_relation),X1)
        | member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
    | ~ spl0_103
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f765]) ).

fof(f3210,plain,
    ( spl0_326
    | ~ spl0_104
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1145,f1094,f768,f3208]) ).

fof(f1145,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,identity_relation),X1)
        | member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
    | ~ spl0_104
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f769]) ).

fof(f3206,plain,
    ( spl0_325
    | ~ spl0_41
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2257,f2234,f385,f3203]) ).

fof(f2257,plain,
    ( subclass(singleton_relation,element_relation)
    | ~ spl0_41
    | ~ spl0_225 ),
    inference(superposition,[],[f2235,f387]) ).

fof(f3199,plain,
    ( spl0_324
    | ~ spl0_43
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1134,f1090,f394,f3197]) ).

fof(f1134,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
        | subclass(identity_relation,X0) )
    | ~ spl0_43
    | ~ spl0_135 ),
    inference(superposition,[],[f1091,f396]) ).

fof(f3194,plain,
    ( spl0_323
    | ~ spl0_41
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1133,f1090,f385,f3192]) ).

fof(f1133,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
        | subclass(singleton_relation,X0) )
    | ~ spl0_41
    | ~ spl0_135 ),
    inference(superposition,[],[f1091,f387]) ).

fof(f3190,plain,
    ( spl0_322
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1128,f1090,f764,f3188]) ).

fof(f1128,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(singleton_relation,X0),X1)
        | member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
    | ~ spl0_103
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f765]) ).

fof(f3184,plain,
    ( spl0_321
    | ~ spl0_104
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1127,f1090,f768,f3182]) ).

fof(f1127,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(identity_relation,X0),X1)
        | member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
    | ~ spl0_104
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f769]) ).

fof(f3180,plain,
    ( spl0_320
    | ~ spl0_22
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1085,f1027,f296,f3178]) ).

fof(f3178,plain,
    ( spl0_320
  <=> ! [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_320])]) ).

fof(f1085,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X1,X0)) )
    | ~ spl0_22
    | ~ spl0_133 ),
    inference(resolution,[],[f1028,f297]) ).

fof(f3176,plain,
    ( spl0_319
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1082,f1023,f296,f3174]) ).

fof(f3174,plain,
    ( spl0_319
  <=> ! [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_319])]) ).

fof(f1082,plain,
    ( ! [X0,X1] :
        ( member(X0,cross_product(universal_class,universal_class))
        | ~ member(X0,universal_class)
        | ~ function(unordered_pair(X0,X1)) )
    | ~ spl0_22
    | ~ spl0_132 ),
    inference(resolution,[],[f1024,f297]) ).

fof(f3172,plain,
    ( spl0_318
    | ~ spl0_20
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1073,f1019,f288,f3170]) ).

fof(f1073,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | subclass(X0,X2)
        | ~ member(not_subclass_element(X0,X2),X1) )
    | ~ spl0_20
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f289]) ).

fof(f3168,plain,
    ( spl0_317
    | ~ spl0_31
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f988,f926,f336,f3166]) ).

fof(f988,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X1) )
    | ~ spl0_31
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f337]) ).

fof(f3164,plain,
    ( spl0_316
    | ~ spl0_32
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f987,f926,f340,f3162]) ).

fof(f987,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,intersection(X1,X2))
        | null_class = X0
        | member(regular(X0),X2) )
    | ~ spl0_32
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f341]) ).

fof(f3160,plain,
    ( spl0_315
    | ~ spl0_28
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f884,f830,f324,f3158]) ).

fof(f884,plain,
    ( ! [X0] :
        ( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
        | subclass(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_28
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f325]) ).

fof(f3141,plain,
    ( spl0_314
    | ~ spl0_237
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f3072,f2949,f2324,f3139]) ).

fof(f2949,plain,
    ( spl0_302
  <=> ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f3072,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | null_class = intersection(X0,singleton_relation) )
    | ~ spl0_237
    | ~ spl0_302 ),
    inference(forward_demodulation,[],[f2952,f2326]) ).

fof(f2952,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_237
    | ~ spl0_302 ),
    inference(forward_demodulation,[],[f2950,f2326]) ).

fof(f2950,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_302 ),
    inference(avatar_component_clause,[],[f2949]) ).

fof(f3120,plain,
    ( spl0_313
    | ~ spl0_237
    | ~ spl0_304 ),
    inference(avatar_split_clause,[],[f2964,f2961,f2324,f3118]) ).

fof(f2961,plain,
    ( spl0_304
  <=> ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f2964,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_237
    | ~ spl0_304 ),
    inference(forward_demodulation,[],[f2962,f2326]) ).

fof(f2962,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_304 ),
    inference(avatar_component_clause,[],[f2961]) ).

fof(f3099,plain,
    ( ~ spl0_312
    | ~ spl0_3
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2946,f2521,f215,f3096]) ).

fof(f3096,plain,
    ( spl0_312
  <=> inductive(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f215,plain,
    ( spl0_3
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f2946,plain,
    ( ~ inductive(choice)
    | ~ spl0_3
    | ~ spl0_271 ),
    inference(resolution,[],[f2522,f217]) ).

fof(f217,plain,
    ( function(choice)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f215]) ).

fof(f3094,plain,
    ( spl0_311
    | ~ spl0_237
    | ~ spl0_299 ),
    inference(avatar_split_clause,[],[f3078,f2876,f2324,f3091]) ).

fof(f2876,plain,
    ( spl0_299
  <=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f3078,plain,
    ( member(regular(singleton_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_237
    | ~ spl0_299 ),
    inference(forward_demodulation,[],[f2878,f2326]) ).

fof(f2878,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | ~ spl0_299 ),
    inference(avatar_component_clause,[],[f2876]) ).

fof(f3089,plain,
    ( spl0_310
    | ~ spl0_237
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f3073,f2853,f2324,f3086]) ).

fof(f2853,plain,
    ( spl0_298
  <=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f3073,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(singleton_relation))))
    | ~ spl0_237
    | ~ spl0_298 ),
    inference(forward_demodulation,[],[f2855,f2326]) ).

fof(f2855,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | ~ spl0_298 ),
    inference(avatar_component_clause,[],[f2853]) ).

fof(f3084,plain,
    ( ~ spl0_309
    | ~ spl0_112
    | spl0_301 ),
    inference(avatar_split_clause,[],[f2945,f2941,f830,f3081]) ).

fof(f3081,plain,
    ( spl0_309
  <=> member(singleton_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f2941,plain,
    ( spl0_301
  <=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f2945,plain,
    ( ~ member(singleton_relation,subset_relation)
    | ~ spl0_112
    | spl0_301 ),
    inference(resolution,[],[f2943,f831]) ).

fof(f2943,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | spl0_301 ),
    inference(avatar_component_clause,[],[f2941]) ).

fof(f3076,plain,
    ( spl0_232
    | ~ spl0_235
    | ~ spl0_237 ),
    inference(avatar_split_clause,[],[f2889,f2324,f2314,f2289]) ).

fof(f2889,plain,
    ( null_class = singleton_relation
    | ~ spl0_235
    | ~ spl0_237 ),
    inference(forward_demodulation,[],[f2316,f2326]) ).

fof(f2316,plain,
    ( null_class = identity_relation
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f2314]) ).

fof(f3065,plain,
    ( spl0_308
    | ~ spl0_232
    | ~ spl0_237
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f2954,f2949,f2324,f2289,f3063]) ).

fof(f3063,plain,
    ( spl0_308
  <=> ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f2954,plain,
    ( ! [X0] :
        ( member(regular(intersection(X0,singleton_relation)),subset_relation)
        | singleton_relation = intersection(X0,singleton_relation) )
    | ~ spl0_232
    | ~ spl0_237
    | ~ spl0_302 ),
    inference(forward_demodulation,[],[f2953,f2326]) ).

fof(f2953,plain,
    ( ! [X0] :
        ( singleton_relation = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_232
    | ~ spl0_237
    | ~ spl0_302 ),
    inference(forward_demodulation,[],[f2952,f2291]) ).

fof(f2291,plain,
    ( null_class = singleton_relation
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f2289]) ).

fof(f2976,plain,
    ( spl0_307
    | ~ spl0_9
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1740,f1718,f241,f2974]) ).

fof(f2974,plain,
    ( spl0_307
  <=> ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f1740,plain,
    ( ! [X0,X1] :
        ( member(regular(cross_product(X0,X1)),universal_class)
        | cross_product(X0,X1) = null_class )
    | ~ spl0_9
    | ~ spl0_199 ),
    inference(superposition,[],[f242,f1719]) ).

fof(f2972,plain,
    ( spl0_306
    | ~ spl0_68
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1416,f1376,f561,f2970]) ).

fof(f2970,plain,
    ( spl0_306
  <=> ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f1416,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(domain_relation,cross_product(X0,X1))
        | ~ member(X2,universal_class)
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f562]) ).

fof(f2968,plain,
    ( spl0_305
    | ~ spl0_103
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1077,f1019,f764,f2966]) ).

fof(f1077,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,singleton_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),element_relation) )
    | ~ spl0_103
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f765]) ).

fof(f2963,plain,
    ( spl0_304
    | ~ spl0_104
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1076,f1019,f768,f2961]) ).

fof(f1076,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,identity_relation)
        | subclass(X0,X1)
        | member(not_subclass_element(X0,X1),subset_relation) )
    | ~ spl0_104
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f769]) ).

fof(f2958,plain,
    ( spl0_303
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1059,f1015,f764,f2956]) ).

fof(f1059,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,singleton_relation)
        | member(regular(intersection(X0,singleton_relation)),element_relation) )
    | ~ spl0_103
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f765]) ).

fof(f2951,plain,
    ( spl0_302
    | ~ spl0_104
    | ~ spl0_130 ),
    inference(avatar_split_clause,[],[f1058,f1015,f768,f2949]) ).

fof(f1058,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,identity_relation)
        | member(regular(intersection(X0,identity_relation)),subset_relation) )
    | ~ spl0_104
    | ~ spl0_130 ),
    inference(resolution,[],[f1016,f769]) ).

