TSTP Solution File: SET468-6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET468-6 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:08:06 EDT 2024
% Result : Unsatisfiable 67.06s 9.98s
% Output : Refutation 67.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1437
% Syntax : Number of formulae : 4580 ( 136 unt; 0 def)
% Number of atoms : 17356 (2232 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 22490 (9714 ~;11444 |; 0 &)
% (1332 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 28 ( 4 avg)
% Number of predicates : 1344 (1342 usr;1333 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 13 con; 0-3 aty)
% Number of variables : 6142 (6142 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f58587,plain,
$false,
inference(avatar_sat_refutation,[],[f211,f215,f219,f224,f229,f233,f237,f242,f246,f250,f256,f260,f264,f268,f273,f278,f283,f287,f292,f301,f305,f309,f313,f317,f321,f325,f329,f333,f337,f342,f348,f356,f360,f364,f368,f372,f376,f380,f384,f388,f392,f396,f400,f419,f423,f427,f432,f437,f467,f471,f475,f482,f487,f491,f495,f499,f503,f507,f511,f546,f550,f554,f564,f568,f572,f578,f582,f591,f600,f604,f608,f612,f620,f624,f628,f638,f642,f656,f660,f669,f674,f678,f684,f688,f692,f696,f701,f705,f710,f714,f720,f736,f741,f745,f754,f758,f762,f768,f773,f780,f784,f805,f809,f821,f825,f830,f847,f851,f883,f887,f892,f907,f914,f920,f948,f961,f969,f982,f987,f991,f995,f999,f1003,f1025,f1031,f1033,f1099,f1106,f1118,f1122,f1126,f1176,f1180,f1218,f1231,f1261,f1270,f1279,f1288,f1292,f1296,f1319,f1323,f1327,f1331,f1353,f1368,f1378,f1382,f1386,f1390,f1394,f1450,f1454,f1458,f1482,f1504,f1511,f1518,f1527,f1536,f1540,f1544,f1572,f1581,f1586,f1596,f1600,f1604,f1608,f1620,f1627,f1638,f1642,f1646,f1650,f1717,f1723,f1727,f1731,f1735,f1739,f1798,f1805,f1809,f1816,f1849,f1854,f1869,f1873,f1879,f1892,f1896,f1902,f1931,f1952,f1956,f2012,f2051,f2101,f2114,f2124,f2130,f2183,f2194,f2207,f2211,f2220,f2260,f2265,f2273,f2282,f2288,f2292,f2301,f2305,f2310,f2326,f2332,f2341,f2361,f2372,f2377,f2384,f2388,f2408,f2412,f2417,f2439,f2451,f2480,f2493,f2498,f2503,f2508,f2514,f2522,f2528,f2532,f2677,f2712,f2716,f2724,f2735,f2777,f2782,f2786,f2791,f2795,f2799,f2803,f2807,f2811,f2820,f2958,f2962,f2966,f2967,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3010,f3172,f3176,f3181,f3185,f3189,f3198,f3202,f3206,f3210,f3273,f3401,f3405,f3409,f3413,f3423,f3488,f3497,f3506,f3511,f3515,f3519,f3523,f3527,f3531,f3540,f3547,f3556,f3562,f3713,f3717,f3721,f3725,f3729,f3733,f3899,f3938,f3944,f3949,f3954,f3959,f4007,f4011,f4015,f4019,f4023,f4121,f4125,f4169,f4173,f4178,f4220,f4224,f4228,f4232,f4240,f4245,f4374,f4378,f4382,f4386,f4390,f4394,f4399,f4403,f4416,f4432,f4874,f4885,f4915,f4919,f4924,f4970,f4976,f4982,f4986,f4992,f4997,f5003,f5008,f5128,f5256,f5260,f5291,f5298,f5302,f5306,f5331,f5335,f5339,f5369,f5378,f5386,f5390,f5395,f5399,f5403,f5407,f5411,f5415,f5558,f5562,f5566,f5570,f5574,f5635,f5640,f5685,f5689,f5693,f5697,f5701,f5709,f5720,f5729,f5733,f5737,f5816,f5820,f5824,f5828,f5837,f5841,f5881,f5892,f5897,f5918,f5922,f5926,f5930,f5934,f5938,f5942,f6033,f6157,f6161,f6165,f6169,f6329,f6336,f6340,f6344,f6348,f6436,f6459,f6466,f6524,f6528,f6532,f6536,f6540,f6548,f6646,f6650,f6654,f6658,f6662,f6900,f6904,f6947,f6951,f6955,f6959,f6963,f7057,f7068,f7150,f7196,f7211,f7231,f7235,f7239,f7258,f7280,f7284,f7288,f7292,f7296,f7300,f7304,f7308,f7348,f7352,f7356,f7360,f7364,f7368,f7432,f7606,f7610,f7614,f7622,f7636,f7661,f7665,f7669,f7673,f7677,f7681,f8004,f8008,f8012,f8016,f8020,f8024,f8028,f8141,f8145,f8149,f8153,f8157,f8229,f8355,f8363,f8375,f8379,f8388,f8392,f8401,f8437,f8441,f8445,f8449,f8607,f8611,f8615,f8619,f8623,f8627,f8631,f8635,f8639,f8643,f8647,f8993,f8997,f9001,f9036,f9092,f9097,f9104,f9108,f9112,f9116,f9120,f9124,f9128,f9138,f9465,f9470,f9522,f9562,f9569,f9577,f9675,f9679,f9683,f9687,f9691,f9695,f9699,f9703,f9707,f9711,f9715,f9719,f9723,f10478,f10570,f10574,f10578,f10584,f10775,f10779,f10910,f10914,f10927,f10937,f10951,f10984,f10992,f10999,f11003,f11007,f11011,f11019,f11147,f11190,f11194,f11238,f11242,f11246,f11393,f11408,f11412,f11420,f11428,f11432,f11497,f11568,f11577,f11584,f11601,f11605,f11609,f11613,f11619,f11717,f11722,f11830,f11880,f12199,f12669,f12674,f12678,f12682,f12686,f12690,f12694,f12702,f12734,f12963,f12967,f13102,f13106,f13111,f13115,f13119,f13123,f13127,f13240,f13261,f13339,f13343,f13347,f13351,f13355,f13356,f13362,f13549,f13591,f13596,f13600,f13620,f13624,f13628,f13632,f13636,f13866,f13870,f13874,f13878,f13913,f13963,f14124,f14310,f14314,f14318,f14322,f14326,f14330,f14334,f14383,f14402,f14527,f14552,f14580,f14582,f14601,f14702,f14736,f14740,f14762,f14869,f14924,f14928,f14932,f15002,f15006,f15120,f15128,f15132,f15246,f15251,f15255,f15337,f15344,f15361,f15410,f15414,f15418,f15422,f15468,f15472,f15476,f15527,f15531,f15535,f15644,f15652,f15657,f15682,f15686,f15690,f15694,f15698,f15702,f15707,f15711,f15719,f15918,f15922,f15930,f15995,f16030,f16110,f16201,f16221,f16225,f16261,f16265,f16270,f16274,f16278,f16282,f16434,f16438,f16442,f16446,f16450,f16454,f16646,f16654,f16662,f16667,f16698,f16752,f16756,f16760,f16814,f16822,f16829,f16833,f17045,f17049,f17070,f17272,f17278,f17283,f17288,f17318,f17451,f17653,f17658,f17664,f17761,f17766,f17789,f18174,f18712,f18842,f19044,f19049,f19055,f19060,f19341,f19345,f19349,f19353,f19465,f19546,f19550,f19572,f19590,f19632,f19636,f19637,f19658,f19662,f19706,f19713,f19742,f19746,f19752,f19833,f19837,f19841,f19842,f19897,f19905,f19909,f19914,f19991,f20004,f20010,f20091,f20101,f20105,f20130,f20134,f20138,f20143,f20147,f20532,f20536,f20540,f20544,f20625,f20630,f20657,f20664,f20668,f20764,f20780,f20784,f20788,f20793,f20797,f21001,f21034,f21038,f21042,f21232,f21236,f21240,f21244,f21345,f21369,f21373,f21377,f21583,f21592,f21596,f21600,f21774,f21797,f21801,f21805,f21809,f21813,f21856,f21888,f21892,f21928,f21962,f21966,f22000,f22018,f22022,f22026,f22030,f22034,f22139,f22164,f22174,f22190,f22221,f22225,f22282,f22286,f22290,f22298,f22306,f22311,f22332,f22404,f22408,f22412,f22416,f22522,f22532,f22536,f22540,f22568,f22619,f22663,f22667,f22671,f22696,f22701,f22705,f22764,f22772,f22776,f22783,f22824,f22825,f22826,f22827,f24034,f24437,f24877,f25779,f26391,f26909,f27624,f27899,f28737,f29385,f29416,f29421,f29501,f29505,f29509,f29721,f29726,f29744,f29748,f29789,f29821,f29825,f29850,f29881,f29897,f29926,f29950,f29965,f29969,f30061,f30071,f30092,f30114,f30118,f30122,f30126,f30409,f30413,f30417,f30495,f30499,f30874,f30889,f31056,f31104,f31108,f31171,f31175,f31180,f31184,f31188,f31192,f31196,f31464,f31468,f31472,f31476,f31501,f31569,f31594,f31598,f31640,f31714,f31756,f31830,f31834,f31839,f31843,f31868,f31915,f31919,f32088,f32092,f32132,f32136,f32158,f32200,f32242,f32288,f32331,f32374,f32418,f32422,f32489,f32493,f32498,f32504,f32570,f32575,f32580,f32585,f32590,f32600,f32605,f32609,f32614,f32625,f32630,f32635,f32640,f32646,f32651,f32657,f32665,f32688,f32717,f32742,f32744,f32748,f32752,f32756,f32760,f33072,f33390,f33395,f33399,f33405,f33411,f33416,f33428,f33432,f33436,f33522,f33527,f33532,f33537,f33542,f33547,f33594,f33595,f33596,f33601,f33607,f33620,f33626,f33630,f33634,f33638,f33642,f33646,f33650,f33807,f33812,f33816,f33820,f33825,f33831,f33835,f33839,f33844,f33849,f33854,f33859,f33883,f33907,f33912,f33918,f33923,f33933,f33937,f33941,f33950,f33954,f33958,f33962,f34270,f34276,f34281,f34285,f34290,f34295,f34301,f34305,f34310,f34315,f34320,f34325,f34330,f34335,f34348,f34354,f34359,f34363,f34368,f34373,f34378,f34383,f34387,f34391,f34395,f34399,f34404,f34419,f34423,f34981,f34986,f34991,f35001,f35006,f35011,f35016,f35021,f35026,f35117,f35124,f35128,f35132,f35136,f35140,f35144,f35434,f35439,f35444,f35449,f35454,f35459,f35464,f35469,f35474,f35479,f35484,f35489,f35494,f35499,f35504,f35509,f35514,f35520,f35524,f35529,f35539,f35543,f35548,f35554,f35559,f35625,f35630,f35634,f35639,f35644,f35649,f35653,f35657,f35662,f35666,f35670,f35674,f35678,f35682,f35686,f35690,f35694,f35698,f35702,f35706,f35710,f35714,f35718,f36246,f36846,f37070,f37075,f37080,f37085,f37090,f37095,f37100,f37105,f37111,f37408,f37413,f37419,f37424,f37429,f37434,f37439,f37445,f37450,f37455,f37982,f37987,f37992,f37997,f38027,f38032,f38056,f38063,f38069,f38073,f38078,f38088,f38097,f38104,f38112,f38119,f38126,f38130,f38134,f38138,f38142,f38146,f38150,f38154,f38158,f38162,f38166,f38291,f38295,f38299,f38303,f38307,f38311,f38315,f38319,f38350,f41671,f41702,f41892,f41953,f41983,f42001,f42005,f42035,f42039,f42462,f43231,f46498,f47873,f48626,f49376,f49500,f49516,f49569,f49571,f49610,f49616,f50260,f50265,f50415,f50475,f50863,f51163,f51164,f51923,f51929,f51930,f52275,f52434,f52476,f53541,f53542,f53592,f53645,f54889,f56407,f56409,f56437,f56441,f56542,f57035,f57040,f57044,f57048,f57052,f57168,f57181,f57185,f57189,f57193,f57198,f57204,f57209,f57213,f57218,f57231,f57244,f57248,f57257,f57409,f57552,f57561,f57713,f57853,f57951,f58277,f58281,f58428,f58433,f58438,f58443,f58448,f58453,f58458,f58463,f58468,f58473,f58475,f58520,f58525,f58530,f58534,f58538,f58555,f58572,f58585,f58586]) ).
fof(f58586,plain,
( ~ spl0_343
| spl0_1
| ~ spl0_1310 ),
inference(avatar_split_clause,[],[f58364,f57949,f208,f4175]) ).
fof(f4175,plain,
( spl0_343
<=> subclass(x,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f208,plain,
( spl0_1
<=> subclass(cross_product(x,x),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f57949,plain,
( spl0_1310
<=> ! [X0] : x = cross_product(X0,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f58364,plain,
( ~ subclass(x,identity_relation)
| spl0_1
| ~ spl0_1310 ),
inference(superposition,[],[f210,f57950]) ).
fof(f57950,plain,
( ! [X0] : x = cross_product(X0,x)
| ~ spl0_1310 ),
inference(avatar_component_clause,[],[f57949]) ).
fof(f210,plain,
( ~ subclass(cross_product(x,x),identity_relation)
| spl0_1 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f58585,plain,
( ~ spl0_1330
| spl0_868
| ~ spl0_1331
| spl0_1332
| ~ spl0_18
| ~ spl0_326 ),
inference(avatar_split_clause,[],[f3875,f3727,f285,f58582,f58578,f21589,f58574]) ).
fof(f58574,plain,
( spl0_1330
<=> inductive(complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f21589,plain,
( spl0_868
<=> omega = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f58578,plain,
( spl0_1331
<=> member(regular(omega),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f58582,plain,
( spl0_1332
<=> member(regular(omega),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f285,plain,
( spl0_18
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f3727,plain,
( spl0_326
<=> ! [X0] :
( ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f3875,plain,
( member(regular(omega),singleton_relation)
| ~ member(regular(omega),element_relation)
| omega = x
| ~ inductive(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_18
| ~ spl0_326 ),
inference(resolution,[],[f3728,f286]) ).
fof(f286,plain,
( ! [X1] :
( subclass(omega,X1)
| ~ inductive(X1) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f3728,plain,
( ! [X0] :
( ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| member(regular(X0),singleton_relation)
| ~ member(regular(X0),element_relation)
| x = X0 )
| ~ spl0_326 ),
inference(avatar_component_clause,[],[f3727]) ).
fof(f58572,plain,
( spl0_1329
| ~ spl0_108
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3794,f3715,f823,f58570]) ).
fof(f58570,plain,
( spl0_1329
<=> ! [X0,X1] :
( member(regular(X0),x)
| x = X1
| ~ subclass(X0,regular(X1))
| x = X0
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f823,plain,
( spl0_108
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f3715,plain,
( spl0_323
<=> ! [X0,X1] :
( member(regular(X0),x)
| ~ member(regular(X0),X1)
| x = X1
| ~ subclass(X0,regular(X1))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3794,plain,
( ! [X0,X1] :
( member(regular(X0),x)
| x = X1
| ~ subclass(X0,regular(X1))
| x = X0
| ~ subclass(X0,X1) )
| ~ spl0_108
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3738]) ).
fof(f3738,plain,
( ! [X0,X1] :
( member(regular(X0),x)
| x = X1
| ~ subclass(X0,regular(X1))
| x = X0
| ~ subclass(X0,X1)
| x = X0 )
| ~ spl0_108
| ~ spl0_323 ),
inference(resolution,[],[f3716,f824]) ).