fof(f2944,plain,
    ( ~ spl0_301
    | ~ spl0_237
    | spl0_259 ),
    inference(avatar_split_clause,[],[f2937,f2440,f2324,f2941]) ).

fof(f2440,plain,
    ( spl0_259
  <=> member(identity_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f2937,plain,
    ( ~ member(singleton_relation,cross_product(universal_class,universal_class))
    | ~ spl0_237
    | spl0_259 ),
    inference(forward_demodulation,[],[f2441,f2326]) ).

fof(f2441,plain,
    ( ~ member(identity_relation,cross_product(universal_class,universal_class))
    | spl0_259 ),
    inference(avatar_component_clause,[],[f2440]) ).

fof(f2933,plain,
    ( spl0_300
    | ~ spl0_38
    | ~ spl0_237
    | ~ spl0_259 ),
    inference(avatar_split_clause,[],[f2898,f2440,f2324,f373,f2931]) ).

fof(f2931,plain,
    ( spl0_300
  <=> ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f2898,plain,
    ( ! [X0] :
        ( member(singleton_relation,X0)
        | ~ subclass(cross_product(universal_class,universal_class),X0) )
    | ~ spl0_38
    | ~ spl0_237
    | ~ spl0_259 ),
    inference(forward_demodulation,[],[f2893,f2326]) ).

fof(f2893,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(identity_relation,X0) )
    | ~ spl0_38
    | ~ spl0_259 ),
    inference(resolution,[],[f2442,f374]) ).

fof(f2442,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_259 ),
    inference(avatar_component_clause,[],[f2440]) ).

fof(f2879,plain,
    ( spl0_235
    | spl0_299
    | ~ spl0_43
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1049,f1011,f394,f2876,f2314]) ).

fof(f1049,plain,
    ( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
    | null_class = identity_relation
    | ~ spl0_43
    | ~ spl0_129 ),
    inference(superposition,[],[f1012,f396]) ).

fof(f2856,plain,
    ( spl0_232
    | spl0_298
    | ~ spl0_41
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1048,f1011,f385,f2853,f2289]) ).

fof(f1048,plain,
    ( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
    | null_class = singleton_relation
    | ~ spl0_41
    | ~ spl0_129 ),
    inference(superposition,[],[f1012,f387]) ).

fof(f2851,plain,
    ( ~ spl0_297
    | ~ spl0_50
    | spl0_279 ),
    inference(avatar_split_clause,[],[f2735,f2615,f453,f2848]) ).

fof(f2848,plain,
    ( spl0_297
  <=> subset_relation = intersection(xr,cross_product(subset_relation,y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f2615,plain,
    ( spl0_279
  <=> subset_relation = intersection(cross_product(subset_relation,y),xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f2735,plain,
    ( subset_relation != intersection(xr,cross_product(subset_relation,y))
    | ~ spl0_50
    | spl0_279 ),
    inference(superposition,[],[f2617,f454]) ).

fof(f2617,plain,
    ( subset_relation != intersection(cross_product(subset_relation,y),xr)
    | spl0_279 ),
    inference(avatar_component_clause,[],[f2615]) ).

fof(f2846,plain,
    ( spl0_296
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1043,f1011,f764,f2844]) ).

fof(f1043,plain,
    ( ! [X0] :
        ( null_class = intersection(singleton_relation,X0)
        | member(regular(intersection(singleton_relation,X0)),element_relation) )
    | ~ spl0_103
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f765]) ).

fof(f2842,plain,
    ( spl0_295
    | ~ spl0_104
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1042,f1011,f768,f2840]) ).

fof(f1042,plain,
    ( ! [X0] :
        ( null_class = intersection(identity_relation,X0)
        | member(regular(intersection(identity_relation,X0)),subset_relation) )
    | ~ spl0_104
    | ~ spl0_129 ),
    inference(resolution,[],[f1012,f769]) ).

fof(f2838,plain,
    ( spl0_294
    | ~ spl0_20
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f989,f926,f288,f2836]) ).

fof(f989,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,complement(X1))
        | null_class = X0
        | ~ member(regular(X0),X1) )
    | ~ spl0_20
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f289]) ).

fof(f2834,plain,
    ( spl0_293
    | ~ spl0_38
    | ~ spl0_112 ),
    inference(avatar_split_clause,[],[f883,f830,f373,f2832]) ).

fof(f883,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,subset_relation)
        | ~ subclass(cross_product(universal_class,universal_class),X1)
        | member(X0,X1) )
    | ~ spl0_38
    | ~ spl0_112 ),
    inference(resolution,[],[f831,f374]) ).

fof(f2830,plain,
    ( spl0_292
    | ~ spl0_38
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f852,f818,f373,f2828]) ).

fof(f2828,plain,
    ( spl0_292
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f852,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | ~ subclass(X0,X1)
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_38
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f374]) ).

fof(f2767,plain,
    ( spl0_290
    | ~ spl0_291
    | ~ spl0_61
    | ~ spl0_166 ),
    inference(avatar_split_clause,[],[f1419,f1376,f527,f2764,f2761]) ).

fof(f2761,plain,
    ( spl0_290
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f1419,plain,
    ( ! [X0] :
        ( ~ subclass(domain_relation,element_relation)
        | ~ member(X0,universal_class)
        | member(X0,domain_of(X0)) )
    | ~ spl0_61
    | ~ spl0_166 ),
    inference(resolution,[],[f1377,f528]) ).

fof(f2759,plain,
    ( spl0_289
    | ~ spl0_27
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1315,f1297,f320,f2757]) ).

fof(f1315,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_158 ),
    inference(duplicate_literal_removal,[],[f1308]) ).

fof(f1308,plain,
    ( ! [X0] :
        ( member(not_subclass_element(universal_class,complement(X0)),X0)
        | subclass(universal_class,complement(X0))
        | subclass(universal_class,complement(X0)) )
    | ~ spl0_27
    | ~ spl0_158 ),
    inference(resolution,[],[f1298,f321]) ).

fof(f2755,plain,
    ( spl0_288
    | ~ spl0_76
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1132,f1090,f610,f2753]) ).

fof(f1132,plain,
    ( ! [X0] :
        ( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
        | subclass(subset_relation,X0) )
    | ~ spl0_76
    | ~ spl0_135 ),
    inference(superposition,[],[f1091,f612]) ).

fof(f2751,plain,
    ( spl0_287
    | ~ spl0_103
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f993,f926,f764,f2749]) ).

fof(f993,plain,
    ( ! [X0] :
        ( ~ subclass(X0,singleton_relation)
        | null_class = X0
        | member(regular(X0),element_relation) )
    | ~ spl0_103
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f765]) ).

fof(f2747,plain,
    ( spl0_286
    | ~ spl0_104
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f992,f926,f768,f2745]) ).

fof(f992,plain,
    ( ! [X0] :
        ( ~ subclass(X0,identity_relation)
        | null_class = X0
        | member(regular(X0),subset_relation) )
    | ~ spl0_104
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f769]) ).

fof(f2734,plain,
    ( spl0_284
    | ~ spl0_276
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2733,f2719,f2551,f2725]) ).

fof(f2725,plain,
    ( spl0_284
  <=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f2733,plain,
    ( member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_276
    | ~ spl0_283 ),
    inference(forward_demodulation,[],[f2721,f2553]) ).

fof(f2553,plain,
    ( null_class = subset_relation
    | ~ spl0_276 ),
    inference(avatar_component_clause,[],[f2551]) ).

fof(f2732,plain,
    ( spl0_285
    | spl0_283
    | ~ spl0_34
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f868,f822,f348,f2719,f2730]) ).

fof(f2730,plain,
    ( spl0_285
  <=> ! [X0] : ~ inductive(flip(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f348,plain,
    ( spl0_34
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f868,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(flip(X0)) )
    | ~ spl0_34
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f349]) ).

fof(f349,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f348]) ).

fof(f2728,plain,
    ( ~ spl0_284
    | ~ spl0_276
    | spl0_283 ),
    inference(avatar_split_clause,[],[f2723,f2719,f2551,f2725]) ).

fof(f2723,plain,
    ( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_276
    | spl0_283 ),
    inference(forward_demodulation,[],[f2720,f2553]) ).

fof(f2720,plain,
    ( ~ member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
    | spl0_283 ),
    inference(avatar_component_clause,[],[f2719]) ).

fof(f2722,plain,
    ( spl0_282
    | spl0_283
    | ~ spl0_33
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f867,f822,f344,f2719,f2716]) ).

fof(f2716,plain,
    ( spl0_282
  <=> ! [X0] : ~ inductive(rotate(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f344,plain,
    ( spl0_33
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f867,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
        | ~ inductive(rotate(X0)) )
    | ~ spl0_33
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f345]) ).

fof(f345,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f344]) ).

fof(f2714,plain,
    ( spl0_281
    | ~ spl0_31
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f856,f818,f336,f2712]) ).

fof(f2712,plain,
    ( spl0_281
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f856,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X0) )
    | ~ spl0_31
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f337]) ).

fof(f2710,plain,
    ( spl0_280
    | ~ spl0_32
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f855,f818,f340,f2708]) ).

fof(f2708,plain,
    ( spl0_280
  <=> ! [X2,X0,X1,X3] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f855,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ subclass(universal_class,intersection(X0,X1))
        | member(unordered_pair(X2,X3),X1) )
    | ~ spl0_32
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f341]) ).

fof(f2618,plain,
    ( ~ spl0_279
    | spl0_1
    | ~ spl0_276 ),
    inference(avatar_split_clause,[],[f2559,f2551,f205,f2615]) ).

fof(f2559,plain,
    ( subset_relation != intersection(cross_product(subset_relation,y),xr)
    | spl0_1
    | ~ spl0_276 ),
    inference(superposition,[],[f207,f2553]) ).

fof(f2578,plain,
    ( spl0_278
    | ~ spl0_4
    | ~ spl0_152 ),
    inference(avatar_split_clause,[],[f1257,f1250,f220,f2576]) ).

fof(f1257,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | member(X0,universal_class) )
    | ~ spl0_4
    | ~ spl0_152 ),
    inference(resolution,[],[f1251,f221]) ).

fof(f2558,plain,
    ( spl0_276
    | spl0_277
    | ~ spl0_76
    | ~ spl0_129 ),
    inference(avatar_split_clause,[],[f1047,f1011,f610,f2555,f2551]) ).

fof(f1047,plain,
    ( member(regular(subset_relation),cross_product(universal_class,universal_class))
    | null_class = subset_relation
    | ~ spl0_76
    | ~ spl0_129 ),
    inference(superposition,[],[f1012,f612]) ).

fof(f2549,plain,
    ( spl0_275
    | ~ spl0_20
    | ~ spl0_125 ),
    inference(avatar_split_clause,[],[f999,f962,f288,f2547]) ).

fof(f999,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | ~ member(X0,compose(element_relation,complement(identity_relation))) )
    | ~ spl0_20
    | ~ spl0_125 ),
    inference(resolution,[],[f963,f289]) ).

fof(f2545,plain,
    ( ~ spl0_274
    | spl0_273
    | ~ spl0_25
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f877,f822,f309,f2536,f2542]) ).

fof(f2542,plain,
    ( spl0_274
  <=> inductive(application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f2536,plain,
    ( spl0_273
  <=> member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f877,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(application_function)
    | ~ spl0_25
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f311]) ).

fof(f2539,plain,
    ( ~ spl0_272
    | spl0_273
    | ~ spl0_24
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f875,f822,f304,f2536,f2532]) ).

fof(f2532,plain,
    ( spl0_272
  <=> inductive(composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f875,plain,
    ( member(null_class,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ inductive(composition_function)
    | ~ spl0_24
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f306]) ).

fof(f306,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f304]) ).

fof(f2523,plain,
    ( spl0_271
    | spl0_183
    | ~ spl0_22
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f863,f822,f296,f1545,f2521]) ).

fof(f863,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(X0)
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f297]) ).

fof(f2519,plain,
    ( spl0_270
    | ~ spl0_20
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f857,f818,f288,f2517]) ).

fof(f857,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,complement(X0))
        | ~ member(unordered_pair(X1,X2),X0) )
    | ~ spl0_20
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f289]) ).

fof(f2515,plain,
    ( spl0_269
    | ~ spl0_72
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f840,f818,f584,f2513]) ).

fof(f2513,plain,
    ( spl0_269
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f840,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,compose_class(X0))
        | compose(X0,X1) = X2 )
    | ~ spl0_72
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f585]) ).

fof(f2506,plain,
    ( ~ spl0_268
    | ~ spl0_50
    | spl0_250 ),
    inference(avatar_split_clause,[],[f2447,f2398,f453,f2503]) ).

fof(f2503,plain,
    ( spl0_268
  <=> identity_relation = intersection(xr,cross_product(identity_relation,y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f2398,plain,
    ( spl0_250
  <=> identity_relation = intersection(cross_product(identity_relation,y),xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f2447,plain,
    ( identity_relation != intersection(xr,cross_product(identity_relation,y))
    | ~ spl0_50
    | spl0_250 ),
    inference(superposition,[],[f2400,f454]) ).

fof(f2400,plain,
    ( identity_relation != intersection(cross_product(identity_relation,y),xr)
    | spl0_250 ),
    inference(avatar_component_clause,[],[f2398]) ).

fof(f2499,plain,
    ( spl0_267
    | ~ spl0_38
    | ~ spl0_183 ),
    inference(avatar_split_clause,[],[f2446,f1545,f373,f2497]) ).

fof(f2446,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_183 ),
    inference(resolution,[],[f1546,f374]) ).

fof(f1546,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1545]) ).

fof(f2481,plain,
    ( spl0_266
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(avatar_split_clause,[],[f1078,f1019,f922,f2479]) ).

fof(f1078,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1) )
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(duplicate_literal_removal,[],[f1067]) ).

fof(f1067,plain,
    ( ! [X0,X1] :
        ( ~ subclass(complement(X0),X0)
        | subclass(complement(X0),X1)
        | subclass(complement(X0),X1) )
    | ~ spl0_116
    | ~ spl0_131 ),
    inference(resolution,[],[f1020,f923]) ).

fof(f2477,plain,
    ( spl0_265
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f994,f926,f891,f2475]) ).

fof(f994,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class )
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(duplicate_literal_removal,[],[f983]) ).

fof(f983,plain,
    ( ! [X0] :
        ( ~ subclass(complement(X0),X0)
        | complement(X0) = null_class
        | complement(X0) = null_class )
    | ~ spl0_113
    | ~ spl0_117 ),
    inference(resolution,[],[f927,f892]) ).

fof(f2473,plain,
    ( ~ spl0_264
    | ~ spl0_50
    | spl0_234 ),
    inference(avatar_split_clause,[],[f2361,f2309,f453,f2470]) ).

fof(f2470,plain,
    ( spl0_264
  <=> singleton_relation = intersection(xr,cross_product(singleton_relation,y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2309,plain,
    ( spl0_234
  <=> singleton_relation = intersection(cross_product(singleton_relation,y),xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f2361,plain,
    ( singleton_relation != intersection(xr,cross_product(singleton_relation,y))
    | ~ spl0_50
    | spl0_234 ),
    inference(superposition,[],[f2311,f454]) ).

fof(f2311,plain,
    ( singleton_relation != intersection(cross_product(singleton_relation,y),xr)
    | spl0_234 ),
    inference(avatar_component_clause,[],[f2309]) ).

fof(f2468,plain,
    ( spl0_263
    | ~ spl0_21
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f918,f899,f292,f2466]) ).

fof(f2466,plain,
    ( spl0_263
  <=> ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f292,plain,
    ( spl0_21
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f918,plain,
    ( ! [X0,X1] :
        ( function(compose(X0,X1))
        | ~ single_valued_class(compose(X0,X1)) )
    | ~ spl0_21
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f293]) ).

fof(f293,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f292]) ).

fof(f2464,plain,
    ( ~ spl0_261
    | spl0_262
    | ~ spl0_6
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f913,f899,f229,f2461,f2457]) ).

fof(f2457,plain,
    ( spl0_261
  <=> single_valued_class(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f2461,plain,
    ( spl0_262
  <=> function(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f913,plain,
    ( function(cross_product(universal_class,universal_class))
    | ~ single_valued_class(cross_product(universal_class,universal_class))
    | ~ spl0_6
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f230]) ).

fof(f2453,plain,
    ( ~ spl0_260
    | ~ spl0_112
    | spl0_259 ),
    inference(avatar_split_clause,[],[f2448,f2440,f830,f2450]) ).

fof(f2450,plain,
    ( spl0_260
  <=> member(identity_relation,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f2448,plain,
    ( ~ member(identity_relation,subset_relation)
    | ~ spl0_112
    | spl0_259 ),
    inference(resolution,[],[f2441,f831]) ).

fof(f2443,plain,
    ( spl0_259
    | ~ spl0_183
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2438,f2314,f1545,f2440]) ).

fof(f2438,plain,
    ( member(identity_relation,cross_product(universal_class,universal_class))
    | ~ spl0_183
    | ~ spl0_235 ),
    inference(forward_demodulation,[],[f1546,f2316]) ).

fof(f2433,plain,
    ( spl0_258
    | spl0_183
    | ~ spl0_18
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f874,f822,f280,f1545,f2431]) ).

fof(f2431,plain,
    ( spl0_258
  <=> ! [X0] : ~ inductive(compose_class(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f874,plain,
    ( ! [X0] :
        ( member(null_class,cross_product(universal_class,universal_class))
        | ~ inductive(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f281]) ).

fof(f2429,plain,
    ( spl0_256
    | ~ spl0_257
    | ~ spl0_103
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f860,f818,f764,f2426,f2423]) ).

fof(f2423,plain,
    ( spl0_256
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f2426,plain,
    ( spl0_257
  <=> subclass(universal_class,singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f860,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,singleton_relation)
        | member(unordered_pair(X0,X1),element_relation) )
    | ~ spl0_103
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f765]) ).

fof(f2421,plain,
    ( spl0_254
    | ~ spl0_255
    | ~ spl0_104
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f859,f818,f768,f2418,f2415]) ).

fof(f2415,plain,
    ( spl0_254
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f2418,plain,
    ( spl0_255
  <=> subclass(universal_class,identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f859,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,identity_relation)
        | member(unordered_pair(X0,X1),subset_relation) )
    | ~ spl0_104
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f769]) ).

fof(f2413,plain,
    ( spl0_252
    | ~ spl0_253
    | ~ spl0_86
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f844,f818,f671,f2410,f2407]) ).

fof(f2407,plain,
    ( spl0_252
  <=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f2410,plain,
    ( spl0_253
  <=> subclass(universal_class,composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f844,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,composition_function)
        | compose(X0,X1) = X2 )
    | ~ spl0_86
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f672]) ).

fof(f2405,plain,
    ( spl0_251
    | ~ spl0_67
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f834,f818,f557,f2403]) ).

fof(f2403,plain,
    ( spl0_251
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f834,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X1) )
    | ~ spl0_67
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f558]) ).

fof(f2401,plain,
    ( ~ spl0_250
    | spl0_1
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2331,f2314,f205,f2398]) ).

fof(f2331,plain,
    ( identity_relation != intersection(cross_product(identity_relation,y),xr)
    | spl0_1
    | ~ spl0_235 ),
    inference(superposition,[],[f207,f2316]) ).

fof(f2396,plain,
    ( spl0_249
    | ~ spl0_68
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f833,f818,f561,f2394]) ).

fof(f2394,plain,
    ( spl0_249
  <=> ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f833,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,cross_product(X0,X1))
        | member(X2,X0) )
    | ~ spl0_68
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f562]) ).