fof(f824,plain,
( ! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| x = X0 )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f3716,plain,
( ! [X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),x)
| x = X1
| ~ subclass(X0,regular(X1))
| x = X0 )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f3715]) ).
fof(f58555,plain,
( spl0_1275
| spl0_1328
| ~ spl0_243
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3781,f3715,f2382,f58553,f53534]) ).
fof(f53534,plain,
( spl0_1275
<=> element_relation = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f58553,plain,
( spl0_1328
<=> ! [X0] :
( member(regular(X0),x)
| ~ subclass(X0,singleton_relation)
| x = X0
| ~ subclass(X0,regular(element_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f2382,plain,
( spl0_243
<=> ! [X0] :
( member(regular(X0),element_relation)
| ~ subclass(X0,singleton_relation)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f3781,plain,
( ! [X0] :
( member(regular(X0),x)
| element_relation = x
| ~ subclass(X0,regular(element_relation))
| x = X0
| ~ subclass(X0,singleton_relation) )
| ~ spl0_243
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3756]) ).
fof(f3756,plain,
( ! [X0] :
( member(regular(X0),x)
| element_relation = x
| ~ subclass(X0,regular(element_relation))
| x = X0
| ~ subclass(X0,singleton_relation)
| x = X0 )
| ~ spl0_243
| ~ spl0_323 ),
inference(resolution,[],[f3716,f2383]) ).
fof(f2383,plain,
( ! [X0] :
( member(regular(X0),element_relation)
| ~ subclass(X0,singleton_relation)
| x = X0 )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2382]) ).
fof(f58538,plain,
( spl0_237
| spl0_1327
| ~ spl0_244
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3778,f3715,f2386,f58536,f2334]) ).
fof(f2334,plain,
( spl0_237
<=> subset_relation = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f58536,plain,
( spl0_1327
<=> ! [X0] :
( member(regular(X0),x)
| ~ subclass(X0,identity_relation)
| x = X0
| ~ subclass(X0,regular(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f2386,plain,
( spl0_244
<=> ! [X0] :
( member(regular(X0),subset_relation)
| ~ subclass(X0,identity_relation)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f3778,plain,
( ! [X0] :
( member(regular(X0),x)
| subset_relation = x
| ~ subclass(X0,regular(subset_relation))
| x = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_244
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3769]) ).
fof(f3769,plain,
( ! [X0] :
( member(regular(X0),x)
| subset_relation = x
| ~ subclass(X0,regular(subset_relation))
| x = X0
| ~ subclass(X0,identity_relation)
| x = X0 )
| ~ spl0_244
| ~ spl0_323 ),
inference(resolution,[],[f3716,f2387]) ).
fof(f2387,plain,
( ! [X0] :
( member(regular(X0),subset_relation)
| ~ subclass(X0,identity_relation)
| x = X0 )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2386]) ).
fof(f58534,plain,
( spl0_1326
| ~ spl0_157
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3706,f3560,f1376,f58532]) ).
fof(f58532,plain,
( spl0_1326
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),x),X0)
| subclass(intersection(regular(X0),X1),x)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f1376,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f3560,plain,
( spl0_321
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X1,x),regular(X0))
| ~ member(not_subclass_element(X1,x),X0)
| subclass(X1,x)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f3706,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),x),X0)
| subclass(intersection(regular(X0),X1),x)
| x = X0 )
| ~ spl0_157
| ~ spl0_321 ),
inference(duplicate_literal_removal,[],[f3689]) ).
fof(f3689,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),x),X0)
| subclass(intersection(regular(X0),X1),x)
| x = X0
| subclass(intersection(regular(X0),X1),x) )
| ~ spl0_157
| ~ spl0_321 ),
inference(resolution,[],[f3561,f1377]) ).
fof(f1377,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f3561,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X1,x),regular(X0))
| ~ member(not_subclass_element(X1,x),X0)
| subclass(X1,x)
| x = X0 )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3560]) ).
fof(f58530,plain,
( spl0_1325
| ~ spl0_158
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3705,f3560,f1380,f58528]) ).
fof(f58528,plain,
( spl0_1325
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),x),X1)
| subclass(intersection(X0,regular(X1)),x)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f1380,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f3705,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),x),X1)
| subclass(intersection(X0,regular(X1)),x)
| x = X1 )
| ~ spl0_158
| ~ spl0_321 ),
inference(duplicate_literal_removal,[],[f3690]) ).
fof(f3690,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),x),X1)
| subclass(intersection(X0,regular(X1)),x)
| x = X1
| subclass(intersection(X0,regular(X1)),x) )
| ~ spl0_158
| ~ spl0_321 ),
inference(resolution,[],[f3561,f1381]) ).
fof(f1381,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1380]) ).
fof(f58525,plain,
( spl0_1324
| ~ spl0_38
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3379,f3208,f374,f58523]) ).
fof(f58523,plain,
( spl0_1324
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,x),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,x),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f374,plain,
( spl0_38
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f3208,plain,
( spl0_297
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,x),X1)
| member(not_subclass_element(intersection(X0,x),X1),X2)
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f3379,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,x),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,x),X1),X2) )
| ~ spl0_38
| ~ spl0_297 ),
inference(resolution,[],[f3209,f375]) ).
fof(f375,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f3209,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,x),X1),X2)
| subclass(intersection(X0,x),X1)
| x = X2 )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f3208]) ).
fof(f58520,plain,
( spl0_1323
| ~ spl0_39
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3378,f3208,f378,f58518]) ).
fof(f58518,plain,
( spl0_1323
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,x),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,x),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f378,plain,
( spl0_39
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f3378,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,x),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,x),X1),X3) )
| ~ spl0_39
| ~ spl0_297 ),
inference(resolution,[],[f3209,f379]) ).
fof(f379,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f58475,plain,
( spl0_188
| ~ spl0_1234
| ~ spl0_1310 ),
inference(avatar_split_clause,[],[f58282,f57949,f38124,f1710]) ).
fof(f1710,plain,
( spl0_188
<=> singleton_relation = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f38124,plain,
( spl0_1234
<=> ! [X0] : singleton_relation = cross_product(singleton_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f58282,plain,
( singleton_relation = x
| ~ spl0_1234
| ~ spl0_1310 ),
inference(superposition,[],[f57950,f38125]) ).
fof(f38125,plain,
( ! [X0] : singleton_relation = cross_product(singleton_relation,X0)
| ~ spl0_1234 ),
inference(avatar_component_clause,[],[f38124]) ).
fof(f58473,plain,
( spl0_1322
| ~ spl0_38
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3350,f3204,f374,f58471]) ).
fof(f58471,plain,
( spl0_1322
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(x,X0),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(x,X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f3204,plain,
( spl0_296
<=> ! [X2,X0,X1] :
( subclass(intersection(x,X0),X1)
| member(not_subclass_element(intersection(x,X0),X1),X2)
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3350,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(x,X0),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(x,X0),X1),X2) )
| ~ spl0_38
| ~ spl0_296 ),
inference(resolution,[],[f3205,f375]) ).
fof(f3205,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(x,X0),X1),X2)
| subclass(intersection(x,X0),X1)
| x = X2 )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3204]) ).
fof(f58468,plain,
( spl0_1321
| ~ spl0_39
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3349,f3204,f378,f58466]) ).
fof(f58466,plain,
( spl0_1321
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(x,X0),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(x,X0),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f3349,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(x,X0),X1)
| x = intersection(X2,X3)
| member(not_subclass_element(intersection(x,X0),X1),X3) )
| ~ spl0_39
| ~ spl0_296 ),
inference(resolution,[],[f3205,f379]) ).
fof(f58463,plain,
( spl0_1320
| ~ spl0_28
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3312,f3187,f327,f58461]) ).
fof(f58461,plain,
( spl0_1320
<=> ! [X2,X0,X1] :
( x = intersection(X0,intersection(complement(X1),X2))
| ~ member(regular(intersection(X0,intersection(complement(X1),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f327,plain,
( spl0_28
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f3187,plain,
( spl0_292
<=> ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3312,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(complement(X1),X2))
| ~ member(regular(intersection(X0,intersection(complement(X1),X2))),X1) )
| ~ spl0_28
| ~ spl0_292 ),
inference(resolution,[],[f3188,f328]) ).
fof(f328,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f3188,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,intersection(X1,X2))),X1)
| x = intersection(X0,intersection(X1,X2)) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3187]) ).
fof(f58458,plain,
( spl0_1319
| ~ spl0_28
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3283,f3183,f327,f58456]) ).
fof(f58456,plain,
( spl0_1319
<=> ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,complement(X2)))
| ~ member(regular(intersection(X0,intersection(X1,complement(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f3183,plain,
( spl0_291
<=> ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f3283,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,complement(X2)))
| ~ member(regular(intersection(X0,intersection(X1,complement(X2)))),X2) )
| ~ spl0_28
| ~ spl0_291 ),
inference(resolution,[],[f3184,f328]) ).
fof(f3184,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,intersection(X1,X2))),X2)
| x = intersection(X0,intersection(X1,X2)) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3183]) ).
fof(f58453,plain,
( spl0_1318
| ~ spl0_28
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3249,f3174,f327,f58451]) ).
fof(f58451,plain,
( spl0_1318
<=> ! [X2,X0,X1] :
( x = intersection(intersection(complement(X0),X1),X2)
| ~ member(regular(intersection(intersection(complement(X0),X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f3174,plain,
( spl0_289
<=> ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3249,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(complement(X0),X1),X2)
| ~ member(regular(intersection(intersection(complement(X0),X1),X2)),X0) )
| ~ spl0_28
| ~ spl0_289 ),
inference(resolution,[],[f3175,f328]) ).
fof(f3175,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(intersection(X0,X1),X2)),X0)
| x = intersection(intersection(X0,X1),X2) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3174]) ).
fof(f58448,plain,
( spl0_1317
| ~ spl0_28
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3220,f3170,f327,f58446]) ).
fof(f58446,plain,
( spl0_1317
<=> ! [X2,X0,X1] :
( x = intersection(intersection(X0,complement(X1)),X2)
| ~ member(regular(intersection(intersection(X0,complement(X1)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f3170,plain,
( spl0_288
<=> ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f3220,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(X0,complement(X1)),X2)
| ~ member(regular(intersection(intersection(X0,complement(X1)),X2)),X1) )
| ~ spl0_28
| ~ spl0_288 ),
inference(resolution,[],[f3171,f328]) ).
fof(f3171,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(intersection(X0,X1),X2)),X1)
| x = intersection(intersection(X0,X1),X2) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3170]) ).
fof(f58443,plain,
( spl0_1316
| ~ spl0_45
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3121,f2992,f417,f58441]) ).
fof(f58441,plain,
( spl0_1316
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,X0)
| x = cross_product(X1,X2)
| ~ subclass(X0,X3)
| member(regular(cross_product(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f417,plain,
( spl0_45
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f2992,plain,
( spl0_285
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f3121,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| x = cross_product(X1,X2)
| ~ subclass(X0,X3)
| member(regular(cross_product(X1,X2)),X3) )
| ~ spl0_45
| ~ spl0_285 ),
inference(resolution,[],[f2993,f418]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f2993,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = x )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f2992]) ).
fof(f58438,plain,
( spl0_1315
| ~ spl0_45
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3068,f2976,f417,f58436]) ).
fof(f58436,plain,
( spl0_1315
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| x = intersection(X2,X0)
| ~ subclass(X1,X3)
| member(regular(intersection(X2,X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f2976,plain,
( spl0_281
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f3068,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X2,X0)
| ~ subclass(X1,X3)
| member(regular(intersection(X2,X0)),X3) )
| ~ spl0_45
| ~ spl0_281 ),
inference(resolution,[],[f2977,f418]) ).
fof(f2977,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,X1)),X2)
| ~ subclass(X1,X2)
| intersection(X0,X1) = x )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f2976]) ).
fof(f58433,plain,
( spl0_1314
| ~ spl0_45
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3015,f2964,f417,f58431]) ).
fof(f58431,plain,
( spl0_1314
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,X2)
| ~ subclass(X1,X3)
| member(regular(intersection(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f2964,plain,
( spl0_279
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f3015,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,X2)
| ~ subclass(X1,X3)
| member(regular(intersection(X0,X2)),X3) )
| ~ spl0_45
| ~ spl0_279 ),
inference(resolution,[],[f2965,f418]) ).
fof(f2965,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,X1)),X2)
| ~ subclass(X0,X2)
| intersection(X0,X1) = x )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f2964]) ).
fof(f58428,plain,
( spl0_1313
| ~ spl0_137
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2933,f2809,f1124,f58426]) ).
fof(f58426,plain,
( spl0_1313
<=> ! [X0] :
( x = intersection(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f1124,plain,
( spl0_137
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f2809,plain,
( spl0_274
<=> ! [X0,X1] :
( x = intersection(X0,complement(X1))
| ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2933,plain,
( ! [X0] :
( x = intersection(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),subset_relation) )
| ~ spl0_137
| ~ spl0_274 ),
inference(resolution,[],[f2810,f1125]) ).
fof(f1125,plain,
( ! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,subset_relation) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1124]) ).
fof(f2810,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X0,complement(X1))),X1)
| x = intersection(X0,complement(X1)) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2809]) ).
fof(f58281,plain,
( spl0_1312
| ~ spl0_137
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2906,f2805,f1124,f58279]) ).
fof(f58279,plain,
( spl0_1312
<=> ! [X0] :
( x = intersection(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f2805,plain,
( spl0_273
<=> ! [X0,X1] :
( x = intersection(complement(X0),X1)
| ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2906,plain,
( ! [X0] :
( x = intersection(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),subset_relation) )
| ~ spl0_137
| ~ spl0_273 ),
inference(resolution,[],[f2806,f1125]) ).
fof(f2806,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(complement(X0),X1)),X0)
| x = intersection(complement(X0),X1) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2805]) ).
fof(f58277,plain,
( spl0_1311
| ~ spl0_55
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2630,f2410,f489,f58275]) ).
fof(f58275,plain,
( spl0_1311
<=> ! [X2,X0,X1] :
( x = X0
| ~ subclass(X0,complement(intersection(X1,X2)))
| ~ member(regular(X0),X2)
| ~ member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f489,plain,
( spl0_55
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f2410,plain,
( spl0_246
<=> ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| x = X0
| ~ member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2630,plain,
( ! [X2,X0,X1] :
( x = X0
| ~ subclass(X0,complement(intersection(X1,X2)))
| ~ member(regular(X0),X2)
| ~ member(regular(X0),X1) )
| ~ spl0_55
| ~ spl0_246 ),
inference(resolution,[],[f2411,f490]) ).
fof(f490,plain,
( ! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f2411,plain,
( ! [X0,X1] :
( ~ member(regular(X0),X1)
| x = X0
| ~ subclass(X0,complement(X1)) )
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f2410]) ).
fof(f57951,plain,
( spl0_1310
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1119 ),
inference(avatar_split_clause,[],[f51056,f34361,f9135,f8637,f57949]) ).
fof(f8637,plain,
( spl0_548
<=> ! [X0] : ~ member(X0,domain_of(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f9135,plain,
( spl0_564
<=> x = domain_of(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f34361,plain,
( spl0_1119
<=> ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f51056,plain,
( ! [X0] : x = cross_product(X0,x)
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1119 ),
inference(forward_demodulation,[],[f51034,f9137]) ).
fof(f9137,plain,
( x = domain_of(x)
| ~ spl0_564 ),
inference(avatar_component_clause,[],[f9135]) ).
fof(f51034,plain,
( ! [X0] : x = cross_product(X0,domain_of(x))
| ~ spl0_548
| ~ spl0_1119 ),
inference(resolution,[],[f34362,f8638]) ).