fof(f2391,plain,
    ( spl0_247
    | ~ spl0_248
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f789,f390,f381,f2388,f2385]) ).

fof(f2385,plain,
    ( spl0_247
  <=> ! [X0] :
        ( member(null_class,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f2388,plain,
    ( spl0_248
  <=> inductive(null_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f390,plain,
    ( spl0_42
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f789,plain,
    ( ! [X0] :
        ( ~ inductive(null_class)
        | member(null_class,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_42 ),
    inference(superposition,[],[f391,f382]) ).

fof(f391,plain,
    ( ! [X0,X1] :
        ( ~ inductive(intersection(X0,X1))
        | member(null_class,X0) )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f390]) ).

fof(f2383,plain,
    ( spl0_246
    | ~ spl0_27
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f781,f768,f320,f2381]) ).

fof(f781,plain,
    ( ! [X0] :
        ( member(not_subclass_element(identity_relation,X0),subset_relation)
        | subclass(identity_relation,X0) )
    | ~ spl0_27
    | ~ spl0_104 ),
    inference(resolution,[],[f769,f321]) ).

fof(f2379,plain,
    ( spl0_245
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f777,f764,f320,f2377]) ).

fof(f777,plain,
    ( ! [X0] :
        ( member(not_subclass_element(singleton_relation,X0),element_relation)
        | subclass(singleton_relation,X0) )
    | ~ spl0_27
    | ~ spl0_103 ),
    inference(resolution,[],[f765,f321]) ).

fof(f2375,plain,
    ( spl0_244
    | ~ spl0_37
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f604,f575,f360,f2373]) ).

fof(f2373,plain,
    ( spl0_244
  <=> ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f575,plain,
    ( spl0_71
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f604,plain,
    ( ! [X0] :
        ( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
        | ~ one_to_one(X0) )
    | ~ spl0_37
    | ~ spl0_71 ),
    inference(resolution,[],[f576,f361]) ).

fof(f576,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f575]) ).

fof(f2371,plain,
    ( ~ spl0_243
    | spl0_183
    | ~ spl0_14
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f876,f822,f263,f1545,f2368]) ).

fof(f2368,plain,
    ( spl0_243
  <=> inductive(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f876,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(domain_relation)
    | ~ spl0_14
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f265]) ).

fof(f2366,plain,
    ( ~ spl0_242
    | spl0_183
    | ~ spl0_11
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f869,f822,f250,f1545,f2363]) ).

fof(f2363,plain,
    ( spl0_242
  <=> inductive(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f869,plain,
    ( member(null_class,cross_product(universal_class,universal_class))
    | ~ inductive(successor_relation)
    | ~ spl0_11
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f252]) ).

fof(f2360,plain,
    ( spl0_240
    | ~ spl0_241
    | ~ spl0_85
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f843,f818,f667,f2357,f2354]) ).

fof(f2354,plain,
    ( spl0_240
  <=> ! [X0,X1] : member(X0,domain_of(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f2357,plain,
    ( spl0_241
  <=> subclass(universal_class,application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f843,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,application_function)
        | member(X0,domain_of(X1)) )
    | ~ spl0_85
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f668]) ).

fof(f2352,plain,
    ( spl0_238
    | ~ spl0_239
    | ~ spl0_64
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f841,f818,f540,f2349,f2346]) ).

fof(f2346,plain,
    ( spl0_238
  <=> ! [X0,X1] : domain_of(X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f2349,plain,
    ( spl0_239
  <=> subclass(universal_class,domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f841,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,domain_relation)
        | domain_of(X0) = X1 )
    | ~ spl0_64
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f541]) ).

fof(f2327,plain,
    ( spl0_237
    | ~ spl0_232
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f2322,f2314,f2289,f2324]) ).

fof(f2322,plain,
    ( identity_relation = singleton_relation
    | ~ spl0_232
    | ~ spl0_235 ),
    inference(forward_demodulation,[],[f2316,f2291]) ).

fof(f2321,plain,
    ( spl0_235
    | spl0_236
    | ~ spl0_23
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f784,f768,f300,f2318,f2314]) ).

fof(f784,plain,
    ( member(regular(identity_relation),subset_relation)
    | null_class = identity_relation
    | ~ spl0_23
    | ~ spl0_104 ),
    inference(resolution,[],[f769,f301]) ).

fof(f2312,plain,
    ( ~ spl0_234
    | spl0_1
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f2297,f2289,f205,f2309]) ).

fof(f2297,plain,
    ( singleton_relation != intersection(cross_product(singleton_relation,y),xr)
    | spl0_1
    | ~ spl0_232 ),
    inference(superposition,[],[f207,f2291]) ).

fof(f2296,plain,
    ( spl0_232
    | spl0_233
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f780,f764,f300,f2293,f2289]) ).

fof(f780,plain,
    ( member(regular(singleton_relation),element_relation)
    | null_class = singleton_relation
    | ~ spl0_23
    | ~ spl0_103 ),
    inference(resolution,[],[f765,f301]) ).

fof(f2286,plain,
    ( ~ spl0_230
    | spl0_231
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(avatar_split_clause,[],[f773,f440,f296,f2283,f2279]) ).

fof(f2279,plain,
    ( spl0_230
  <=> function(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f440,plain,
    ( spl0_47
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f773,plain,
    ( member(omega,cross_product(universal_class,universal_class))
    | ~ function(universal_class)
    | ~ spl0_22
    | ~ spl0_47 ),
    inference(resolution,[],[f441,f297]) ).

fof(f441,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f440]) ).

fof(f2274,plain,
    ( spl0_229
    | ~ spl0_38
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f2178,f693,f373,f2272]) ).

fof(f2178,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(null_class,X0) )
    | ~ spl0_38
    | ~ spl0_91 ),
    inference(resolution,[],[f694,f374]) ).

fof(f694,plain,
    ( member(null_class,universal_class)
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f693]) ).

fof(f2270,plain,
    ( spl0_228
    | ~ spl0_18
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f919,f899,f280,f2268]) ).

fof(f2268,plain,
    ( spl0_228
  <=> ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f919,plain,
    ( ! [X0] :
        ( function(compose_class(X0))
        | ~ single_valued_class(compose_class(X0)) )
    | ~ spl0_18
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f281]) ).

fof(f2266,plain,
    ( spl0_226
    | ~ spl0_227
    | ~ spl0_61
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f836,f818,f527,f2263,f2260]) ).

fof(f2260,plain,
    ( spl0_226
  <=> ! [X0,X1] : member(X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f2263,plain,
    ( spl0_227
  <=> subclass(universal_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f836,plain,
    ( ! [X0,X1] :
        ( ~ subclass(universal_class,element_relation)
        | member(X0,X1) )
    | ~ spl0_61
    | ~ spl0_109 ),
    inference(resolution,[],[f819,f528]) ).

fof(f2236,plain,
    ( spl0_225
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1153,f1094,f324,f2234]) ).

fof(f1153,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1136]) ).

fof(f1136,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f325]) ).

fof(f2232,plain,
    ( spl0_224
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1135,f1090,f324,f2230]) ).

fof(f1135,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(duplicate_literal_removal,[],[f1118]) ).

fof(f1118,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f325]) ).

fof(f2148,plain,
    ( ~ spl0_2
    | ~ spl0_223 ),
    inference(avatar_contradiction_clause,[],[f2147]) ).

fof(f2147,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_223 ),
    inference(resolution,[],[f2145,f212]) ).

fof(f212,plain,
    ( inductive(omega)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f2145,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2144]) ).

fof(f2144,plain,
    ( spl0_223
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f2146,plain,
    ( spl0_223
    | spl0_91
    | ~ spl0_4
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f861,f822,f220,f693,f2144]) ).

fof(f861,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_4
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f221]) ).

fof(f2133,plain,
    ( spl0_222
    | ~ spl0_89
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f712,f708,f684,f2131]) ).

fof(f712,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_89
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f685]) ).

fof(f2129,plain,
    ( spl0_221
    | ~ spl0_50
    | ~ spl0_89
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f757,f752,f684,f453,f2127]) ).

fof(f2127,plain,
    ( spl0_221
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f757,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_50
    | ~ spl0_89
    | ~ spl0_101 ),
    inference(forward_demodulation,[],[f755,f454]) ).

fof(f755,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(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_89
    | ~ spl0_101 ),
    inference(resolution,[],[f753,f685]) ).

fof(f2119,plain,
    ( spl0_220
    | ~ spl0_70
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f756,f752,f569,f2117]) ).

fof(f756,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_70
    | ~ spl0_101 ),
    inference(resolution,[],[f753,f570]) ).

fof(f2106,plain,
    ( spl0_219
    | ~ spl0_83
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f715,f708,f652,f2104]) ).

fof(f715,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_83
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f653]) ).

fof(f2102,plain,
    ( spl0_218
    | ~ spl0_79
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f657,f652,f630,f2100]) ).

fof(f2100,plain,
    ( spl0_218
  <=> ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f657,plain,
    ( ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) )
    | ~ spl0_79
    | ~ spl0_83 ),
    inference(resolution,[],[f653,f631]) ).

fof(f2089,plain,
    ( spl0_217
    | ~ spl0_27
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f713,f708,f320,f2087]) ).

fof(f713,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f321]) ).

fof(f2076,plain,
    ( spl0_216
    | ~ spl0_23
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f716,f708,f300,f2074]) ).

fof(f716,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_23
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f301]) ).

fof(f2065,plain,
    ( spl0_215
    | ~ spl0_77
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f750,f747,f615,f2063]) ).

fof(f750,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) )
    | ~ spl0_77
    | ~ spl0_100 ),
    inference(resolution,[],[f748,f616]) ).

fof(f2035,plain,
    ( ~ spl0_214
    | spl0_192
    | ~ spl0_12
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f782,f768,f255,f1608,f2032]) ).

fof(f2032,plain,
    ( spl0_214
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f782,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_12
    | ~ spl0_104 ),
    inference(resolution,[],[f769,f256]) ).

fof(f2007,plain,
    ( spl0_213
    | ~ spl0_77
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f745,f741,f615,f2005]) ).

fof(f745,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_77
    | ~ spl0_99 ),
    inference(resolution,[],[f742,f616]) ).

fof(f2003,plain,
    ( spl0_212
    | ~ spl0_77
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f744,f737,f615,f2001]) ).

fof(f744,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_77
    | ~ spl0_98 ),
    inference(resolution,[],[f738,f616]) ).

fof(f1954,plain,
    ( spl0_211
    | ~ spl0_77
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f633,f630,f615,f1952]) ).

fof(f1952,plain,
    ( spl0_211
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f633,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) )
    | ~ spl0_77
    | ~ spl0_79 ),
    inference(resolution,[],[f631,f616]) ).

fof(f1944,plain,
    ( spl0_210
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f721,f708,f381,f1942]) ).

fof(f721,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f382]) ).

fof(f1932,plain,
    ( spl0_209
    | ~ spl0_70
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f711,f708,f569,f1930]) ).

fof(f711,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_70
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f570]) ).

fof(f1922,plain,
    ( spl0_208
    | ~ spl0_48
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f656,f652,f445,f1920]) ).

fof(f656,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_48
    | ~ spl0_83 ),
    inference(resolution,[],[f653,f446]) ).

fof(f1915,plain,
    ( spl0_207
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f718,f708,f381,f1913]) ).

fof(f718,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f382]) ).

fof(f1877,plain,
    ( spl0_206
    | ~ spl0_38
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f706,f702,f373,f1875]) ).

fof(f706,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) )
    | ~ spl0_38
    | ~ spl0_93 ),
    inference(resolution,[],[f703,f374]) ).

fof(f1821,plain,
    ( spl0_205
    | ~ spl0_50
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f720,f708,f453,f1819]) ).

fof(f720,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f454]) ).

fof(f1817,plain,
    ( spl0_204
    | ~ spl0_50
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f717,f708,f453,f1815]) ).

fof(f717,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_94 ),
    inference(superposition,[],[f709,f454]) ).

fof(f1807,plain,
    ( ~ spl0_203
    | ~ spl0_12
    | spl0_192 ),
    inference(avatar_split_clause,[],[f1690,f1608,f255,f1804]) ).

fof(f1804,plain,
    ( spl0_203
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1690,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_12
    | spl0_192 ),
    inference(resolution,[],[f1610,f256]) ).

fof(f1610,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_192 ),
    inference(avatar_component_clause,[],[f1608]) ).

fof(f1802,plain,
    ( spl0_202
    | ~ spl0_12
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f714,f708,f255,f1800]) ).

fof(f714,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_12
    | ~ spl0_94 ),
    inference(resolution,[],[f709,f256]) ).

fof(f1782,plain,
    ( spl0_201
    | ~ spl0_27
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f636,f630,f320,f1780]) ).

fof(f636,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_79 ),
    inference(resolution,[],[f631,f321]) ).

fof(f1754,plain,
    ( spl0_200
    | ~ spl0_38
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f687,f684,f373,f1752]) ).

fof(f687,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) )
    | ~ spl0_38
    | ~ spl0_89 ),
    inference(resolution,[],[f685,f374]) ).

fof(f1720,plain,
    ( spl0_199
    | ~ spl0_23
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f635,f630,f300,f1718]) ).

fof(f635,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_79 ),
    inference(resolution,[],[f631,f301]) ).

fof(f1714,plain,
    ( spl0_198
    | ~ spl0_77
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f727,f724,f615,f1712]) ).

fof(f727,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_95 ),
    inference(resolution,[],[f725,f616]) ).

fof(f1669,plain,
    ( spl0_197
    | ~ spl0_31
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f659,f652,f336,f1667]) ).

fof(f659,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_31
    | ~ spl0_83 ),
    inference(resolution,[],[f653,f337]) ).

fof(f1665,plain,
    ( spl0_196
    | ~ spl0_32
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f658,f652,f340,f1663]) ).

fof(f658,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_32
    | ~ spl0_83 ),
    inference(resolution,[],[f653,f341]) ).

fof(f1648,plain,
    ( spl0_195
    | ~ spl0_20
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f660,f652,f288,f1646]) ).

fof(f660,plain,
    ( ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_20
    | ~ spl0_83 ),
    inference(resolution,[],[f653,f289]) ).

fof(f1629,plain,
    ( spl0_194
    | ~ spl0_38
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f655,f652,f373,f1627]) ).

fof(f655,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_38
    | ~ spl0_83 ),
    inference(resolution,[],[f653,f374]) ).

fof(f1623,plain,
    ( spl0_193
    | ~ spl0_39
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f538,f535,f377,f1621]) ).

fof(f538,plain,
    ( ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_39
    | ~ spl0_63 ),
    inference(resolution,[],[f536,f378]) ).

fof(f1611,plain,
    ( ~ spl0_192
    | ~ spl0_112
    | spl0_183 ),
    inference(avatar_split_clause,[],[f1553,f1545,f830,f1608]) ).

fof(f1553,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_112
    | spl0_183 ),
    inference(resolution,[],[f1547,f831]) ).

fof(f1547,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_183 ),
    inference(avatar_component_clause,[],[f1545]) ).

fof(f1606,plain,
    ( ~ spl0_189
    | ~ spl0_190
    | spl0_191
    | ~ spl0_73
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f618,f610,f588,f1603,f1599,f1595]) ).

fof(f1595,plain,
    ( spl0_189
  <=> function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1599,plain,
    ( spl0_190
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1603,plain,
    ( spl0_191
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f588,plain,
    ( spl0_73
  <=> ! [X0,X8] :
        ( ~ function(X8)
        | ~ member(X0,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f618,plain,
    ( member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(universal_class,universal_class)
    | ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_73
    | ~ spl0_76 ),
    inference(superposition,[],[f589,f612]) ).

fof(f589,plain,
    ( ! [X0,X8] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X8) )
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f588]) ).

fof(f1593,plain,
    ( spl0_188
    | ~ spl0_28
    | ~ spl0_50
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f582,f569,f453,f324,f1591]) ).

fof(f582,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_50
    | ~ spl0_70 ),
    inference(forward_demodulation,[],[f581,f454]) ).

fof(f581,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_70 ),
    inference(resolution,[],[f570,f325]) ).

fof(f1587,plain,
    ( spl0_187
    | ~ spl0_77
    | ~ spl0_87 ),
    inference(avatar_split_clause,[],[f678,f675,f615,f1585]) ).

fof(f678,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_87 ),
    inference(resolution,[],[f676,f616]) ).

fof(f1565,plain,
    ( spl0_186
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f619,f610,f449,f1563]) ).

fof(f619,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_49
    | ~ spl0_76 ),
    inference(superposition,[],[f450,f612]) ).

fof(f1558,plain,
    ( spl0_185
    | ~ spl0_38
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f624,f615,f373,f1556]) ).

fof(f624,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_38
    | ~ spl0_77 ),
    inference(resolution,[],[f616,f374]) ).

fof(f1552,plain,
    ( ~ spl0_182
    | ~ spl0_183
    | spl0_184
    | ~ spl0_22
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f608,f596,f296,f1549,f1545,f1541]) ).

fof(f1541,plain,
    ( spl0_182
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f1549,plain,
    ( spl0_184
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f596,plain,
    ( spl0_75
  <=> ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f608,plain,
    ( inductive(cross_product(universal_class,universal_class))
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | ~ spl0_22
    | ~ spl0_75 ),
    inference(resolution,[],[f597,f297]) ).

fof(f597,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f596]) ).

fof(f1539,plain,
    ( spl0_181
    | ~ spl0_39
    | ~ spl0_57 ),
    inference(avatar_split_clause,[],[f517,f505,f377,f1537]) ).

fof(f1537,plain,
    ( spl0_181
  <=> ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f517,plain,
    ( ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
    | ~ spl0_39
    | ~ spl0_57 ),
    inference(resolution,[],[f506,f378]) ).

fof(f1532,plain,
    ( spl0_179
    | spl0_180
    | ~ spl0_40
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f601,f588,f381,f1529,f1526]) ).

fof(f1526,plain,
    ( spl0_179
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | null_class = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f601,plain,
    ( ! [X0] :
        ( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | null_class = cross_product(X0,universal_class) )
    | ~ spl0_40
    | ~ spl0_73 ),
    inference(superposition,[],[f589,f382]) ).

fof(f1524,plain,
    ( spl0_178
    | ~ spl0_63
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f548,f544,f535,f1522]) ).

fof(f1522,plain,
    ( spl0_178
  <=> ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f544,plain,
    ( spl0_65
  <=> ! [X1,X8] :
        ( ~ function(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | maps(X8,domain_of(X8),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f548,plain,
    ( ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) )
    | ~ spl0_63
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f536]) ).

fof(f545,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f544]) ).

fof(f1486,plain,
    ( spl0_177
    | ~ spl0_77
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f665,f662,f615,f1484]) ).

fof(f665,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_77
    | ~ spl0_84 ),
    inference(resolution,[],[f663,f616]) ).

fof(f1482,plain,
    ( spl0_175
    | spl0_176
    | ~ spl0_12
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f634,f630,f255,f1479,f1476]) ).

fof(f1476,plain,
    ( spl0_175
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f1479,plain,
    ( spl0_176
  <=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f634,plain,
    ( ! [X0,X1] :
        ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
        | ~ inductive(cross_product(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_79 ),
    inference(resolution,[],[f631,f256]) ).

fof(f1474,plain,
    ( ~ spl0_173
    | spl0_174
    | ~ spl0_14
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f920,f899,f263,f1471,f1467]) ).

fof(f1467,plain,
    ( spl0_173
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1471,plain,
    ( spl0_174
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f920,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_14
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f265]) ).

fof(f1465,plain,
    ( spl0_172
    | ~ spl0_38
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f605,f592,f373,f1463]) ).

fof(f592,plain,
    ( spl0_74
  <=> ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f605,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) )
    | ~ spl0_38
    | ~ spl0_74 ),
    inference(resolution,[],[f593,f374]) ).