fof(f8638,plain,
( ! [X0] : ~ member(X0,domain_of(x))
| ~ spl0_548 ),
inference(avatar_component_clause,[],[f8637]) ).
fof(f34362,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = x )
| ~ spl0_1119 ),
inference(avatar_component_clause,[],[f34361]) ).
fof(f57853,plain,
( spl0_1309
| ~ spl0_9
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f18037,f11878,f244,f57851]) ).
fof(f57851,plain,
( spl0_1309
<=> ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f244,plain,
( spl0_9
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f11878,plain,
( spl0_639
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f18037,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_9
| ~ spl0_639 ),
inference(resolution,[],[f11879,f245]) ).
fof(f245,plain,
( ! [X1] : subclass(X1,X1)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f11879,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_639 ),
inference(avatar_component_clause,[],[f11878]) ).
fof(f57713,plain,
( spl0_1307
| spl0_1275
| spl0_1308
| ~ spl0_251
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4804,f4384,f2491,f57710,f53534,f57706]) ).
fof(f57706,plain,
( spl0_1307
<=> x = intersection(singleton_relation,regular(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f57710,plain,
( spl0_1308
<=> member(regular(intersection(singleton_relation,regular(element_relation))),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f2491,plain,
( spl0_251
<=> ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| x = intersection(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f4384,plain,
( spl0_354
<=> ! [X0,X1] :
( member(regular(intersection(X0,regular(X1))),x)
| ~ member(regular(intersection(X0,regular(X1))),X1)
| x = X1
| x = intersection(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f4804,plain,
( member(regular(intersection(singleton_relation,regular(element_relation))),x)
| element_relation = x
| x = intersection(singleton_relation,regular(element_relation))
| ~ spl0_251
| ~ spl0_354 ),
inference(duplicate_literal_removal,[],[f4770]) ).
fof(f4770,plain,
( member(regular(intersection(singleton_relation,regular(element_relation))),x)
| element_relation = x
| x = intersection(singleton_relation,regular(element_relation))
| x = intersection(singleton_relation,regular(element_relation))
| ~ spl0_251
| ~ spl0_354 ),
inference(resolution,[],[f4385,f2492]) ).
fof(f2492,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| x = intersection(singleton_relation,X0) )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2491]) ).
fof(f4385,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X0,regular(X1))),X1)
| member(regular(intersection(X0,regular(X1))),x)
| x = X1
| x = intersection(X0,regular(X1)) )
| ~ spl0_354 ),
inference(avatar_component_clause,[],[f4384]) ).
fof(f57561,plain,
( spl0_1305
| spl0_237
| spl0_1306
| ~ spl0_253
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4802,f4384,f2501,f57558,f2334,f57554]) ).
fof(f57554,plain,
( spl0_1305
<=> x = intersection(identity_relation,regular(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f57558,plain,
( spl0_1306
<=> member(regular(intersection(identity_relation,regular(subset_relation))),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f2501,plain,
( spl0_253
<=> ! [X0] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| x = intersection(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f4802,plain,
( member(regular(intersection(identity_relation,regular(subset_relation))),x)
| subset_relation = x
| x = intersection(identity_relation,regular(subset_relation))
| ~ spl0_253
| ~ spl0_354 ),
inference(duplicate_literal_removal,[],[f4779]) ).
fof(f4779,plain,
( member(regular(intersection(identity_relation,regular(subset_relation))),x)
| subset_relation = x
| x = intersection(identity_relation,regular(subset_relation))
| x = intersection(identity_relation,regular(subset_relation))
| ~ spl0_253
| ~ spl0_354 ),
inference(resolution,[],[f4385,f2502]) ).
fof(f2502,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| x = intersection(identity_relation,X0) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2501]) ).
fof(f57552,plain,
( spl0_1304
| ~ spl0_111
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4760,f4380,f849,f57550]) ).
fof(f57550,plain,
( spl0_1304
<=> ! [X0] :
( member(regular(intersection(regular(X0),X0)),x)
| x = X0
| x = intersection(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f849,plain,
( spl0_111
<=> ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f4380,plain,
( spl0_353
<=> ! [X0,X1] :
( member(regular(intersection(regular(X0),X1)),x)
| ~ member(regular(intersection(regular(X0),X1)),X0)
| x = X0
| x = intersection(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f4760,plain,
( ! [X0] :
( member(regular(intersection(regular(X0),X0)),x)
| x = X0
| x = intersection(regular(X0),X0) )
| ~ spl0_111
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4713]) ).
fof(f4713,plain,
( ! [X0] :
( member(regular(intersection(regular(X0),X0)),x)
| x = X0
| x = intersection(regular(X0),X0)
| x = intersection(regular(X0),X0) )
| ~ spl0_111
| ~ spl0_353 ),
inference(resolution,[],[f4381,f850]) ).
fof(f850,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = x )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f849]) ).
fof(f4381,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(regular(X0),X1)),X0)
| member(regular(intersection(regular(X0),X1)),x)
| x = X0
| x = intersection(regular(X0),X1) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f4380]) ).
fof(f57409,plain,
( spl0_1302
| spl0_1275
| spl0_1303
| ~ spl0_252
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4753,f4380,f2496,f57406,f53534,f57402]) ).
fof(f57402,plain,
( spl0_1302
<=> x = intersection(regular(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f57406,plain,
( spl0_1303
<=> member(regular(intersection(regular(element_relation),singleton_relation)),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f2496,plain,
( spl0_252
<=> ! [X0] :
( member(regular(intersection(X0,singleton_relation)),element_relation)
| x = intersection(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f4753,plain,
( member(regular(intersection(regular(element_relation),singleton_relation)),x)
| element_relation = x
| x = intersection(regular(element_relation),singleton_relation)
| ~ spl0_252
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4721]) ).
fof(f4721,plain,
( member(regular(intersection(regular(element_relation),singleton_relation)),x)
| element_relation = x
| x = intersection(regular(element_relation),singleton_relation)
| x = intersection(regular(element_relation),singleton_relation)
| ~ spl0_252
| ~ spl0_353 ),
inference(resolution,[],[f4381,f2497]) ).
fof(f2497,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),element_relation)
| x = intersection(X0,singleton_relation) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2496]) ).
fof(f57257,plain,
( spl0_1300
| spl0_237
| spl0_1301
| ~ spl0_254
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4751,f4380,f2506,f57254,f2334,f57250]) ).
fof(f57250,plain,
( spl0_1300
<=> x = intersection(regular(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f57254,plain,
( spl0_1301
<=> member(regular(intersection(regular(subset_relation),identity_relation)),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f2506,plain,
( spl0_254
<=> ! [X0] :
( member(regular(intersection(X0,identity_relation)),subset_relation)
| x = intersection(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f4751,plain,
( member(regular(intersection(regular(subset_relation),identity_relation)),x)
| subset_relation = x
| x = intersection(regular(subset_relation),identity_relation)
| ~ spl0_254
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4730]) ).
fof(f4730,plain,
( member(regular(intersection(regular(subset_relation),identity_relation)),x)
| subset_relation = x
| x = intersection(regular(subset_relation),identity_relation)
| x = intersection(regular(subset_relation),identity_relation)
| ~ spl0_254
| ~ spl0_353 ),
inference(resolution,[],[f4381,f2507]) ).
fof(f2507,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),subset_relation)
| x = intersection(X0,identity_relation) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2506]) ).
fof(f57248,plain,
( spl0_1299
| ~ spl0_108
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3586,f3517,f823,f57246]) ).
fof(f57246,plain,
( spl0_1299
<=> ! [X0] :
( member(regular(regular(X0)),x)
| x = X0
| regular(X0) = x
| ~ subclass(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f3517,plain,
( spl0_312
<=> ! [X0] :
( member(regular(regular(X0)),x)
| ~ member(regular(regular(X0)),X0)
| x = X0
| regular(X0) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f3586,plain,
( ! [X0] :
( member(regular(regular(X0)),x)
| x = X0
| regular(X0) = x
| ~ subclass(regular(X0),X0) )
| ~ spl0_108
| ~ spl0_312 ),
inference(duplicate_literal_removal,[],[f3569]) ).
fof(f3569,plain,
( ! [X0] :
( member(regular(regular(X0)),x)
| x = X0
| regular(X0) = x
| ~ subclass(regular(X0),X0)
| regular(X0) = x )
| ~ spl0_108
| ~ spl0_312 ),
inference(resolution,[],[f3518,f824]) ).
fof(f3518,plain,
( ! [X0] :
( ~ member(regular(regular(X0)),X0)
| member(regular(regular(X0)),x)
| x = X0
| regular(X0) = x )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f3517]) ).
fof(f57244,plain,
( ~ spl0_1296
| spl0_1297
| spl0_1275
| spl0_1298
| ~ spl0_243
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3585,f3517,f2382,f57241,f53534,f57237,f57233]) ).
fof(f57233,plain,
( spl0_1296
<=> subclass(regular(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f57237,plain,
( spl0_1297
<=> x = regular(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f57241,plain,
( spl0_1298
<=> member(regular(regular(element_relation)),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f3585,plain,
( member(regular(regular(element_relation)),x)
| element_relation = x
| x = regular(element_relation)
| ~ subclass(regular(element_relation),singleton_relation)
| ~ spl0_243
| ~ spl0_312 ),
inference(duplicate_literal_removal,[],[f3571]) ).
fof(f3571,plain,
( member(regular(regular(element_relation)),x)
| element_relation = x
| x = regular(element_relation)
| ~ subclass(regular(element_relation),singleton_relation)
| x = regular(element_relation)
| ~ spl0_243
| ~ spl0_312 ),
inference(resolution,[],[f3518,f2383]) ).
fof(f57231,plain,
( ~ spl0_1293
| spl0_1294
| spl0_237
| spl0_1295
| ~ spl0_244
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f3584,f3517,f2386,f57228,f2334,f57224,f57220]) ).
fof(f57220,plain,
( spl0_1293
<=> subclass(regular(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f57224,plain,
( spl0_1294
<=> x = regular(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f57228,plain,
( spl0_1295
<=> member(regular(regular(subset_relation)),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f3584,plain,
( member(regular(regular(subset_relation)),x)
| subset_relation = x
| x = regular(subset_relation)
| ~ subclass(regular(subset_relation),identity_relation)
| ~ spl0_244
| ~ spl0_312 ),
inference(duplicate_literal_removal,[],[f3579]) ).
fof(f3579,plain,
( member(regular(regular(subset_relation)),x)
| subset_relation = x
| x = regular(subset_relation)
| ~ subclass(regular(subset_relation),identity_relation)
| x = regular(subset_relation)
| ~ spl0_244
| ~ spl0_312 ),
inference(resolution,[],[f3518,f2387]) ).
fof(f57218,plain,
( ~ spl0_1292
| spl0_1023
| ~ spl0_1234 ),
inference(avatar_split_clause,[],[f57054,f38124,f32567,f57215]) ).
fof(f57215,plain,
( spl0_1292
<=> operation(domain_of(flip(singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f32567,plain,
( spl0_1023
<=> operation(domain_of(flip(cross_product(singleton_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f57054,plain,
( ~ operation(domain_of(flip(singleton_relation)))
| spl0_1023
| ~ spl0_1234 ),
inference(superposition,[],[f32569,f38125]) ).
fof(f32569,plain,
( ~ operation(domain_of(flip(cross_product(singleton_relation,universal_class))))
| spl0_1023 ),
inference(avatar_component_clause,[],[f32567]) ).
fof(f57213,plain,
( spl0_1291
| ~ spl0_108
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3566,f3513,f823,f57211]) ).
fof(f57211,plain,
( spl0_1291
<=> ! [X0] :
( member(regular(complement(complement(X0))),X0)
| x = complement(complement(X0))
| ~ subclass(complement(complement(X0)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f3513,plain,
( spl0_311
<=> ! [X0] :
( x = complement(complement(X0))
| member(regular(complement(complement(X0))),X0)
| ~ member(regular(complement(complement(X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f3566,plain,
( ! [X0] :
( member(regular(complement(complement(X0))),X0)
| x = complement(complement(X0))
| ~ subclass(complement(complement(X0)),universal_class) )
| ~ spl0_108
| ~ spl0_311 ),
inference(duplicate_literal_removal,[],[f3564]) ).
fof(f3564,plain,
( ! [X0] :
( member(regular(complement(complement(X0))),X0)
| x = complement(complement(X0))
| ~ subclass(complement(complement(X0)),universal_class)
| x = complement(complement(X0)) )
| ~ spl0_108
| ~ spl0_311 ),
inference(resolution,[],[f3514,f824]) ).
fof(f3514,plain,
( ! [X0] :
( ~ member(regular(complement(complement(X0))),universal_class)
| member(regular(complement(complement(X0))),X0)
| x = complement(complement(X0)) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f3513]) ).
fof(f57209,plain,
( spl0_319
| ~ spl0_1290
| ~ spl0_108
| spl0_320 ),
inference(avatar_split_clause,[],[f3558,f3553,f823,f57206,f3549]) ).
fof(f3549,plain,
( spl0_319
<=> x = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f57206,plain,
( spl0_1290
<=> subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f3553,plain,
( spl0_320
<=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3558,plain,
( ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| x = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_108
| spl0_320 ),
inference(resolution,[],[f3555,f824]) ).
fof(f3555,plain,
( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| spl0_320 ),
inference(avatar_component_clause,[],[f3553]) ).
fof(f57204,plain,
( spl0_316
| ~ spl0_1289
| ~ spl0_108
| spl0_317 ),
inference(avatar_split_clause,[],[f3542,f3537,f823,f57201,f3533]) ).
fof(f3533,plain,
( spl0_316
<=> x = complement(complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f57201,plain,
( spl0_1289
<=> subclass(complement(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f3537,plain,
( spl0_317
<=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f3542,plain,
( ~ subclass(complement(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| x = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_108
| spl0_317 ),
inference(resolution,[],[f3539,f824]) ).
fof(f3539,plain,
( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| spl0_317 ),
inference(avatar_component_clause,[],[f3537]) ).
fof(f57198,plain,
( spl0_1288
| ~ spl0_28
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3381,f3208,f327,f57196]) ).
fof(f57196,plain,
( spl0_1288
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,x),X1)
| x = complement(X2)
| ~ member(not_subclass_element(intersection(X0,x),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f3381,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,x),X1)
| x = complement(X2)
| ~ member(not_subclass_element(intersection(X0,x),X1),X2) )
| ~ spl0_28
| ~ spl0_297 ),
inference(resolution,[],[f3209,f328]) ).
fof(f57193,plain,
( spl0_1287
| ~ spl0_28
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3352,f3204,f327,f57191]) ).
fof(f57191,plain,
( spl0_1287
<=> ! [X2,X0,X1] :
( subclass(intersection(x,X0),X1)
| x = complement(X2)
| ~ member(not_subclass_element(intersection(x,X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f3352,plain,
( ! [X2,X0,X1] :
( subclass(intersection(x,X0),X1)
| x = complement(X2)
| ~ member(not_subclass_element(intersection(x,X0),X1),X2) )
| ~ spl0_28
| ~ spl0_296 ),
inference(resolution,[],[f3205,f328]) ).
fof(f57189,plain,
( spl0_1286
| ~ spl0_38
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3125,f2992,f374,f57187]) ).
fof(f57187,plain,
( spl0_1286
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| x = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f3125,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| x = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X0) )
| ~ spl0_38
| ~ spl0_285 ),
inference(resolution,[],[f2993,f375]) ).
fof(f57185,plain,
( spl0_1285
| ~ spl0_39
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3124,f2992,f378,f57183]) ).
fof(f57183,plain,
( spl0_1285
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| x = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f3124,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| x = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X1) )
| ~ spl0_39
| ~ spl0_285 ),
inference(resolution,[],[f2993,f379]) ).
fof(f57181,plain,
( spl0_1284
| ~ spl0_38
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3072,f2976,f374,f57179]) ).
fof(f57179,plain,
( spl0_1284
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f3072,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X1) )
| ~ spl0_38
| ~ spl0_281 ),
inference(resolution,[],[f2977,f375]) ).
fof(f57168,plain,
( spl0_1181
| ~ spl0_1234 ),
inference(avatar_contradiction_clause,[],[f57167]) ).
fof(f57167,plain,
( $false
| spl0_1181
| ~ spl0_1234 ),
inference(trivial_inequality_removal,[],[f57059]) ).
fof(f57059,plain,
( singleton_relation != singleton_relation
| spl0_1181
| ~ spl0_1234 ),
inference(superposition,[],[f35661,f38125]) ).
fof(f35661,plain,
( singleton_relation != cross_product(singleton_relation,universal_class)
| spl0_1181 ),
inference(avatar_component_clause,[],[f35659]) ).
fof(f35659,plain,
( spl0_1181
<=> singleton_relation = cross_product(singleton_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f57052,plain,
( spl0_1283
| ~ spl0_39
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3071,f2976,f378,f57050]) ).
fof(f57050,plain,
( spl0_1283
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f3071,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X2) )
| ~ spl0_39
| ~ spl0_281 ),
inference(resolution,[],[f2977,f379]) ).
fof(f57048,plain,
( spl0_1282
| ~ spl0_38
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3019,f2964,f374,f57046]) ).
fof(f57046,plain,
( spl0_1282
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f3019,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X1) )
| ~ spl0_38
| ~ spl0_279 ),
inference(resolution,[],[f2965,f375]) ).
fof(f57044,plain,
( spl0_1281
| ~ spl0_39
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3018,f2964,f378,f57042]) ).
fof(f57042,plain,
( spl0_1281
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f3018,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X2) )
| ~ spl0_39
| ~ spl0_279 ),
inference(resolution,[],[f2965,f379]) ).
fof(f57040,plain,
( spl0_1280
| ~ spl0_50
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2633,f2410,f465,f57038]) ).
fof(f57038,plain,
( spl0_1280
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(complement(X1)))
| member(regular(X0),X1)
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f465,plain,
( spl0_50
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f2633,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(complement(X1)))
| member(regular(X0),X1)
| ~ member(regular(X0),universal_class) )
| ~ spl0_50
| ~ spl0_246 ),
inference(resolution,[],[f2411,f466]) ).
fof(f466,plain,
( ! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f57035,plain,
( spl0_120
| ~ spl0_81
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2378,f2369,f658,f958]) ).
fof(f958,plain,
( spl0_120
<=> x = unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f658,plain,
( spl0_81
<=> ! [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_81])]) ).
fof(f2369,plain,
( spl0_241
<=> member(x,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2378,plain,
( x = unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x))))
| ~ spl0_81
| ~ spl0_241 ),
inference(resolution,[],[f2371,f659]) ).
fof(f659,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_81 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f2371,plain,
( member(x,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2369]) ).
fof(f56542,plain,
( spl0_1050
| ~ spl0_339
| ~ spl0_1266 ),
inference(avatar_split_clause,[],[f55586,f50861,f4119,f33070]) ).
fof(f33070,plain,
( spl0_1050
<=> ! [X0] : subclass(singleton_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f4119,plain,
( spl0_339
<=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f50861,plain,
( spl0_1266
<=> ! [X0] : singleton_relation = intersection(X0,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f55586,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_339
| ~ spl0_1266 ),
inference(superposition,[],[f4120,f50862]) ).
fof(f50862,plain,
( ! [X0] : singleton_relation = intersection(X0,x)
| ~ spl0_1266 ),
inference(avatar_component_clause,[],[f50861]) ).
fof(f4120,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f4119]) ).
fof(f56441,plain,
( spl0_1279
| ~ spl0_533
| ~ spl0_1213
| ~ spl0_1266 ),
inference(avatar_split_clause,[],[f56410,f50861,f37437,f8386,f56439]) ).
fof(f56439,plain,
( spl0_1279
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,singleton_relation))
| member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f8386,plain,
( spl0_533
<=> ! [X0] : x = intersection(X0,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f37437,plain,
( spl0_1213
<=> ! [X0,X1] :
( x = intersection(X0,intersection(X1,singleton_relation))
| member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f56410,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,singleton_relation))
| member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) )
| ~ spl0_533
| ~ spl0_1213
| ~ spl0_1266 ),
inference(forward_demodulation,[],[f37438,f55556]) ).
fof(f55556,plain,
( singleton_relation = x
| ~ spl0_533
| ~ spl0_1266 ),
inference(superposition,[],[f50862,f8387]) ).
fof(f8387,plain,
( ! [X0] : x = intersection(X0,x)
| ~ spl0_533 ),
inference(avatar_component_clause,[],[f8386]) ).
fof(f37438,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation)
| x = intersection(X0,intersection(X1,singleton_relation)) )
| ~ spl0_1213 ),
inference(avatar_component_clause,[],[f37437]) ).
fof(f56437,plain,
( spl0_1278
| ~ spl0_533
| ~ spl0_1205
| ~ spl0_1266 ),
inference(avatar_split_clause,[],[f56408,f50861,f37103,f8386,f56435]) ).
fof(f56435,plain,
( spl0_1278
<=> ! [X0,X1] :
( singleton_relation = intersection(intersection(X0,singleton_relation),X1)
| member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f37103,plain,
( spl0_1205
<=> ! [X0,X1] :
( x = intersection(intersection(X0,singleton_relation),X1)
| member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f56408,plain,
( ! [X0,X1] :
( singleton_relation = intersection(intersection(X0,singleton_relation),X1)
| member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) )
| ~ spl0_533
| ~ spl0_1205
| ~ spl0_1266 ),
inference(forward_demodulation,[],[f37104,f55556]) ).
fof(f37104,plain,
( ! [X0,X1] :
( member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation)
| x = intersection(intersection(X0,singleton_relation),X1) )
| ~ spl0_1205 ),
inference(avatar_component_clause,[],[f37103]) ).
fof(f56409,plain,
( spl0_1213
| ~ spl0_129
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f46204,f3183,f997,f37437]) ).
fof(f997,plain,
( spl0_129
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f46204,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation)
| x = intersection(X0,intersection(X1,singleton_relation)) )
| ~ spl0_129
| ~ spl0_291 ),
inference(resolution,[],[f998,f3184]) ).
fof(f998,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f56407,plain,
( spl0_1205
| ~ spl0_129
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f46185,f3170,f997,f37103]) ).
fof(f46185,plain,
( ! [X0,X1] :
( member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation)
| x = intersection(intersection(X0,singleton_relation),X1) )
| ~ spl0_129
| ~ spl0_288 ),
inference(resolution,[],[f998,f3171]) ).
fof(f54889,plain,
( spl0_1050
| ~ spl0_340
| ~ spl0_1265 ),
inference(avatar_split_clause,[],[f53864,f50473,f4123,f33070]) ).
fof(f4123,plain,
( spl0_340
<=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f50473,plain,
( spl0_1265
<=> ! [X0] : singleton_relation = intersection(x,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f53864,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_340
| ~ spl0_1265 ),
inference(superposition,[],[f4124,f50474]) ).
fof(f50474,plain,
( ! [X0] : singleton_relation = intersection(x,X0)
| ~ spl0_1265 ),
inference(avatar_component_clause,[],[f50473]) ).
fof(f4124,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f4123]) ).
fof(f53645,plain,
( spl0_1277
| ~ spl0_149
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2634,f2410,f1290,f53643]) ).
fof(f53643,plain,
( spl0_1277
<=> ! [X0] :
( x = X0
| ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(regular(X0),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1290,plain,
( spl0_149
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f2634,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(regular(X0),singleton_relation) )
| ~ spl0_149
| ~ spl0_246 ),
inference(resolution,[],[f2411,f1291]) ).
fof(f1291,plain,
( ! [X0] :
( member(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,singleton_relation) )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f53592,plain,
( spl0_1160
| ~ spl0_129
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f46203,f2964,f997,f35497]) ).
fof(f35497,plain,
( spl0_1160
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| intersection(X0,X1) = x
| member(regular(intersection(X0,X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f46203,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),element_relation)
| ~ subclass(X0,singleton_relation)
| intersection(X0,X1) = x )
| ~ spl0_129
| ~ spl0_279 ),
inference(resolution,[],[f998,f2965]) ).
fof(f53542,plain,
( spl0_1163
| ~ spl0_129
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f46202,f2976,f997,f35512]) ).
fof(f35512,plain,
( spl0_1163
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| x = intersection(X1,X0)
| member(regular(intersection(X1,X0)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f46202,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),element_relation)
| ~ subclass(X1,singleton_relation)
| intersection(X0,X1) = x )
| ~ spl0_129
| ~ spl0_281 ),
inference(resolution,[],[f998,f2977]) ).
fof(f53541,plain,
( spl0_188
| ~ spl0_1274
| spl0_1275
| spl0_1276
| ~ spl0_189
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f41663,f3715,f1714,f53538,f53534,f53530,f1710]) ).
fof(f53530,plain,
( spl0_1274
<=> subclass(singleton_relation,regular(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f53538,plain,
( spl0_1276
<=> member(regular(singleton_relation),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1714,plain,
( spl0_189
<=> member(regular(singleton_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f41663,plain,
( member(regular(singleton_relation),x)
| element_relation = x
| ~ subclass(singleton_relation,regular(element_relation))
| singleton_relation = x
| ~ spl0_189
| ~ spl0_323 ),
inference(resolution,[],[f1716,f3716]) ).
fof(f1716,plain,
( member(regular(singleton_relation),element_relation)
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1714]) ).
fof(f52476,plain,
( ~ spl0_1273
| ~ spl0_1068
| spl0_1229 ),
inference(avatar_split_clause,[],[f52298,f38085,f33618,f52473]) ).
fof(f52473,plain,
( spl0_1273
<=> subclass(universal_class,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f33618,plain,
( spl0_1068
<=> ! [X0] :
( member(not_subclass_element(cross_product(x,x),identity_relation),X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f38085,plain,
( spl0_1229
<=> member(not_subclass_element(cross_product(x,x),identity_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f52298,plain,
( ~ subclass(universal_class,subset_relation)
| ~ spl0_1068
| spl0_1229 ),
inference(resolution,[],[f33619,f38087]) ).
fof(f38087,plain,
( ~ member(not_subclass_element(cross_product(x,x),identity_relation),subset_relation)
| spl0_1229 ),
inference(avatar_component_clause,[],[f38085]) ).
fof(f33619,plain,
( ! [X0] :
( member(not_subclass_element(cross_product(x,x),identity_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_1068 ),
inference(avatar_component_clause,[],[f33618]) ).
fof(f52434,plain,
( spl0_1272
| ~ spl0_108
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f46274,f6163,f823,f52432]) ).
fof(f52432,plain,
( spl0_1272
<=> ! [X0] :
( ~ member(regular(X0),singleton_relation)
| ~ subclass(X0,compose(element_relation,complement(identity_relation)))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f6163,plain,
( spl0_444
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f46274,plain,
( ! [X0] :
( ~ member(regular(X0),singleton_relation)
| ~ subclass(X0,compose(element_relation,complement(identity_relation)))
| x = X0 )
| ~ spl0_108
| ~ spl0_444 ),
inference(resolution,[],[f6164,f824]) ).
fof(f6164,plain,
( ! [X0] :
( ~ member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,singleton_relation) )
| ~ spl0_444 ),
inference(avatar_component_clause,[],[f6163]) ).
fof(f52275,plain,
( spl0_1271
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1120 ),
inference(avatar_split_clause,[],[f51987,f34366,f30059,f9685,f52273]) ).
fof(f52273,plain,
( spl0_1271
<=> ! [X0,X3,X2,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f9685,plain,
( spl0_576
<=> ! [X0] : ~ member(X0,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f30059,plain,
( spl0_963
<=> ! [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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f34366,plain,
( spl0_1120
<=> ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f51987,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f51986,f51107]) ).
fof(f51107,plain,
( ! [X0] : x = cross_product(x,X0)
| ~ spl0_576
| ~ spl0_1120 ),
inference(resolution,[],[f34367,f9686]) ).
fof(f9686,plain,
( ! [X0] : ~ member(X0,x)
| ~ spl0_576 ),
inference(avatar_component_clause,[],[f9685]) ).
fof(f34367,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = x )
| ~ spl0_1120 ),
inference(avatar_component_clause,[],[f34366]) ).
fof(f51986,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f51985,f51107]) ).
fof(f51985,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f51984,f51107]) ).
fof(f51984,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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f51983,f51107]) ).
fof(f51983,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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(x))),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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f30060,f51107]) ).
fof(f30060,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_963 ),
inference(avatar_component_clause,[],[f30059]) ).
fof(f51930,plain,
( spl0_188
| ~ spl0_576
| ~ spl0_1120
| ~ spl0_1130 ),
inference(avatar_split_clause,[],[f51158,f34421,f34366,f9685,f1710]) ).
fof(f34421,plain,
( spl0_1130
<=> ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(first(regular(cross_product(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f51158,plain,
( singleton_relation = x
| ~ spl0_576
| ~ spl0_1120
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f51107,f34953]) ).
fof(f34953,plain,
( ! [X0] : singleton_relation = cross_product(x,X0)
| ~ spl0_576
| ~ spl0_1130 ),
inference(resolution,[],[f34422,f9686]) ).
fof(f34422,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = singleton_relation )
| ~ spl0_1130 ),
inference(avatar_component_clause,[],[f34421]) ).
fof(f51929,plain,
( ~ spl0_1270
| ~ spl0_576
| ~ spl0_1120
| ~ spl0_1130
| spl0_1268 ),
inference(avatar_split_clause,[],[f51924,f51916,f34421,f34366,f9685,f51926]) ).
fof(f51926,plain,
( spl0_1270
<=> compose(element_relation,complement(identity_relation)) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f51916,plain,
( spl0_1268
<=> compose(element_relation,complement(identity_relation)) = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f51924,plain,
( compose(element_relation,complement(identity_relation)) != singleton_relation
| ~ spl0_576
| ~ spl0_1120
| ~ spl0_1130
| spl0_1268 ),
inference(forward_demodulation,[],[f51917,f51158]) ).
fof(f51917,plain,
( compose(element_relation,complement(identity_relation)) != x
| spl0_1268 ),
inference(avatar_component_clause,[],[f51916]) ).
fof(f51923,plain,
( spl0_1268
| ~ spl0_1269
| ~ spl0_3
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f46250,f6163,f217,f51920,f51916]) ).
fof(f51920,plain,
( spl0_1269
<=> member(regular(compose(element_relation,complement(identity_relation))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f217,plain,
( spl0_3
<=> ! [X0] :
( x = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f46250,plain,
( ~ member(regular(compose(element_relation,complement(identity_relation))),singleton_relation)
| compose(element_relation,complement(identity_relation)) = x
| ~ spl0_3
| ~ spl0_444 ),
inference(resolution,[],[f6164,f218]) ).
fof(f218,plain,
( ! [X0] :
( member(regular(X0),X0)
| x = X0 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f51164,plain,
( spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_576
| ~ spl0_1119
| ~ spl0_1129 ),
inference(avatar_split_clause,[],[f51057,f34417,f34361,f9685,f9135,f8637,f1710]) ).
fof(f34417,plain,
( spl0_1129
<=> ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(second(regular(cross_product(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f51057,plain,
( singleton_relation = x
| ~ spl0_548
| ~ spl0_564
| ~ spl0_576
| ~ spl0_1119
| ~ spl0_1129 ),
inference(forward_demodulation,[],[f51056,f34884]) ).