fof(f593,plain,
    ( ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f592]) ).

fof(f1461,plain,
    ( spl0_171
    | ~ spl0_38
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f599,f588,f373,f1459]) ).

fof(f599,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) )
    | ~ spl0_38
    | ~ spl0_73 ),
    inference(resolution,[],[f589,f374]) ).

fof(f1457,plain,
    ( spl0_170
    | ~ spl0_39
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f496,f461,f377,f1455]) ).

fof(f1455,plain,
    ( spl0_170
  <=> ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f496,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_39
    | ~ spl0_52 ),
    inference(resolution,[],[f462,f378]) ).

fof(f1453,plain,
    ( spl0_169
    | ~ spl0_39
    | ~ spl0_51 ),
    inference(avatar_split_clause,[],[f495,f457,f377,f1451]) ).

fof(f1451,plain,
    ( spl0_169
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f495,plain,
    ( ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_39
    | ~ spl0_51 ),
    inference(resolution,[],[f458,f378]) ).

fof(f1386,plain,
    ( spl0_168
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f646,f643,f1384]) ).

fof(f643,plain,
    ( spl0_81
  <=> ! [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_81])]) ).

fof(f646,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_81 ),
    inference(equality_resolution,[],[f644]) ).

fof(f644,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_81 ),
    inference(avatar_component_clause,[],[f643]) ).

fof(f1382,plain,
    ( spl0_167
    | ~ spl0_38
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f580,f569,f373,f1380]) ).

fof(f580,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_70 ),
    inference(resolution,[],[f570,f374]) ).

fof(f1378,plain,
    ( spl0_166
    | ~ spl0_38
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f573,f553,f373,f1376]) ).

fof(f573,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) )
    | ~ spl0_38
    | ~ spl0_66 ),
    inference(resolution,[],[f554,f374]) ).

fof(f1374,plain,
    ( spl0_165
    | ~ spl0_28
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f484,f449,f324,f1372]) ).

fof(f484,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_28
    | ~ spl0_49 ),
    inference(resolution,[],[f450,f325]) ).

fof(f1370,plain,
    ( spl0_164
    | ~ spl0_27
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f476,f445,f320,f1368]) ).

fof(f476,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_48 ),
    inference(resolution,[],[f446,f321]) ).

fof(f1360,plain,
    ( spl0_163
    | ~ spl0_32
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f620,f610,f340,f1358]) ).

fof(f620,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_32
    | ~ spl0_76 ),
    inference(superposition,[],[f341,f612]) ).

fof(f1329,plain,
    ( spl0_162
    | ~ spl0_50
    | ~ spl0_73 ),
    inference(avatar_split_clause,[],[f600,f588,f453,f1327]) ).

fof(f600,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_50
    | ~ spl0_73 ),
    inference(superposition,[],[f589,f454]) ).

fof(f1325,plain,
    ( spl0_161
    | ~ spl0_23
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f475,f445,f300,f1323]) ).

fof(f475,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_48 ),
    inference(resolution,[],[f446,f301]) ).

fof(f1307,plain,
    ( spl0_160
    | ~ spl0_22
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f551,f544,f296,f1305]) ).

fof(f1305,plain,
    ( spl0_160
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f551,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_22
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f297]) ).

fof(f1303,plain,
    ( spl0_159
    | ~ spl0_40
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f525,f519,f381,f1301]) ).

fof(f519,plain,
    ( spl0_60
  <=> ! [X4,X0] :
        ( ~ member(X4,domain_of(X0))
        | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f525,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_60 ),
    inference(trivial_inequality_removal,[],[f523]) ).

fof(f523,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_40
    | ~ spl0_60 ),
    inference(superposition,[],[f520,f382]) ).

fof(f520,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f519]) ).

fof(f1299,plain,
    ( spl0_158
    | ~ spl0_28
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f438,f425,f324,f1297]) ).

fof(f438,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_28
    | ~ spl0_44 ),
    inference(resolution,[],[f426,f325]) ).

fof(f1295,plain,
    ( spl0_157
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f410,f377,f348,f1293]) ).

fof(f410,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_34
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f349]) ).

fof(f1291,plain,
    ( spl0_156
    | ~ spl0_33
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f409,f377,f344,f1289]) ).

fof(f409,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_33
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f345]) ).

fof(f1287,plain,
    ( ~ spl0_154
    | spl0_155
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f916,f899,f250,f1284,f1280]) ).

fof(f1280,plain,
    ( spl0_154
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f1284,plain,
    ( spl0_155
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f916,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f252]) ).

fof(f1256,plain,
    ( spl0_153
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f499,f469,f373,f1254]) ).

fof(f469,plain,
    ( spl0_54
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f499,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_38
    | ~ spl0_54 ),
    inference(resolution,[],[f470,f374]) ).

fof(f470,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f469]) ).

fof(f1252,plain,
    ( spl0_152
    | ~ spl0_38
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f483,f449,f373,f1250]) ).

fof(f483,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_38
    | ~ spl0_49 ),
    inference(resolution,[],[f450,f374]) ).

fof(f1248,plain,
    ( spl0_150
    | ~ spl0_151
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f417,f377,f309,f1245,f1241]) ).

fof(f1241,plain,
    ( spl0_150
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f417,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
    | ~ spl0_25
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f311]) ).

fof(f1239,plain,
    ( spl0_148
    | ~ spl0_149
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f415,f377,f304,f1236,f1232]) ).

fof(f415,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f306]) ).

fof(f1230,plain,
    ( spl0_147
    | ~ spl0_21
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f413,f377,f292,f1228]) ).

fof(f413,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_21
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f293]) ).

fof(f1180,plain,
    ( spl0_146
    | ~ spl0_50
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f522,f519,f453,f1178]) ).

fof(f522,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_50
    | ~ spl0_60 ),
    inference(superposition,[],[f520,f454]) ).

fof(f1176,plain,
    ( spl0_145
    | ~ spl0_43
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f487,f449,f394,f1174]) ).

fof(f487,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_43
    | ~ spl0_49 ),
    inference(superposition,[],[f450,f396]) ).

fof(f1172,plain,
    ( spl0_144
    | ~ spl0_41
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f486,f449,f385,f1170]) ).

fof(f486,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_41
    | ~ spl0_49 ),
    inference(superposition,[],[f450,f387]) ).

fof(f1168,plain,
    ( spl0_143
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f485,f449,f381,f1166]) ).

fof(f485,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_40
    | ~ spl0_49 ),
    inference(superposition,[],[f450,f382]) ).

fof(f1164,plain,
    ( spl0_142
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f437,f425,f373,f1162]) ).

fof(f437,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_38
    | ~ spl0_44 ),
    inference(resolution,[],[f426,f374]) ).

fof(f1117,plain,
    ( spl0_141
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f550,f544,f229,f1115]) ).

fof(f1115,plain,
    ( spl0_141
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f550,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_6
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f230]) ).

fof(f1113,plain,
    ( spl0_140
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f414,f377,f280,f1111]) ).

fof(f414,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_18
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f281]) ).

fof(f1109,plain,
    ( spl0_139
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f407,f377,f296,f1107]) ).

fof(f407,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_22
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f297]) ).

fof(f1105,plain,
    ( ~ spl0_137
    | spl0_138
    | ~ spl0_10
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f914,f899,f245,f1102,f1098]) ).

fof(f1098,plain,
    ( spl0_137
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1102,plain,
    ( spl0_138
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f914,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_10
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f247]) ).

fof(f1096,plain,
    ( spl0_136
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f371,f340,f320,f1094]) ).

fof(f371,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_32 ),
    inference(resolution,[],[f341,f321]) ).

fof(f1092,plain,
    ( spl0_135
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f368,f336,f320,f1090]) ).

fof(f368,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(resolution,[],[f337,f321]) ).

fof(f1033,plain,
    ( spl0_134
    | ~ spl0_57
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f547,f544,f505,f1031]) ).

fof(f1031,plain,
    ( spl0_134
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f547,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_57
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f506]) ).

fof(f1029,plain,
    ( spl0_133
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f404,f373,f332,f1027]) ).

fof(f404,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_30
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f333]) ).

fof(f1025,plain,
    ( spl0_132
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f403,f373,f328,f1023]) ).

fof(f403,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f329]) ).

fof(f1021,plain,
    ( spl0_131
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f402,f373,f320,f1019]) ).

fof(f402,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_27
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f321]) ).

fof(f1017,plain,
    ( spl0_130
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f370,f340,f300,f1015]) ).

fof(f370,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_32 ),
    inference(resolution,[],[f341,f301]) ).

fof(f1013,plain,
    ( spl0_129
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f367,f336,f300,f1011]) ).

fof(f367,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_23
    | ~ spl0_31 ),
    inference(resolution,[],[f337,f301]) ).

fof(f977,plain,
    ( ~ spl0_128
    | ~ spl0_12
    | spl0_108 ),
    inference(avatar_split_clause,[],[f938,f810,f255,f974]) ).

fof(f974,plain,
    ( spl0_128
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

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

fof(f938,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_12
    | spl0_108 ),
    inference(resolution,[],[f811,f256]) ).

fof(f811,plain,
    ( ~ member(null_class,element_relation)
    | spl0_108 ),
    inference(avatar_component_clause,[],[f810]) ).

fof(f972,plain,
    ( spl0_127
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(avatar_split_clause,[],[f474,f445,f255,f970]) ).

fof(f474,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_48 ),
    inference(resolution,[],[f446,f256]) ).

fof(f968,plain,
    ( spl0_126
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f423,f394,f336,f966]) ).

fof(f423,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(superposition,[],[f337,f396]) ).

fof(f964,plain,
    ( spl0_125
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f421,f385,f336,f962]) ).

fof(f421,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(superposition,[],[f337,f387]) ).

fof(f960,plain,
    ( spl0_124
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f418,f381,f340,f958]) ).

fof(f418,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_32
    | ~ spl0_40 ),
    inference(superposition,[],[f341,f382]) ).

fof(f956,plain,
    ( spl0_122
    | ~ spl0_123
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f416,f377,f263,f953,f949]) ).

fof(f949,plain,
    ( spl0_122
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f416,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_14
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f265]) ).

fof(f947,plain,
    ( spl0_120
    | ~ spl0_121
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f411,f377,f250,f944,f940]) ).

fof(f940,plain,
    ( spl0_120
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f411,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_11
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f252]) ).

fof(f937,plain,
    ( spl0_118
    | ~ spl0_119
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f408,f377,f245,f934,f930]) ).

fof(f408,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f247]) ).

fof(f928,plain,
    ( spl0_117
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f401,f373,f300,f926]) ).

fof(f401,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_23
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f301]) ).

fof(f924,plain,
    ( spl0_116
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f363,f320,f288,f922]) ).

fof(f363,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_20
    | ~ spl0_27 ),
    inference(resolution,[],[f321,f289]) ).

fof(f901,plain,
    ( spl0_115
    | ~ spl0_51
    | ~ spl0_69 ),
    inference(avatar_split_clause,[],[f579,f565,f457,f899]) ).

fof(f565,plain,
    ( spl0_69
  <=> ! [X8] :
        ( function(X8)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f579,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_51
    | ~ spl0_69 ),
    inference(resolution,[],[f566,f458]) ).

fof(f566,plain,
    ( ! [X8] :
        ( ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | function(X8) )
    | ~ spl0_69 ),
    inference(avatar_component_clause,[],[f565]) ).

fof(f897,plain,
    ( spl0_114
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f419,f381,f336,f895]) ).

fof(f419,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_31
    | ~ spl0_40 ),
    inference(superposition,[],[f337,f382]) ).

fof(f893,plain,
    ( spl0_113
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f318,f300,f288,f891]) ).

fof(f318,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_20
    | ~ spl0_23 ),
    inference(resolution,[],[f301,f289]) ).

fof(f832,plain,
    ( spl0_112
    | ~ spl0_31
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f621,f610,f336,f830]) ).

fof(f621,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_31
    | ~ spl0_76 ),
    inference(superposition,[],[f337,f612]) ).

fof(f828,plain,
    ( spl0_111
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f412,f377,f259,f826]) ).

fof(f412,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f260]) ).

fof(f824,plain,
    ( spl0_110
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f400,f373,f255,f822]) ).

fof(f400,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_12
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f256]) ).

fof(f820,plain,
    ( spl0_109
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f399,f373,f241,f818]) ).

fof(f399,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_9
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f242]) ).

fof(f813,plain,
    ( ~ spl0_107
    | spl0_108
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(avatar_split_clause,[],[f778,f764,f255,f810,f806]) ).

fof(f806,plain,
    ( spl0_107
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f778,plain,
    ( member(null_class,element_relation)
    | ~ inductive(singleton_relation)
    | ~ spl0_12
    | ~ spl0_103 ),
    inference(resolution,[],[f765,f256]) ).

fof(f798,plain,
    ( spl0_106
    | ~ spl0_4
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f549,f544,f220,f796]) ).

fof(f796,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f549,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_4
    | ~ spl0_65 ),
    inference(resolution,[],[f545,f221]) ).

fof(f788,plain,
    ( spl0_105
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f369,f340,f255,f786]) ).

fof(f786,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f369,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_12
    | ~ spl0_32 ),
    inference(resolution,[],[f341,f256]) ).

fof(f770,plain,
    ( spl0_104
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f422,f394,f340,f768]) ).

fof(f422,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_32
    | ~ spl0_43 ),
    inference(superposition,[],[f341,f396]) ).

fof(f766,plain,
    ( spl0_103
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f420,f385,f340,f764]) ).

fof(f420,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_32
    | ~ spl0_41 ),
    inference(superposition,[],[f341,f387]) ).

fof(f761,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f203,f759]) ).

fof(f759,plain,
    ( spl0_102
  <=> ! [X9,X11,X10] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
        | ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f203,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f202,f129]) ).

fof(f129,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).

fof(f202,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f201,f129]) ).

fof(f201,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f200,f129]) ).

fof(f200,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f199,f129]) ).

fof(f199,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f198,f129]) ).

fof(f198,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f197,f129]) ).

fof(f197,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f196,f129]) ).

fof(f196,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f195,f129]) ).

fof(f195,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f194,f129]) ).

fof(f194,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f176,f129]) ).

fof(f176,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f91,f117,f118,f117,f117,f117,f117,f118]) ).

fof(f118,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).

fof(f117,plain,
    ! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
    inference(definition_unfolding,[],[f68,f114,f116,f12]) ).

fof(f116,plain,
    ! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
    inference(definition_unfolding,[],[f42,f115,f29]) ).

fof(f115,plain,
    ! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
    inference(definition_unfolding,[],[f39,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

fof(f39,axiom,
    ! [X4] : domain_of(inverse(X4)) = range_of(X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).

fof(f42,axiom,
    ! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).

fof(f114,plain,
    ! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
    inference(definition_unfolding,[],[f53,f29]) ).

fof(f53,axiom,
    ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).

fof(f68,axiom,
    ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).

fof(f91,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).

fof(f754,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f193,f752]) ).

fof(f193,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f192,f129]) ).

fof(f192,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f191,f129]) ).

fof(f191,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f190,f129]) ).

fof(f190,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f189,f129]) ).

fof(f189,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f168,f129]) ).

fof(f168,plain,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f89,f118,f117,f118,f117,f117,f117,f117,f118]) ).

fof(f89,axiom,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(ordered_pair(X0,X1),domain_of(X10))
      | apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).

fof(f749,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f188,f747]) ).

fof(f188,plain,
    ! [X0,X1,X4] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
      | ~ member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(forward_demodulation,[],[f167,f129]) ).

fof(f167,plain,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(definition_unfolding,[],[f108,f118,f118,f117,f118,f118]) ).

fof(f108,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).

fof(f743,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f172,f741]) ).

fof(f172,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f37,f118,f118,f118,f118,f118,f118]) ).

fof(f37,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).

fof(f739,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f171,f737]) ).

fof(f171,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f34,f118,f118,f118,f118,f118,f118]) ).

fof(f34,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).

fof(f735,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f156,f733]) ).

fof(f156,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
    inference(definition_unfolding,[],[f36,f118,f118,f118,f118]) ).

fof(f36,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).

fof(f731,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f155,f729]) ).

fof(f155,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
    inference(definition_unfolding,[],[f33,f118,f118,f118,f118]) ).

fof(f33,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).

fof(f726,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f179,f724]) ).

fof(f179,plain,
    ! [X0] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f166]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f46,f124,f118,f118]) ).

fof(f124,plain,
    ! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
    inference(definition_unfolding,[],[f43,f26,f12]) ).

fof(f26,axiom,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).

fof(f43,axiom,
    ! [X0] : union(X0,singleton(X0)) = successor(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).

fof(f46,axiom,
    ! [X0,X1] :
      ( successor(X0) != X1
      | member(ordered_pair(X0,X1),successor_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).

fof(f710,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f170,f708]) ).

fof(f170,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f59,f118,f118,f116,f116,f12]) ).

fof(f59,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
      | member(ordered_pair(X1,X4),compose(X7,X5))
      | ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).

fof(f704,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f153,f702]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
    inference(definition_unfolding,[],[f97,f118,f118,f118]) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
      | member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).

fof(f700,plain,
    ( ~ spl0_91
    | spl0_92
    | ~ spl0_4
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f607,f596,f220,f697,f693]) ).

fof(f697,plain,
    ( spl0_92
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f607,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_4
    | ~ spl0_75 ),
    inference(resolution,[],[f597,f221]) ).

fof(f691,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f184,f689]) ).

fof(f184,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(forward_demodulation,[],[f150,f129]) ).

fof(f150,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f107,f117,f118,f118]) ).

fof(f107,axiom,
    ! [X0,X1,X4] :
      ( apply(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).

fof(f686,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f175,f684]) ).

fof(f175,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
    inference(definition_unfolding,[],[f90,f118]) ).

fof(f90,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).

fof(f682,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f154,f680]) ).

fof(f154,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f58,f118,f116,f116,f12]) ).

fof(f58,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),compose(X7,X5))
      | member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).

fof(f677,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f180,f675]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f169]) ).

fof(f169,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f94,f118,f118]) ).

fof(f94,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(ordered_pair(X1,X4),compose_class(X0))
      | ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).

fof(f673,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f152,f671]) ).

fof(f152,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
    inference(definition_unfolding,[],[f96,f118,f118]) ).

fof(f96,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).

fof(f669,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f148,f667]) ).

fof(f148,plain,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f106,f118,f118]) ).

fof(f106,axiom,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).

fof(f664,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f163,f662]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f20,f118,f118]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(ordered_pair(X0,X1),element_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).

fof(f654,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f187,f652]) ).

fof(f187,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f186,f129]) ).

fof(f186,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f164,f129]) ).

fof(f164,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
    inference(definition_unfolding,[],[f70,f117]) ).

fof(f70,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(apply(choice,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).

fof(f650,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f173,f648]) ).

fof(f648,plain,
    ( spl0_82
  <=> ! [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_82])]) ).

fof(f173,plain,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f81,f115]) ).

fof(f81,axiom,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(range_of(X8),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).

fof(f645,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f174,f643]) ).

fof(f174,plain,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f85,f115]) ).

fof(f85,axiom,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).

fof(f641,plain,
    ( spl0_80
    | ~ spl0_3
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f603,f575,f215,f638]) ).

fof(f638,plain,
    ( spl0_80
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f603,plain,
    ( single_valued_class(choice)
    | ~ spl0_3
    | ~ spl0_71 ),
    inference(resolution,[],[f576,f217]) ).

fof(f632,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f149,f630]) ).

fof(f149,plain,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
    inference(definition_unfolding,[],[f17,f118]) ).

fof(f17,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).