fof(f34884,plain,
( ! [X0] : singleton_relation = cross_product(X0,x)
| ~ spl0_576
| ~ spl0_1129 ),
inference(resolution,[],[f34418,f9686]) ).
fof(f34418,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = singleton_relation )
| ~ spl0_1129 ),
inference(avatar_component_clause,[],[f34417]) ).
fof(f51163,plain,
( spl0_1267
| ~ spl0_48
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4163,f4123,f429,f51160]) ).
fof(f51160,plain,
( spl0_1267
<=> subclass(singleton_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f429,plain,
( spl0_48
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f4163,plain,
( subclass(singleton_relation,element_relation)
| ~ spl0_48
| ~ spl0_340 ),
inference(superposition,[],[f4124,f431]) ).
fof(f431,plain,
( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f50863,plain,
( spl0_1266
| ~ spl0_7
| ~ spl0_233
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f33734,f33644,f2307,f235,f50861]) ).
fof(f235,plain,
( spl0_7
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f2307,plain,
( spl0_233
<=> x = complement(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f33644,plain,
( spl0_1074
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,complement(X0))
| ~ subclass(complement(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f33734,plain,
( ! [X0] : singleton_relation = intersection(X0,x)
| ~ spl0_7
| ~ spl0_233
| ~ spl0_1074 ),
inference(forward_demodulation,[],[f33729,f2309]) ).
fof(f2309,plain,
( x = complement(universal_class)
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2307]) ).
fof(f33729,plain,
( ! [X0] : singleton_relation = intersection(X0,complement(universal_class))
| ~ spl0_7
| ~ spl0_1074 ),
inference(resolution,[],[f33645,f236]) ).
fof(f236,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f33645,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| singleton_relation = intersection(X1,complement(X0)) )
| ~ spl0_1074 ),
inference(avatar_component_clause,[],[f33644]) ).
fof(f50475,plain,
( spl0_1265
| ~ spl0_7
| ~ spl0_233
| ~ spl0_1073 ),
inference(avatar_split_clause,[],[f33724,f33640,f2307,f235,f50473]) ).
fof(f33640,plain,
( spl0_1073
<=> ! [X0,X1] :
( singleton_relation = intersection(complement(X0),X1)
| ~ subclass(complement(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f33724,plain,
( ! [X0] : singleton_relation = intersection(x,X0)
| ~ spl0_7
| ~ spl0_233
| ~ spl0_1073 ),
inference(forward_demodulation,[],[f33719,f2309]) ).
fof(f33719,plain,
( ! [X0] : singleton_relation = intersection(complement(universal_class),X0)
| ~ spl0_7
| ~ spl0_1073 ),
inference(resolution,[],[f33641,f236]) ).
fof(f33641,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| singleton_relation = intersection(complement(X0),X1) )
| ~ spl0_1073 ),
inference(avatar_component_clause,[],[f33640]) ).
fof(f50415,plain,
( ~ spl0_1264
| spl0_188
| ~ spl0_246
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2632,f2414,f2410,f1710,f50412]) ).
fof(f50412,plain,
( spl0_1264
<=> subclass(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f2414,plain,
( spl0_247
<=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2632,plain,
( singleton_relation = x
| ~ subclass(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation)))))
| ~ spl0_246
| ~ spl0_247 ),
inference(resolution,[],[f2411,f2416]) ).
fof(f2416,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2414]) ).
fof(f50265,plain,
( spl0_1263
| ~ spl0_56
| ~ spl0_491
| ~ spl0_495
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f49450,f38067,f7354,f7302,f493,f50262]) ).
fof(f50262,plain,
( spl0_1263
<=> subclass(singleton_relation,intersection(singleton_relation,complement(compose(element_relation,complement(identity_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f493,plain,
( spl0_56
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f7302,plain,
( spl0_491
<=> ! [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_491])]) ).
fof(f7354,plain,
( spl0_495
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f38067,plain,
( spl0_1225
<=> ! [X0] : singleton_relation = cross_product(X0,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f49450,plain,
( subclass(singleton_relation,intersection(singleton_relation,complement(compose(element_relation,complement(identity_relation)))))
| ~ spl0_56
| ~ spl0_491
| ~ spl0_495
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f7579,f38167]) ).
fof(f38167,plain,
( ! [X1] : intersection(X1,singleton_relation) = intersection(singleton_relation,X1)
| ~ spl0_56
| ~ spl0_1225 ),
inference(superposition,[],[f494,f38068]) ).
fof(f38068,plain,
( ! [X0] : singleton_relation = cross_product(X0,singleton_relation)
| ~ spl0_1225 ),
inference(avatar_component_clause,[],[f38067]) ).
fof(f494,plain,
( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f7579,plain,
( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(identity_relation))),singleton_relation))
| ~ spl0_491
| ~ spl0_495 ),
inference(duplicate_literal_removal,[],[f7547]) ).
fof(f7547,plain,
( subclass(singleton_relation,intersection(complement(compose(element_relation,complement(identity_relation))),singleton_relation))
| subclass(singleton_relation,intersection(complement(compose(element_relation,complement(identity_relation))),singleton_relation))
| ~ spl0_491
| ~ spl0_495 ),
inference(resolution,[],[f7355,f7303]) ).
fof(f7303,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X0) )
| ~ spl0_491 ),
inference(avatar_component_clause,[],[f7302]) ).
fof(f7355,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f7354]) ).
fof(f50260,plain,
( spl0_1262
| ~ spl0_576
| ~ spl0_1092
| ~ spl0_1129 ),
inference(avatar_split_clause,[],[f46616,f34417,f33921,f9685,f50258]) ).
fof(f50258,plain,
( spl0_1262
<=> ! [X0] :
( ~ member(not_subclass_element(singleton_relation,identity_relation),X0)
| ~ subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f33921,plain,
( spl0_1092
<=> ! [X0] :
( ~ member(not_subclass_element(cross_product(x,x),identity_relation),X0)
| ~ subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f46616,plain,
( ! [X0] :
( ~ member(not_subclass_element(singleton_relation,identity_relation),X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_576
| ~ spl0_1092
| ~ spl0_1129 ),
inference(forward_demodulation,[],[f33922,f34884]) ).
fof(f33922,plain,
( ! [X0] :
( ~ member(not_subclass_element(cross_product(x,x),identity_relation),X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_1092 ),
inference(avatar_component_clause,[],[f33921]) ).
fof(f49616,plain,
( spl0_1261
| ~ spl0_56
| ~ spl0_411
| ~ spl0_495
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f49451,f38067,f7354,f5687,f493,f49613]) ).
fof(f49613,plain,
( spl0_1261
<=> subclass(singleton_relation,intersection(singleton_relation,element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f5687,plain,
( spl0_411
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f49451,plain,
( subclass(singleton_relation,intersection(singleton_relation,element_relation))
| ~ spl0_56
| ~ spl0_411
| ~ spl0_495
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f7583,f38167]) ).
fof(f7583,plain,
( subclass(singleton_relation,intersection(element_relation,singleton_relation))
| ~ spl0_411
| ~ spl0_495 ),
inference(duplicate_literal_removal,[],[f7541]) ).
fof(f7541,plain,
( subclass(singleton_relation,intersection(element_relation,singleton_relation))
| subclass(singleton_relation,intersection(element_relation,singleton_relation))
| ~ spl0_411
| ~ spl0_495 ),
inference(resolution,[],[f7355,f5688]) ).
fof(f5688,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f5687]) ).
fof(f49610,plain,
( spl0_188
| ~ spl0_340
| ~ spl0_1032
| ~ spl0_1242 ),
inference(avatar_split_clause,[],[f49515,f38156,f32623,f4123,f1710]) ).
fof(f32623,plain,
( spl0_1032
<=> ! [X0,X1] : x = intersection(intersection(X0,X1),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f38156,plain,
( spl0_1242
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f49515,plain,
( singleton_relation = x
| ~ spl0_340
| ~ spl0_1032
| ~ spl0_1242 ),
inference(forward_demodulation,[],[f32624,f43070]) ).
fof(f43070,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_340
| ~ spl0_1242 ),
inference(resolution,[],[f38157,f4124]) ).
fof(f38157,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(intersection(X0,X1),X2),complement(X1))
| singleton_relation = intersection(intersection(X0,X1),X2) )
| ~ spl0_1242 ),
inference(avatar_component_clause,[],[f38156]) ).
fof(f32624,plain,
( ! [X0,X1] : x = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_1032 ),
inference(avatar_component_clause,[],[f32623]) ).
fof(f49571,plain,
( spl0_188
| ~ spl0_339
| ~ spl0_1033
| ~ spl0_1058 ),
inference(avatar_split_clause,[],[f49501,f33430,f32628,f4119,f1710]) ).
fof(f32628,plain,
( spl0_1033
<=> ! [X0,X1] : x = intersection(intersection(X0,X1),complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f33430,plain,
( spl0_1058
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,complement(X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f49501,plain,
( singleton_relation = x
| ~ spl0_339
| ~ spl0_1033
| ~ spl0_1058 ),
inference(forward_demodulation,[],[f32629,f33445]) ).
fof(f33445,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_339
| ~ spl0_1058 ),
inference(resolution,[],[f33431,f4120]) ).
fof(f33431,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| singleton_relation = intersection(X0,complement(X1)) )
| ~ spl0_1058 ),
inference(avatar_component_clause,[],[f33430]) ).
fof(f32629,plain,
( ! [X0,X1] : x = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_1033 ),
inference(avatar_component_clause,[],[f32628]) ).
fof(f49569,plain,
( spl0_1260
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1130 ),
inference(avatar_split_clause,[],[f47432,f34421,f30059,f9685,f49567]) ).
fof(f49567,plain,
( spl0_1260
<=> ! [X0,X3,X2,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f47432,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f47431,f34953]) ).
fof(f47431,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f47430,f34953]) ).
fof(f47430,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f47429,f34953]) ).
fof(f47429,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f47428,f34953]) ).
fof(f47428,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_576
| ~ spl0_963
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f30060,f34953]) ).
fof(f49516,plain,
( spl0_411
| ~ spl0_33
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f46148,f997,f354,f5687]) ).
fof(f354,plain,
( spl0_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f46148,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_33
| ~ spl0_129 ),
inference(resolution,[],[f998,f355]) ).
fof(f355,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f49500,plain,
( spl0_188
| ~ spl0_1032
| ~ spl0_1046 ),
inference(avatar_split_clause,[],[f40347,f32746,f32623,f1710]) ).
fof(f32746,plain,
( spl0_1046
<=> ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f40347,plain,
( singleton_relation = x
| ~ spl0_1032
| ~ spl0_1046 ),
inference(forward_demodulation,[],[f32624,f32747]) ).
fof(f32747,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_1046 ),
inference(avatar_component_clause,[],[f32746]) ).
fof(f49376,plain,
( spl0_188
| ~ spl0_1033
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f40346,f32750,f32628,f1710]) ).
fof(f32750,plain,
( spl0_1047
<=> ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f40346,plain,
( singleton_relation = x
| ~ spl0_1033
| ~ spl0_1047 ),
inference(forward_demodulation,[],[f32629,f32751]) ).
fof(f32751,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_1047 ),
inference(avatar_component_clause,[],[f32750]) ).
fof(f48626,plain,
( spl0_188
| ~ spl0_339
| ~ spl0_1035
| ~ spl0_1059 ),
inference(avatar_split_clause,[],[f47876,f33434,f32638,f4119,f1710]) ).
fof(f32638,plain,
( spl0_1035
<=> ! [X0,X1] : x = intersection(complement(X0),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f33434,plain,
( spl0_1059
<=> ! [X0,X1] :
( singleton_relation = intersection(complement(X1),X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f47876,plain,
( singleton_relation = x
| ~ spl0_339
| ~ spl0_1035
| ~ spl0_1059 ),
inference(forward_demodulation,[],[f32639,f33486]) ).
fof(f33486,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_339
| ~ spl0_1059 ),
inference(resolution,[],[f33435,f4120]) ).
fof(f33435,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| singleton_relation = intersection(complement(X1),X0) )
| ~ spl0_1059 ),
inference(avatar_component_clause,[],[f33434]) ).
fof(f32639,plain,
( ! [X0,X1] : x = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_1035 ),
inference(avatar_component_clause,[],[f32638]) ).
fof(f47873,plain,
( spl0_188
| ~ spl0_1034
| ~ spl0_1048 ),
inference(avatar_split_clause,[],[f40345,f32754,f32633,f1710]) ).
fof(f32633,plain,
( spl0_1034
<=> ! [X0,X1] : x = intersection(complement(X0),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f32754,plain,
( spl0_1048
<=> ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f40345,plain,
( singleton_relation = x
| ~ spl0_1034
| ~ spl0_1048 ),
inference(forward_demodulation,[],[f32634,f32755]) ).
fof(f32755,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_1048 ),
inference(avatar_component_clause,[],[f32754]) ).
fof(f32634,plain,
( ! [X0,X1] : x = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f32633]) ).
fof(f46498,plain,
( spl0_188
| ~ spl0_339
| ~ spl0_1049
| ~ spl0_1219 ),
inference(avatar_split_clause,[],[f42219,f37990,f32758,f4119,f1710]) ).
fof(f32758,plain,
( spl0_1049
<=> ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f37990,plain,
( spl0_1219
<=> ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f42219,plain,
( singleton_relation = x
| ~ spl0_339
| ~ spl0_1049
| ~ spl0_1219 ),
inference(forward_demodulation,[],[f42182,f32759]) ).
fof(f32759,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_1049 ),
inference(avatar_component_clause,[],[f32758]) ).
fof(f42182,plain,
( ! [X0,X1] : x = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_339
| ~ spl0_1219 ),
inference(resolution,[],[f37991,f4120]) ).
fof(f37991,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1))
| x = intersection(X0,intersection(X1,X2)) )
| ~ spl0_1219 ),
inference(avatar_component_clause,[],[f37990]) ).
fof(f43231,plain,
( spl0_1050
| ~ spl0_339
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f37489,f36844,f4119,f33070]) ).
fof(f36844,plain,
( spl0_1197
<=> ! [X0] : singleton_relation = intersection(X0,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f37489,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_339
| ~ spl0_1197 ),
inference(superposition,[],[f4120,f36845]) ).
fof(f36845,plain,
( ! [X0] : singleton_relation = intersection(X0,singleton_relation)
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f36844]) ).
fof(f42462,plain,
( spl0_1050
| ~ spl0_340
| ~ spl0_1196 ),
inference(avatar_split_clause,[],[f37144,f36244,f4123,f33070]) ).
fof(f36244,plain,
( spl0_1196
<=> ! [X0] : singleton_relation = intersection(singleton_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f37144,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_340
| ~ spl0_1196 ),
inference(superposition,[],[f4124,f36245]) ).
fof(f36245,plain,
( ! [X0] : singleton_relation = intersection(singleton_relation,X0)
| ~ spl0_1196 ),
inference(avatar_component_clause,[],[f36244]) ).
fof(f42039,plain,
( spl0_1259
| ~ spl0_527
| ~ spl0_1160
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f39378,f36844,f35497,f8227,f42037]) ).
fof(f42037,plain,
( spl0_1259
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X0,X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f8227,plain,
( spl0_527
<=> ! [X0] : x = intersection(x,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f39378,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X0,X1)),element_relation) )
| ~ spl0_527
| ~ spl0_1160
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f35498,f37709]) ).
fof(f37709,plain,
( singleton_relation = x
| ~ spl0_527
| ~ spl0_1197 ),
inference(superposition,[],[f8228,f36845]) ).
fof(f8228,plain,
( ! [X0] : x = intersection(x,X0)
| ~ spl0_527 ),
inference(avatar_component_clause,[],[f8227]) ).
fof(f35498,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),element_relation)
| intersection(X0,X1) = x
| ~ subclass(X0,singleton_relation) )
| ~ spl0_1160 ),
inference(avatar_component_clause,[],[f35497]) ).
fof(f42035,plain,
( spl0_1258
| ~ spl0_527
| ~ spl0_1163
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f39375,f36844,f35512,f8227,f42033]) ).
fof(f42033,plain,
( spl0_1258
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X1,X0)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f39375,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X1,X0)),element_relation) )
| ~ spl0_527
| ~ spl0_1163
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f35513,f37709]) ).
fof(f35513,plain,
( ! [X0,X1] :
( member(regular(intersection(X1,X0)),element_relation)
| x = intersection(X1,X0)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_1163 ),
inference(avatar_component_clause,[],[f35512]) ).
fof(f42005,plain,
( spl0_1257
| ~ spl0_527
| ~ spl0_1109
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f39868,f36844,f34313,f8227,f42003]) ).
fof(f42003,plain,
( spl0_1257
<=> ! [X0] :
( singleton_relation = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f34313,plain,
( spl0_1109
<=> ! [X0] :
( x = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f39868,plain,
( ! [X0] :
( singleton_relation = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
| ~ spl0_527
| ~ spl0_1109
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f34314,f37709]) ).
fof(f34314,plain,
( ! [X0] :
( ~ subclass(intersection(complement(element_relation),X0),singleton_relation)
| x = intersection(complement(element_relation),X0) )
| ~ spl0_1109 ),
inference(avatar_component_clause,[],[f34313]) ).
fof(f42001,plain,
( spl0_1256
| ~ spl0_527
| ~ spl0_1112
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f39865,f36844,f34328,f8227,f41999]) ).
fof(f41999,plain,
( spl0_1256
<=> ! [X0] :
( singleton_relation = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f34328,plain,
( spl0_1112
<=> ! [X0] :
( x = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f39865,plain,
( ! [X0] :
( singleton_relation = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
| ~ spl0_527
| ~ spl0_1112
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f34329,f37709]) ).
fof(f34329,plain,
( ! [X0] :
( ~ subclass(intersection(X0,complement(element_relation)),singleton_relation)
| x = intersection(X0,complement(element_relation)) )
| ~ spl0_1112 ),
inference(avatar_component_clause,[],[f34328]) ).
fof(f41983,plain,
( spl0_1255
| ~ spl0_527
| ~ spl0_1062
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f40079,f36844,f33530,f8227,f41981]) ).
fof(f41981,plain,
( spl0_1255
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f33530,plain,
( spl0_1062
<=> ! [X0] :
( x = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f40079,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_527
| ~ spl0_1062
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f33531,f37709]) ).
fof(f33531,plain,
( ! [X0] :
( ~ subclass(X0,complement(element_relation))
| x = X0
| ~ subclass(X0,singleton_relation) )
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f33530]) ).
fof(f41953,plain,
( spl0_1254
| ~ spl0_527
| ~ spl0_1106
| ~ spl0_1177
| ~ spl0_1197
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f39361,f38067,f36844,f35642,f34298,f8227,f41951]) ).
fof(f41951,plain,
( spl0_1254
<=> ! [X0,X1] :
( member(singleton_relation,X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f34298,plain,
( spl0_1106
<=> singleton_relation = domain_of(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f35642,plain,
( spl0_1177
<=> ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,x))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f39361,plain,
( ! [X0,X1] :
( member(singleton_relation,X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) )
| ~ spl0_527
| ~ spl0_1106
| ~ spl0_1177
| ~ spl0_1197
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f39360,f34300]) ).
fof(f34300,plain,
( singleton_relation = domain_of(singleton_relation)
| ~ spl0_1106 ),
inference(avatar_component_clause,[],[f34298]) ).
fof(f39360,plain,
( ! [X0,X1] :
( member(domain_of(singleton_relation),X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) )
| ~ spl0_527
| ~ spl0_1177
| ~ spl0_1197
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f39359,f36845]) ).
fof(f39359,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,singleton_relation)),X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) )
| ~ spl0_527
| ~ spl0_1177
| ~ spl0_1197
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f39358,f38068]) ).
fof(f39358,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,singleton_relation))),X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) )
| ~ spl0_527
| ~ spl0_1177
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f35643,f37709]) ).
fof(f35643,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,x))),X1) )
| ~ spl0_1177 ),
inference(avatar_component_clause,[],[f35642]) ).
fof(f41892,plain,
( ~ spl0_21
| spl0_200
| ~ spl0_1020 ),
inference(avatar_split_clause,[],[f41695,f32491,f1851,f298]) ).
fof(f298,plain,
( spl0_21
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1851,plain,
( spl0_200
<=> member(singleton_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f32491,plain,
( spl0_1020
<=> ! [X0] :
( member(singleton_relation,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f41695,plain,
( ~ inductive(universal_class)
| spl0_200
| ~ spl0_1020 ),
inference(resolution,[],[f1852,f32492]) ).
fof(f32492,plain,
( ! [X0] :
( member(singleton_relation,X0)
| ~ inductive(X0) )
| ~ spl0_1020 ),
inference(avatar_component_clause,[],[f32491]) ).
fof(f1852,plain,
( ~ member(singleton_relation,universal_class)
| spl0_200 ),
inference(avatar_component_clause,[],[f1851]) ).
fof(f41702,plain,
( ~ spl0_942
| ~ spl0_1094 ),
inference(avatar_contradiction_clause,[],[f41698]) ).
fof(f41698,plain,
( $false
| ~ spl0_942
| ~ spl0_1094 ),
inference(resolution,[],[f29420,f33936]) ).
fof(f33936,plain,
( ! [X0] : ~ member(X0,singleton_relation)
| ~ spl0_1094 ),
inference(avatar_component_clause,[],[f33935]) ).
fof(f33935,plain,
( spl0_1094
<=> ! [X0] : ~ member(X0,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f29420,plain,
( member(regular(singleton_relation),singleton_relation)
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f29418]) ).
fof(f29418,plain,
( spl0_942
<=> member(regular(singleton_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f41671,plain,
( spl0_1253
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(avatar_split_clause,[],[f41482,f38124,f36844,f30059,f8227,f41669]) ).
fof(f41669,plain,
( spl0_1253
<=> ! [X0,X3,X2,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f41482,plain,
( ! [X2,X3,X0,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41481,f37709]) ).
fof(f41481,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41480,f38125]) ).
fof(f41480,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41479,f37709]) ).
fof(f41479,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41478,f38125]) ).
fof(f41478,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41477,f37709]) ).
fof(f41477,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41476,f38125]) ).
fof(f41476,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41475,f37709]) ).
fof(f41475,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41474,f38125]) ).
fof(f41474,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41473,f37709]) ).
fof(f41473,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197
| ~ spl0_1234 ),
inference(forward_demodulation,[],[f41472,f38125]) ).
fof(f41472,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_527
| ~ spl0_963
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f30060,f37709]) ).
fof(f38350,plain,
( ~ spl0_928
| spl0_1019
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f38246,f38067,f32486,f24031]) ).
fof(f24031,plain,
( spl0_928
<=> subclass(singleton_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f32486,plain,
( spl0_1019
<=> subclass(cross_product(singleton_relation,singleton_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f38246,plain,
( ~ subclass(singleton_relation,identity_relation)
| spl0_1019
| ~ spl0_1225 ),
inference(superposition,[],[f32488,f38068]) ).
fof(f32488,plain,
( ~ subclass(cross_product(singleton_relation,singleton_relation),identity_relation)
| spl0_1019 ),
inference(avatar_component_clause,[],[f32486]) ).
fof(f38319,plain,
( spl0_1252
| ~ spl0_188
| ~ spl0_1224 ),
inference(avatar_split_clause,[],[f38065,f38061,f1710,f38317]) ).
fof(f38317,plain,
( spl0_1252
<=> ! [X0,X1] :
( singleton_relation = X0
| member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1)
| ~ subclass(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f38061,plain,
( spl0_1224
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),x)
| ~ subclass(X0,regular(X0))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f38065,plain,
( ! [X0,X1] :
( singleton_relation = X0
| member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1)
| ~ subclass(X0,regular(X0)) )
| ~ spl0_188
| ~ spl0_1224 ),
inference(forward_demodulation,[],[f38064,f1712]) ).
fof(f1712,plain,
( singleton_relation = x
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f38064,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1)
| ~ subclass(X0,regular(X0))
| x = X0 )
| ~ spl0_188
| ~ spl0_1224 ),
inference(forward_demodulation,[],[f38062,f1712]) ).
fof(f38062,plain,
( ! [X0,X1] :
( ~ subclass(X0,regular(X0))
| member(not_subclass_element(X0,X1),x)
| subclass(X0,X1)
| x = X0 )
| ~ spl0_1224 ),
inference(avatar_component_clause,[],[f38061]) ).
fof(f38315,plain,
( spl0_1251
| ~ spl0_188
| ~ spl0_1223 ),
inference(avatar_split_clause,[],[f38059,f38054,f1710,f38313]) ).
fof(f38313,plain,
( spl0_1251
<=> ! [X0,X1] :
( singleton_relation = X1
| subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),X1)
| ~ subclass(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f38054,plain,
( spl0_1223
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,x),X1)
| subclass(X0,x)
| x = X1
| ~ subclass(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f38059,plain,
( ! [X0,X1] :
( singleton_relation = X1
| subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),X1)
| ~ subclass(X0,regular(X1)) )
| ~ spl0_188
| ~ spl0_1223 ),
inference(forward_demodulation,[],[f38058,f1712]) ).
fof(f38058,plain,
( ! [X0,X1] :
( subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),X1)
| x = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_188
| ~ spl0_1223 ),
inference(forward_demodulation,[],[f38057,f1712]) ).
fof(f38057,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,singleton_relation),X1)
| subclass(X0,x)
| x = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_188
| ~ spl0_1223 ),
inference(forward_demodulation,[],[f38055,f1712]) ).
fof(f38055,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,x),X1)
| subclass(X0,x)
| x = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_1223 ),
inference(avatar_component_clause,[],[f38054]) ).
fof(f38311,plain,
( spl0_1250
| ~ spl0_188
| ~ spl0_1219 ),
inference(avatar_split_clause,[],[f37993,f37990,f1710,f38309]) ).
fof(f38309,plain,
( spl0_1250
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f37993,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
| ~ spl0_188
| ~ spl0_1219 ),
inference(forward_demodulation,[],[f37991,f1712]) ).
fof(f38307,plain,
( spl0_1249
| ~ spl0_188
| ~ spl0_1218 ),
inference(avatar_split_clause,[],[f37988,f37985,f1710,f38305]) ).
fof(f38305,plain,
( spl0_1249
<=> ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f37985,plain,
( spl0_1218
<=> ! [X0] :
( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
| x = intersection(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f37988,plain,
( ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_188
| ~ spl0_1218 ),
inference(forward_demodulation,[],[f37986,f1712]) ).
fof(f37986,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
| x = intersection(X0,identity_relation) )
| ~ spl0_1218 ),
inference(avatar_component_clause,[],[f37985]) ).
fof(f38303,plain,
( spl0_1248
| ~ spl0_188
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f37451,f37448,f1710,f38301]) ).
fof(f38301,plain,
( spl0_1248
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f37448,plain,
( spl0_1215
<=> ! [X0,X1] :
( x = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f37451,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
| ~ spl0_188
| ~ spl0_1215 ),
inference(forward_demodulation,[],[f37449,f1712]) ).
fof(f37449,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation)
| x = intersection(X0,intersection(identity_relation,X1)) )
| ~ spl0_1215 ),
inference(avatar_component_clause,[],[f37448]) ).
fof(f38299,plain,
( spl0_1247
| ~ spl0_188
| ~ spl0_1214 ),
inference(avatar_split_clause,[],[f37446,f37443,f1710,f38297]) ).
fof(f38297,plain,
( spl0_1247
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f37443,plain,
( spl0_1214
<=> ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f37446,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
| ~ spl0_188
| ~ spl0_1214 ),
inference(forward_demodulation,[],[f37444,f1712]) ).
fof(f37444,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2))
| x = intersection(X0,intersection(X1,X2)) )
| ~ spl0_1214 ),
inference(avatar_component_clause,[],[f37443]) ).
fof(f38295,plain,
( spl0_1246
| ~ spl0_188
| ~ spl0_1212 ),
inference(avatar_split_clause,[],[f37435,f37432,f1710,f38293]) ).
fof(f38293,plain,
( spl0_1246
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f37432,plain,
( spl0_1212
<=> ! [X0,X1] :
( x = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f37435,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
| ~ spl0_188
| ~ spl0_1212 ),
inference(forward_demodulation,[],[f37433,f1712]) ).
fof(f37433,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation)
| x = intersection(X0,intersection(X1,identity_relation)) )
| ~ spl0_1212 ),
inference(avatar_component_clause,[],[f37432]) ).
fof(f38291,plain,
( spl0_1245
| ~ spl0_188
| ~ spl0_1211 ),
inference(avatar_split_clause,[],[f37430,f37427,f1710,f38289]) ).
fof(f38289,plain,
( spl0_1245
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f37427,plain,
( spl0_1211
<=> ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f37430,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
| ~ spl0_188
| ~ spl0_1211 ),
inference(forward_demodulation,[],[f37428,f1712]) ).
fof(f37428,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(intersection(X0,X1),X2),complement(X0))
| x = intersection(intersection(X0,X1),X2) )
| ~ spl0_1211 ),
inference(avatar_component_clause,[],[f37427]) ).
fof(f38166,plain,
( spl0_1244
| ~ spl0_188
| ~ spl0_1210 ),
inference(avatar_split_clause,[],[f37425,f37422,f1710,f38164]) ).
fof(f38164,plain,
( spl0_1244
<=> ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f37422,plain,
( spl0_1210
<=> ! [X0] :
( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
| x = intersection(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f37425,plain,
( ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_188
| ~ spl0_1210 ),
inference(forward_demodulation,[],[f37423,f1712]) ).
fof(f37423,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
| x = intersection(identity_relation,X0) )
| ~ spl0_1210 ),
inference(avatar_component_clause,[],[f37422]) ).
fof(f38162,plain,
( spl0_1243
| ~ spl0_188
| ~ spl0_1207 ),
inference(avatar_split_clause,[],[f37409,f37406,f1710,f38160]) ).
fof(f38160,plain,
( spl0_1243
<=> ! [X0,X1] :
( singleton_relation = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f37406,plain,
( spl0_1207
<=> ! [X0,X1] :
( x = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f37409,plain,
( ! [X0,X1] :
( singleton_relation = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
| ~ spl0_188
| ~ spl0_1207 ),
inference(forward_demodulation,[],[f37407,f1712]) ).
fof(f37407,plain,
( ! [X0,X1] :
( member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation)
| x = intersection(intersection(identity_relation,X0),X1) )
| ~ spl0_1207 ),
inference(avatar_component_clause,[],[f37406]) ).
fof(f38158,plain,
( spl0_1242
| ~ spl0_188
| ~ spl0_1206 ),
inference(avatar_split_clause,[],[f37112,f37109,f1710,f38156]) ).
fof(f37109,plain,
( spl0_1206
<=> ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f37112,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
| ~ spl0_188
| ~ spl0_1206 ),
inference(forward_demodulation,[],[f37110,f1712]) ).
fof(f37110,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(intersection(X0,X1),X2),complement(X1))
| x = intersection(intersection(X0,X1),X2) )
| ~ spl0_1206 ),
inference(avatar_component_clause,[],[f37109]) ).