fof(f628,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f146,f626]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
    inference(definition_unfolding,[],[f45,f124,f118]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( successor(X0) = X1
      | ~ member(ordered_pair(X0,X1),successor_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).

fof(f617,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f162,f615]) ).

fof(f162,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f16,f118]) ).

fof(f16,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f613,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f130,f610]) ).

fof(f130,plain,
    subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
    inference(definition_unfolding,[],[f74,f38]) ).

fof(f74,axiom,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).

fof(f598,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f185,f596]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | inductive(X0)
      | ~ member(null_class,X0) ),
    inference(forward_demodulation,[],[f160,f129]) ).

fof(f160,plain,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f49,f116]) ).

fof(f49,axiom,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).

fof(f594,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f182,f592]) ).

fof(f182,plain,
    ! [X2] :
      ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
      | ~ member(X2,universal_class) ),
    inference(forward_demodulation,[],[f137,f129]) ).

fof(f137,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
    inference(definition_unfolding,[],[f56,f125]) ).

fof(f125,plain,
    ! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
    inference(definition_unfolding,[],[f55,f116]) ).

fof(f55,axiom,
    ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).

fof(f56,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(power_class(X2),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).

fof(f590,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f158,f588]) ).

fof(f158,plain,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
    inference(definition_unfolding,[],[f65,f116]) ).

fof(f65,axiom,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(image(X8,X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).

fof(f586,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f151,f584]) ).

fof(f151,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
    inference(definition_unfolding,[],[f93,f118]) ).

fof(f93,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).

fof(f577,plain,
    ( spl0_71
    | ~ spl0_52
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f497,f465,f461,f575]) ).

fof(f497,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_52
    | ~ spl0_53 ),
    inference(resolution,[],[f466,f462]) ).

fof(f571,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f165,f569]) ).

fof(f165,plain,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f31,f29,f12]) ).

fof(f31,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).

fof(f567,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f161,f565]) ).

fof(f161,plain,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f64,f38]) ).

fof(f64,axiom,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).

fof(f563,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f142,f561]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f14,f118]) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).

fof(f559,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f141,f557]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f15,f118]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).

fof(f555,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f139,f553]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
    inference(definition_unfolding,[],[f100,f118]) ).

fof(f100,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).

fof(f546,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f159,f544]) ).

fof(f159,plain,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
      | maps(X8,domain_of(X8),X1) ),
    inference(definition_unfolding,[],[f112,f115]) ).

fof(f112,axiom,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(range_of(X8),X1)
      | maps(X8,domain_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).

fof(f542,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f147,f540]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
    inference(definition_unfolding,[],[f99,f118]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(ordered_pair(X0,X1),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).

fof(f537,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f181,f535]) ).

fof(f181,plain,
    ! [X0] :
      ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | ~ inductive(X0) ),
    inference(forward_demodulation,[],[f133,f129]) ).

fof(f133,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f48,f116]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).

fof(f533,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f145,f531]) ).

fof(f531,plain,
    ( spl0_62
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f145,plain,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f84,f115]) ).

fof(f84,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).

fof(f529,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f140,f527]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
    inference(definition_unfolding,[],[f19,f118]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(ordered_pair(X0,X1),element_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).

fof(f521,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f143,f519]) ).

fof(f143,plain,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f30,f29,f12]) ).

fof(f30,axiom,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) != null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).

fof(f516,plain,
    ( ~ spl0_59
    | spl0_1
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f491,f453,f205,f513]) ).

fof(f491,plain,
    ( null_class != intersection(xr,cross_product(null_class,y))
    | spl0_1
    | ~ spl0_50 ),
    inference(superposition,[],[f207,f454]) ).

fof(f511,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f144,f509]) ).

fof(f509,plain,
    ( spl0_58
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f144,plain,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
    inference(definition_unfolding,[],[f111,f115]) ).

fof(f111,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(range_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).

fof(f507,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f134,f505]) ).

fof(f134,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f115]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).

fof(f503,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f79,f501]) ).

fof(f501,plain,
    ( spl0_56
  <=> ! [X8] :
        ( ~ operation(X8)
        | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f79,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).

fof(f480,plain,
    ( spl0_55
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f405,f377,f220,f478]) ).

fof(f405,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_4
    | ~ spl0_39 ),
    inference(resolution,[],[f378,f221]) ).

fof(f471,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f183,f469]) ).

fof(f183,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f138,f129]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f114]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).

fof(f467,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f136,f465]) ).

fof(f136,plain,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f61,f38]) ).

fof(f61,axiom,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).

fof(f463,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f135,f461]) ).

fof(f135,plain,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f63,f38]) ).

fof(f63,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).

fof(f459,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f131,f457]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f60,f38]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f455,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f129,f453]) ).

fof(f451,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f23,f449]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,X1)
      | member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).

fof(f447,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f8,f445]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | X0 = X2
      | ~ member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f442,plain,
    ( spl0_47
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f398,f373,f224,f440]) ).

fof(f224,plain,
    ( spl0_5
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f398,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_5
    | ~ spl0_38 ),
    inference(resolution,[],[f374,f226]) ).

fof(f226,plain,
    ( member(omega,universal_class)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f224]) ).

fof(f435,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f157,f433]) ).

fof(f433,plain,
    ( spl0_46
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f157,plain,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f73,f38]) ).

fof(f73,axiom,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).

fof(f431,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f83,f429]) ).

fof(f429,plain,
    ( spl0_45
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f83,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) = domain_of(X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).

fof(f427,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f25,f425]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,X0)
      | member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).

fof(f397,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f128,f394]) ).

fof(f128,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).

fof(f392,plain,
    ( spl0_42
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f366,f336,f255,f390]) ).

fof(f366,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_12
    | ~ spl0_31 ),
    inference(resolution,[],[f337,f256]) ).

fof(f388,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f104,f385]) ).

fof(f104,axiom,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).

fof(f383,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f67,f381]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).

fof(f379,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f7,f377]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f375,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f1,f373]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).

fof(f362,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f132,f360]) ).

fof(f132,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).

fof(f358,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f110,f356]) ).

fof(f356,plain,
    ( spl0_36
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).

fof(f354,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f88,f352]) ).

fof(f352,plain,
    ( spl0_35
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).

fof(f350,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f35,f348]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).

fof(f346,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f32,f344]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).

fof(f342,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f22,f340]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).

fof(f338,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f21,f336]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).

fof(f334,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f10,f332]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f330,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f9,f328]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f326,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f3,f324]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f322,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f2,f320]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f317,plain,
    ( spl0_26
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f313,f288,f255,f315]) ).

fof(f315,plain,
    ( spl0_26
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f313,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_12
    | ~ spl0_20 ),
    inference(resolution,[],[f289,f256]) ).

fof(f312,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f105,f309]) ).

fof(f105,axiom,
    subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).

fof(f307,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f95,f304]) ).

fof(f95,axiom,
    subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).

fof(f302,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f66,f300]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f298,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f62,f296]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f294,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f57,f292]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).

fof(f290,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f24,f288]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f286,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f109,f284]) ).

fof(f284,plain,
    ( spl0_19
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).

fof(f282,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f92,f280]) ).

fof(f92,axiom,
    ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).

fof(f278,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f87,f276]) ).

fof(f276,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).

fof(f274,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f86,f272]) ).

fof(f272,plain,
    ( spl0_16
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).

fof(f270,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f82,f268]) ).

fof(f268,plain,
    ( spl0_15
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).

fof(f266,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f98,f263]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f261,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f51,f259]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f257,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f47,f255]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).

fof(f253,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f44,f250]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).

fof(f248,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f18,f245]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).

fof(f243,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f11,f241]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f239,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f78,f237]) ).

fof(f237,plain,
    ( spl0_8
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).

fof(f235,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f71,f233]) ).

fof(f233,plain,
    ( spl0_7
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).

fof(f231,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f177,f229]) ).

fof(f177,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).

fof(f227,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f52,f224]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f222,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f4,f220]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f218,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f69,f215]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f213,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f50,f210]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f208,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f127,f205]) ).

fof(f127,plain,
    null_class != intersection(cross_product(null_class,y),xr),
    inference(definition_unfolding,[],[f113,f29]) ).

fof(f113,axiom,
    null_class != restrict(xr,null_class,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_with_null_class2_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET246-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n009.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 16:21:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (10440)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (10443)WARNING: value z3 for option sas not known
% 0.14/0.39  % (10442)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (10447)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39  % (10444)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  % (10443)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39  % (10446)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39  % (10445)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39  % (10441)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.42  TRYING [1]
% 0.20/0.43  TRYING [2]
% 0.20/0.47  TRYING [3]
% 1.30/0.56  TRYING [1]
% 1.30/0.57  TRYING [2]
% 1.30/0.59  TRYING [4]
% 2.35/0.71  TRYING [3]
% 4.45/1.02  TRYING [5]
% 7.71/1.49  TRYING [1]
% 7.71/1.49  TRYING [2]
% 7.71/1.51  TRYING [3]
% 8.50/1.59  TRYING [4]
% 9.18/1.73  TRYING [4]
% 9.78/1.81  TRYING [5]
% 14.67/2.48  TRYING [6]
% 17.67/2.90  TRYING [6]
% 24.88/3.95  % (10445)First to succeed.
% 25.83/4.08  % (10445)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10440"
% 25.83/4.09  % (10445)Refutation found. Thanks to Tanya!
% 25.83/4.09  % SZS status Unsatisfiable for theBenchmark
% 25.83/4.09  % SZS output start Proof for theBenchmark
% See solution above
% 26.21/4.15  % (10445)------------------------------
% 26.21/4.15  % (10445)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 26.21/4.15  % (10445)Termination reason: Refutation
% 26.21/4.15  
% 26.21/4.15  % (10445)Memory used [KB]: 29107
% 26.21/4.15  % (10445)Time elapsed: 3.700 s
% 26.21/4.15  % (10445)Instructions burned: 6991 (million)
% 26.21/4.15  % (10440)Success in time 3.753 s
%------------------------------------------------------------------------------