fof(f38154,plain,
( spl0_1241
| ~ spl0_188
| ~ spl0_1204 ),
inference(avatar_split_clause,[],[f37101,f37098,f1710,f38152]) ).
fof(f38152,plain,
( spl0_1241
<=> ! [X0,X1] :
( singleton_relation = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f37098,plain,
( spl0_1204
<=> ! [X0,X1] :
( x = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f37101,plain,
( ! [X0,X1] :
( singleton_relation = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
| ~ spl0_188
| ~ spl0_1204 ),
inference(forward_demodulation,[],[f37099,f1712]) ).
fof(f37099,plain,
( ! [X0,X1] :
( member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation)
| x = intersection(intersection(X0,identity_relation),X1) )
| ~ spl0_1204 ),
inference(avatar_component_clause,[],[f37098]) ).
fof(f38150,plain,
( spl0_1240
| ~ spl0_188
| ~ spl0_1203 ),
inference(avatar_split_clause,[],[f37096,f37093,f1710,f38148]) ).
fof(f38148,plain,
( spl0_1240
<=> ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,complement(X0))
| ~ member(regular(cross_product(X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f37093,plain,
( spl0_1203
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| x = cross_product(X1,X2)
| ~ member(regular(cross_product(X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f37096,plain,
( ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,complement(X0))
| ~ member(regular(cross_product(X1,X2)),X0) )
| ~ spl0_188
| ~ spl0_1203 ),
inference(forward_demodulation,[],[f37094,f1712]) ).
fof(f37094,plain,
( ! [X2,X0,X1] :
( ~ member(regular(cross_product(X1,X2)),X0)
| x = cross_product(X1,X2)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_1203 ),
inference(avatar_component_clause,[],[f37093]) ).
fof(f38146,plain,
( spl0_1239
| ~ spl0_188
| ~ spl0_1202 ),
inference(avatar_split_clause,[],[f37091,f37088,f1710,f38144]) ).
fof(f38144,plain,
( spl0_1239
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X2,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f37088,plain,
( spl0_1202
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| x = intersection(X2,X0)
| ~ member(regular(intersection(X2,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f37091,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X2,X0)),X1) )
| ~ spl0_188
| ~ spl0_1202 ),
inference(forward_demodulation,[],[f37089,f1712]) ).
fof(f37089,plain,
( ! [X2,X0,X1] :
( ~ member(regular(intersection(X2,X0)),X1)
| x = intersection(X2,X0)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_1202 ),
inference(avatar_component_clause,[],[f37088]) ).
fof(f38142,plain,
( spl0_1238
| ~ spl0_188
| ~ spl0_1201 ),
inference(avatar_split_clause,[],[f37086,f37083,f1710,f38140]) ).
fof(f38140,plain,
( spl0_1238
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f37083,plain,
( spl0_1201
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| x = intersection(X0,X2)
| ~ member(regular(intersection(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f37086,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X0,X2)),X1) )
| ~ spl0_188
| ~ spl0_1201 ),
inference(forward_demodulation,[],[f37084,f1712]) ).
fof(f37084,plain,
( ! [X2,X0,X1] :
( ~ member(regular(intersection(X0,X2)),X1)
| x = intersection(X0,X2)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_1201 ),
inference(avatar_component_clause,[],[f37083]) ).
fof(f38138,plain,
( spl0_1237
| ~ spl0_188
| ~ spl0_1200 ),
inference(avatar_split_clause,[],[f37081,f37078,f1710,f38136]) ).
fof(f38136,plain,
( spl0_1237
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f37078,plain,
( spl0_1200
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f37081,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_188
| ~ spl0_1200 ),
inference(forward_demodulation,[],[f37079,f1712]) ).
fof(f37079,plain,
( ! [X0,X1] :
( ~ subclass(X0,flip(X1))
| x = X0
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_1200 ),
inference(avatar_component_clause,[],[f37078]) ).
fof(f38134,plain,
( spl0_1236
| ~ spl0_188
| ~ spl0_1199 ),
inference(avatar_split_clause,[],[f37076,f37073,f1710,f38132]) ).
fof(f38132,plain,
( spl0_1236
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f37073,plain,
( spl0_1199
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f37076,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_188
| ~ spl0_1199 ),
inference(forward_demodulation,[],[f37074,f1712]) ).
fof(f37074,plain,
( ! [X0,X1] :
( ~ subclass(X0,rotate(X1))
| x = X0
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_1199 ),
inference(avatar_component_clause,[],[f37073]) ).
fof(f38130,plain,
( spl0_1235
| ~ spl0_188
| ~ spl0_1198 ),
inference(avatar_split_clause,[],[f37071,f37068,f1710,f38128]) ).
fof(f38128,plain,
( spl0_1235
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f37068,plain,
( spl0_1198
<=> ! [X0] :
( x = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f37071,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) )
| ~ spl0_188
| ~ spl0_1198 ),
inference(forward_demodulation,[],[f37069,f1712]) ).
fof(f37069,plain,
( ! [X0] :
( ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| x = X0
| ~ member(regular(X0),identity_relation) )
| ~ spl0_1198 ),
inference(avatar_component_clause,[],[f37068]) ).
fof(f38126,plain,
( spl0_1234
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130 ),
inference(avatar_split_clause,[],[f34969,f34421,f9135,f8637,f1710,f38124]) ).
fof(f34969,plain,
( ! [X0] : singleton_relation = cross_product(singleton_relation,X0)
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f34968,f1712]) ).
fof(f34968,plain,
( ! [X0] : singleton_relation = cross_product(x,X0)
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130 ),
inference(forward_demodulation,[],[f34945,f9137]) ).
fof(f34945,plain,
( ! [X0] : singleton_relation = cross_product(domain_of(x),X0)
| ~ spl0_548
| ~ spl0_1130 ),
inference(resolution,[],[f34422,f8638]) ).
fof(f38119,plain,
( ~ spl0_1233
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130
| spl0_1232 ),
inference(avatar_split_clause,[],[f38114,f38109,f34421,f9135,f8637,f1710,f38116]) ).
fof(f38116,plain,
( spl0_1233
<=> member(second(not_subclass_element(singleton_relation,identity_relation)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f38109,plain,
( spl0_1232
<=> member(second(not_subclass_element(cross_product(x,x),identity_relation)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f38114,plain,
( ~ member(second(not_subclass_element(singleton_relation,identity_relation)),universal_class)
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130
| spl0_1232 ),
inference(forward_demodulation,[],[f38113,f34969]) ).
fof(f38113,plain,
( ~ member(second(not_subclass_element(cross_product(singleton_relation,singleton_relation),identity_relation)),universal_class)
| ~ spl0_188
| spl0_1232 ),
inference(forward_demodulation,[],[f38110,f1712]) ).
fof(f38110,plain,
( ~ member(second(not_subclass_element(cross_product(x,x),identity_relation)),universal_class)
| spl0_1232 ),
inference(avatar_component_clause,[],[f38109]) ).
fof(f38112,plain,
( spl0_1232
| ~ spl0_1229
| ~ spl0_454
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f8667,f8609,f6463,f38085,f38109]) ).
fof(f6463,plain,
( spl0_454
<=> not_subclass_element(cross_product(x,x),identity_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),first(not_subclass_element(cross_product(x,x),identity_relation))),unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),unordered_pair(second(not_subclass_element(cross_product(x,x),identity_relation)),second(not_subclass_element(cross_product(x,x),identity_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f8609,plain,
( spl0_541
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f8667,plain,
( ~ member(not_subclass_element(cross_product(x,x),identity_relation),subset_relation)
| member(second(not_subclass_element(cross_product(x,x),identity_relation)),universal_class)
| ~ spl0_454
| ~ spl0_541 ),
inference(superposition,[],[f8610,f6465]) ).
fof(f6465,plain,
( not_subclass_element(cross_product(x,x),identity_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),first(not_subclass_element(cross_product(x,x),identity_relation))),unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),unordered_pair(second(not_subclass_element(cross_product(x,x),identity_relation)),second(not_subclass_element(cross_product(x,x),identity_relation)))))
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f6463]) ).
fof(f8610,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) )
| ~ spl0_541 ),
inference(avatar_component_clause,[],[f8609]) ).
fof(f38104,plain,
( ~ spl0_1231
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130
| spl0_1228 ),
inference(avatar_split_clause,[],[f38092,f38081,f34421,f9135,f8637,f1710,f38101]) ).
fof(f38101,plain,
( spl0_1231
<=> member(first(not_subclass_element(singleton_relation,identity_relation)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f38081,plain,
( spl0_1228
<=> member(first(not_subclass_element(cross_product(x,x),identity_relation)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f38092,plain,
( ~ member(first(not_subclass_element(singleton_relation,identity_relation)),universal_class)
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130
| spl0_1228 ),
inference(forward_demodulation,[],[f38091,f34969]) ).
fof(f38091,plain,
( ~ member(first(not_subclass_element(cross_product(singleton_relation,singleton_relation),identity_relation)),universal_class)
| ~ spl0_188
| spl0_1228 ),
inference(forward_demodulation,[],[f38082,f1712]) ).
fof(f38082,plain,
( ~ member(first(not_subclass_element(cross_product(x,x),identity_relation)),universal_class)
| spl0_1228 ),
inference(avatar_component_clause,[],[f38081]) ).
fof(f38097,plain,
( ~ spl0_1230
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130
| spl0_1229 ),
inference(avatar_split_clause,[],[f38090,f38085,f34421,f9135,f8637,f1710,f38094]) ).
fof(f38094,plain,
( spl0_1230
<=> member(not_subclass_element(singleton_relation,identity_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f38090,plain,
( ~ member(not_subclass_element(singleton_relation,identity_relation),subset_relation)
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1130
| spl0_1229 ),
inference(forward_demodulation,[],[f38089,f34969]) ).
fof(f38089,plain,
( ~ member(not_subclass_element(cross_product(singleton_relation,singleton_relation),identity_relation),subset_relation)
| ~ spl0_188
| spl0_1229 ),
inference(forward_demodulation,[],[f38087,f1712]) ).
fof(f38088,plain,
( spl0_1228
| ~ spl0_1229
| ~ spl0_454
| ~ spl0_540 ),
inference(avatar_split_clause,[],[f8657,f8605,f6463,f38085,f38081]) ).
fof(f8605,plain,
( spl0_540
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f8657,plain,
( ~ member(not_subclass_element(cross_product(x,x),identity_relation),subset_relation)
| member(first(not_subclass_element(cross_product(x,x),identity_relation)),universal_class)
| ~ spl0_454
| ~ spl0_540 ),
inference(superposition,[],[f8606,f6465]) ).
fof(f8606,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) )
| ~ spl0_540 ),
inference(avatar_component_clause,[],[f8605]) ).
fof(f38078,plain,
( spl0_1227
| ~ spl0_15
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f8263,f8143,f271,f38076]) ).
fof(f38076,plain,
( spl0_1227
<=> ! [X2,X0,X1] :
( member(regular(intersection(X0,cross_product(X1,X2))),universal_class)
| x = intersection(X0,cross_product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f271,plain,
( spl0_15
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f8143,plain,
( spl0_523
<=> ! [X2,X0,X1] :
( x = intersection(X0,cross_product(X1,X2))
| regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f8263,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,cross_product(X1,X2))),universal_class)
| x = intersection(X0,cross_product(X1,X2)) )
| ~ spl0_15
| ~ spl0_523 ),
inference(superposition,[],[f272,f8144]) ).
fof(f8144,plain,
( ! [X2,X0,X1] :
( regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2)))))))
| x = intersection(X0,cross_product(X1,X2)) )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f8143]) ).
fof(f272,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f38073,plain,
( spl0_1226
| ~ spl0_15
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f8191,f8139,f271,f38071]) ).
fof(f38071,plain,
( spl0_1226
<=> ! [X2,X0,X1] :
( member(regular(intersection(cross_product(X0,X1),X2)),universal_class)
| x = intersection(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f8139,plain,
( spl0_522
<=> ! [X2,X0,X1] :
( x = intersection(cross_product(X0,X1),X2)
| regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f8191,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(cross_product(X0,X1),X2)),universal_class)
| x = intersection(cross_product(X0,X1),X2) )
| ~ spl0_15
| ~ spl0_522 ),
inference(superposition,[],[f272,f8140]) ).
fof(f8140,plain,
( ! [X2,X0,X1] :
( regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2))))))
| x = intersection(cross_product(X0,X1),X2) )
| ~ spl0_522 ),
inference(avatar_component_clause,[],[f8139]) ).
fof(f38069,plain,
( spl0_1225
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1129 ),
inference(avatar_split_clause,[],[f34906,f34417,f9135,f8637,f1710,f38067]) ).
fof(f34906,plain,
( ! [X0] : singleton_relation = cross_product(X0,singleton_relation)
| ~ spl0_188
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1129 ),
inference(forward_demodulation,[],[f34905,f1712]) ).
fof(f34905,plain,
( ! [X0] : singleton_relation = cross_product(X0,x)
| ~ spl0_548
| ~ spl0_564
| ~ spl0_1129 ),
inference(forward_demodulation,[],[f34876,f9137]) ).
fof(f34876,plain,
( ! [X0] : singleton_relation = cross_product(X0,domain_of(x))
| ~ spl0_548
| ~ spl0_1129 ),
inference(resolution,[],[f34418,f8638]) ).
fof(f38063,plain,
( spl0_1224
| ~ spl0_33
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4117,f4021,f354,f38061]) ).
fof(f4021,plain,
( spl0_338
<=> ! [X2,X0,X1] :
( ~ subclass(X0,regular(X1))
| subclass(X0,X2)
| member(not_subclass_element(X0,X2),x)
| ~ member(not_subclass_element(X0,X2),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f4117,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),x)
| ~ subclass(X0,regular(X0))
| x = X0 )
| ~ spl0_33
| ~ spl0_338 ),
inference(duplicate_literal_removal,[],[f4086]) ).
fof(f4086,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),x)
| ~ subclass(X0,regular(X0))
| x = X0
| subclass(X0,X1) )
| ~ spl0_33
| ~ spl0_338 ),
inference(resolution,[],[f4022,f355]) ).
fof(f4022,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2)
| member(not_subclass_element(X0,X2),x)
| ~ subclass(X0,regular(X1))
| x = X1 )
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f4021]) ).
fof(f38056,plain,
( spl0_1223
| ~ spl0_151
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3702,f3560,f1317,f38054]) ).
fof(f1317,plain,
( spl0_151
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f3702,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,x),X1)
| subclass(X0,x)
| x = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_151
| ~ spl0_321 ),
inference(duplicate_literal_removal,[],[f3693]) ).
fof(f3693,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,x),X1)
| subclass(X0,x)
| x = X1
| ~ subclass(X0,regular(X1))
| subclass(X0,x) )
| ~ spl0_151
| ~ spl0_321 ),
inference(resolution,[],[f3561,f1318]) ).
fof(f1318,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1317]) ).
fof(f38032,plain,
( spl0_1222
| ~ spl0_188
| ~ spl0_1221 ),
inference(avatar_split_clause,[],[f38028,f38025,f1710,f38030]) ).
fof(f38030,plain,
( spl0_1222
<=> ! [X2] :
( singleton_relation = X2
| ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f38025,plain,
( spl0_1221
<=> ! [X2] :
( ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2)
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f38028,plain,
( ! [X2] :
( singleton_relation = X2
| ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2) )
| ~ spl0_188
| ~ spl0_1221 ),
inference(forward_demodulation,[],[f38026,f1712]) ).
fof(f38026,plain,
( ! [X2] :
( ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2)
| x = X2 )
| ~ spl0_1221 ),
inference(avatar_component_clause,[],[f38025]) ).
fof(f38027,plain,
( spl0_1221
| spl0_1116
| ~ spl0_135
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3658,f3529,f1116,f34346,f38025]) ).
fof(f34346,plain,
( spl0_1116
<=> ! [X0,X1] : member(unordered_pair(X0,X1),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1116,plain,
( spl0_135
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f3529,plain,
( spl0_315
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,regular(X0))
| member(unordered_pair(X1,X2),x)
| ~ member(unordered_pair(X1,X2),X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3658,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),x)
| ~ subclass(universal_class,regular(X2))
| x = X2
| ~ subclass(universal_class,X2) )
| ~ spl0_135
| ~ spl0_315 ),
inference(resolution,[],[f3530,f1117]) ).
fof(f1117,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f3530,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| member(unordered_pair(X1,X2),x)
| ~ subclass(universal_class,regular(X0))
| x = X0 )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3529]) ).
fof(f37997,plain,
( spl0_1220
| spl0_868
| ~ spl0_18
| ~ spl0_299 ),
inference(avatar_split_clause,[],[f3418,f3399,f285,f21589,f37995]) ).
fof(f37995,plain,
( spl0_1220
<=> ! [X0,X1] :
( regular(omega) = X0
| ~ inductive(unordered_pair(X0,X1))
| regular(omega) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f3399,plain,
( spl0_299
<=> ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| x = X0
| regular(X0) = X1
| regular(X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f3418,plain,
( ! [X0,X1] :
( omega = x
| regular(omega) = X0
| regular(omega) = X1
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_18
| ~ spl0_299 ),
inference(resolution,[],[f3400,f286]) ).
fof(f3400,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| x = X0
| regular(X0) = X1
| regular(X0) = X2 )
| ~ spl0_299 ),
inference(avatar_component_clause,[],[f3399]) ).
fof(f37992,plain,
( spl0_1219
| ~ spl0_246
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3330,f3187,f2410,f37990]) ).
fof(f3330,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
| ~ spl0_246
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f3304]) ).
fof(f3304,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| x = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
| ~ spl0_246
| ~ spl0_292 ),
inference(resolution,[],[f3188,f2411]) ).
fof(f37987,plain,
( spl0_1218
| ~ spl0_49
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3327,f3187,f434,f37985]) ).
fof(f434,plain,
( spl0_49
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f3327,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
| x = intersection(X0,identity_relation) )
| ~ spl0_49
| ~ spl0_292 ),
inference(superposition,[],[f3188,f436]) ).
fof(f436,plain,
( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f37982,plain,
( spl0_1217
| ~ spl0_48
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3326,f3187,f429,f37980]) ).
fof(f37980,plain,
( spl0_1217
<=> ! [X0] :
( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(identity_relation))))
| x = intersection(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f3326,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(identity_relation))))
| x = intersection(X0,singleton_relation) )
| ~ spl0_48
| ~ spl0_292 ),
inference(superposition,[],[f3188,f431]) ).
fof(f37455,plain,
( spl0_1216
| ~ spl0_129
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3320,f3187,f997,f37453]) ).
fof(f37453,plain,
( spl0_1216
<=> ! [X0,X1] :
( x = intersection(X0,intersection(singleton_relation,X1))
| member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f3320,plain,
( ! [X0,X1] :
( x = intersection(X0,intersection(singleton_relation,X1))
| member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) )
| ~ spl0_129
| ~ spl0_292 ),
inference(resolution,[],[f3188,f998]) ).
fof(f37450,plain,
( spl0_1215
| ~ spl0_130
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3318,f3187,f1001,f37448]) ).
fof(f1001,plain,
( spl0_130
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f3318,plain,
( ! [X0,X1] :
( x = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
| ~ spl0_130
| ~ spl0_292 ),
inference(resolution,[],[f3188,f1002]) ).
fof(f1002,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f37445,plain,
( spl0_1214
| ~ spl0_246
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3301,f3183,f2410,f37443]) ).
fof(f3301,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
| ~ spl0_246
| ~ spl0_291 ),
inference(duplicate_literal_removal,[],[f3275]) ).
fof(f3275,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| x = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
| ~ spl0_246
| ~ spl0_291 ),
inference(resolution,[],[f3184,f2411]) ).
fof(f37439,plain,
( spl0_1213
| ~ spl0_129
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3291,f3183,f997,f37437]) ).
fof(f3291,plain,
( ! [X0,X1] :
( x = intersection(X0,intersection(X1,singleton_relation))
| member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) )
| ~ spl0_129
| ~ spl0_291 ),
inference(resolution,[],[f3184,f998]) ).
fof(f37434,plain,
( spl0_1212
| ~ spl0_130
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3289,f3183,f1001,f37432]) ).
fof(f3289,plain,
( ! [X0,X1] :
( x = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
| ~ spl0_130
| ~ spl0_291 ),
inference(resolution,[],[f3184,f1002]) ).
fof(f37429,plain,
( spl0_1211
| ~ spl0_246
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3267,f3174,f2410,f37427]) ).
fof(f3267,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
| ~ spl0_246
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3241]) ).
fof(f3241,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| x = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
| ~ spl0_246
| ~ spl0_289 ),
inference(resolution,[],[f3175,f2411]) ).
fof(f37424,plain,
( spl0_1210
| ~ spl0_49
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3264,f3174,f434,f37422]) ).
fof(f3264,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
| x = intersection(identity_relation,X0) )
| ~ spl0_49
| ~ spl0_289 ),
inference(superposition,[],[f3175,f436]) ).
fof(f37419,plain,
( spl0_1209
| ~ spl0_48
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3263,f3174,f429,f37417]) ).
fof(f37417,plain,
( spl0_1209
<=> ! [X0] :
( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(identity_relation))))
| x = intersection(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f3263,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(identity_relation))))
| x = intersection(singleton_relation,X0) )
| ~ spl0_48
| ~ spl0_289 ),
inference(superposition,[],[f3175,f431]) ).
fof(f37413,plain,
( spl0_1208
| ~ spl0_129
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3257,f3174,f997,f37411]) ).
fof(f37411,plain,
( spl0_1208
<=> ! [X0,X1] :
( x = intersection(intersection(singleton_relation,X0),X1)
| member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f3257,plain,
( ! [X0,X1] :
( x = intersection(intersection(singleton_relation,X0),X1)
| member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) )
| ~ spl0_129
| ~ spl0_289 ),
inference(resolution,[],[f3175,f998]) ).
fof(f37408,plain,
( spl0_1207
| ~ spl0_130
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3255,f3174,f1001,f37406]) ).
fof(f3255,plain,
( ! [X0,X1] :
( x = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
| ~ spl0_130
| ~ spl0_289 ),
inference(resolution,[],[f3175,f1002]) ).
fof(f37111,plain,
( spl0_1206
| ~ spl0_246
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3238,f3170,f2410,f37109]) ).
fof(f3238,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
| ~ spl0_246
| ~ spl0_288 ),
inference(duplicate_literal_removal,[],[f3212]) ).
fof(f3212,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| x = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
| ~ spl0_246
| ~ spl0_288 ),
inference(resolution,[],[f3171,f2411]) ).
fof(f37105,plain,
( spl0_1205
| ~ spl0_129
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3228,f3170,f997,f37103]) ).
fof(f3228,plain,
( ! [X0,X1] :
( x = intersection(intersection(X0,singleton_relation),X1)
| member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) )
| ~ spl0_129
| ~ spl0_288 ),
inference(resolution,[],[f3171,f998]) ).
fof(f37100,plain,
( spl0_1204
| ~ spl0_130
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3226,f3170,f1001,f37098]) ).
fof(f3226,plain,
( ! [X0,X1] :
( x = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
| ~ spl0_130
| ~ spl0_288 ),
inference(resolution,[],[f3171,f1002]) ).
fof(f37095,plain,
( spl0_1203
| ~ spl0_28
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3127,f2992,f327,f37093]) ).
fof(f3127,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| x = cross_product(X1,X2)
| ~ member(regular(cross_product(X1,X2)),X0) )
| ~ spl0_28
| ~ spl0_285 ),
inference(resolution,[],[f2993,f328]) ).
fof(f37090,plain,
( spl0_1202
| ~ spl0_28
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3074,f2976,f327,f37088]) ).
fof(f3074,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| x = intersection(X2,X0)
| ~ member(regular(intersection(X2,X0)),X1) )
| ~ spl0_28
| ~ spl0_281 ),
inference(resolution,[],[f2977,f328]) ).
fof(f37085,plain,
( spl0_1201
| ~ spl0_28
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3021,f2964,f327,f37083]) ).
fof(f3021,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| x = intersection(X0,X2)
| ~ member(regular(intersection(X0,X2)),X1) )
| ~ spl0_28
| ~ spl0_279 ),
inference(resolution,[],[f2965,f328]) ).
fof(f37080,plain,
( spl0_1200
| ~ spl0_41
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2866,f2797,f386,f37078]) ).
fof(f386,plain,
( spl0_41
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2797,plain,
( spl0_271
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = X0
| ~ subclass(X1,X2)
| member(regular(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2866,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_41
| ~ spl0_271 ),
inference(resolution,[],[f2798,f387]) ).
fof(f387,plain,
( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f2798,plain,
( ! [X2,X0,X1] :
( ~ subclass(X1,X2)
| x = X0
| ~ subclass(X0,X1)
| member(regular(X0),X2) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2797]) ).
fof(f37075,plain,
( spl0_1199
| ~ spl0_40
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2865,f2797,f382,f37073]) ).
fof(f382,plain,
( spl0_40
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f2865,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_40
| ~ spl0_271 ),
inference(resolution,[],[f2798,f383]) ).
fof(f383,plain,
( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f37070,plain,
( spl0_1198
| ~ spl0_150
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2636,f2410,f1294,f37068]) ).
fof(f1294,plain,
( spl0_150
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f2636,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) )
| ~ spl0_150
| ~ spl0_246 ),
inference(resolution,[],[f2411,f1295]) ).
fof(f1295,plain,
( ! [X0] :
( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,identity_relation) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f36846,plain,
( spl0_1197
| ~ spl0_188
| ~ spl0_533 ),
inference(avatar_split_clause,[],[f13943,f8386,f1710,f36844]) ).
fof(f13943,plain,
( ! [X0] : singleton_relation = intersection(X0,singleton_relation)
| ~ spl0_188
| ~ spl0_533 ),
inference(superposition,[],[f8387,f1712]) ).
fof(f36246,plain,
( spl0_1196
| ~ spl0_188
| ~ spl0_527 ),
inference(avatar_split_clause,[],[f13940,f8227,f1710,f36244]) ).
fof(f13940,plain,
( ! [X0] : singleton_relation = intersection(singleton_relation,X0)
| ~ spl0_188
| ~ spl0_527 ),
inference(superposition,[],[f8228,f1712]) ).
fof(f35718,plain,
( spl0_1195
| ~ spl0_188
| ~ spl0_1170 ),
inference(avatar_split_clause,[],[f35549,f35546,f1710,f35716]) ).
fof(f35716,plain,
( spl0_1195
<=> ! [X0,X1] :
( singleton_relation = unordered_pair(X1,X0)
| member(X0,universal_class)
| regular(unordered_pair(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f35546,plain,
( spl0_1170
<=> ! [X0,X1] :
( member(X0,universal_class)
| x = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f35549,plain,
( ! [X0,X1] :
( singleton_relation = unordered_pair(X1,X0)
| member(X0,universal_class)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_188
| ~ spl0_1170 ),
inference(forward_demodulation,[],[f35547,f1712]) ).
fof(f35547,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| x = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_1170 ),
inference(avatar_component_clause,[],[f35546]) ).
fof(f35714,plain,
( spl0_1194
| ~ spl0_188
| ~ spl0_1169 ),
inference(avatar_split_clause,[],[f35544,f35541,f1710,f35712]) ).
fof(f35712,plain,
( spl0_1194
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = singleton_relation
| member(X0,universal_class)
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f35541,plain,
( spl0_1169
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f35544,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = singleton_relation
| member(X0,universal_class)
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_188
| ~ spl0_1169 ),
inference(forward_demodulation,[],[f35542,f1712]) ).
fof(f35542,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_1169 ),
inference(avatar_component_clause,[],[f35541]) ).
fof(f35710,plain,
( spl0_1193
| ~ spl0_188
| ~ spl0_1166 ),
inference(avatar_split_clause,[],[f35530,f35527,f1710,f35708]) ).
fof(f35708,plain,
( spl0_1193
<=> ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,X0)
| ~ subclass(cross_product(X1,X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f35527,plain,
( spl0_1166
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| x = cross_product(X1,X2)
| ~ subclass(cross_product(X1,X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f35530,plain,
( ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,X0)
| ~ subclass(cross_product(X1,X2),complement(X0)) )
| ~ spl0_188
| ~ spl0_1166 ),
inference(forward_demodulation,[],[f35528,f1712]) ).
fof(f35528,plain,
( ! [X2,X0,X1] :
( ~ subclass(cross_product(X1,X2),complement(X0))
| x = cross_product(X1,X2)
| ~ subclass(universal_class,X0) )
| ~ spl0_1166 ),
inference(avatar_component_clause,[],[f35527]) ).
fof(f35706,plain,
( spl0_1192
| ~ spl0_188
| ~ spl0_1165 ),
inference(avatar_split_clause,[],[f35525,f35522,f1710,f35704]) ).
fof(f35704,plain,
( spl0_1192
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X2,X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f35522,plain,
( spl0_1165
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X2,X0)
| ~ subclass(intersection(X2,X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f35525,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X2,X0),complement(X1)) )
| ~ spl0_188
| ~ spl0_1165 ),
inference(forward_demodulation,[],[f35523,f1712]) ).
fof(f35523,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X2,X0),complement(X1))
| x = intersection(X2,X0)
| ~ subclass(X0,X1) )
| ~ spl0_1165 ),
inference(avatar_component_clause,[],[f35522]) ).
fof(f35702,plain,
( spl0_1191
| ~ spl0_188
| ~ spl0_1162 ),
inference(avatar_split_clause,[],[f35510,f35507,f1710,f35700]) ).
fof(f35700,plain,
( spl0_1191
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X1,X0)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f35507,plain,
( spl0_1162
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| x = intersection(X1,X0)
| member(regular(intersection(X1,X0)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f35510,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X1,X0)),subset_relation) )
| ~ spl0_188
| ~ spl0_1162 ),
inference(forward_demodulation,[],[f35508,f1712]) ).
fof(f35508,plain,
( ! [X0,X1] :
( member(regular(intersection(X1,X0)),subset_relation)
| x = intersection(X1,X0)
| ~ subclass(X0,identity_relation) )
| ~ spl0_1162 ),
inference(avatar_component_clause,[],[f35507]) ).
fof(f35698,plain,
( spl0_1190
| ~ spl0_188
| ~ spl0_1161 ),
inference(avatar_split_clause,[],[f35505,f35502,f1710,f35696]) ).
fof(f35696,plain,
( spl0_1190
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X0,X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f35502,plain,
( spl0_1161
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,X2)
| ~ subclass(intersection(X0,X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f35505,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X0,X2),complement(X1)) )
| ~ spl0_188
| ~ spl0_1161 ),
inference(forward_demodulation,[],[f35503,f1712]) ).
fof(f35503,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X0,X2),complement(X1))
| x = intersection(X0,X2)
| ~ subclass(X0,X1) )
| ~ spl0_1161 ),
inference(avatar_component_clause,[],[f35502]) ).
fof(f35694,plain,
( spl0_1189
| ~ spl0_188
| ~ spl0_1159 ),
inference(avatar_split_clause,[],[f35495,f35492,f1710,f35692]) ).
fof(f35692,plain,
( spl0_1189
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X0,X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f35492,plain,
( spl0_1159
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| intersection(X0,X1) = x
| member(regular(intersection(X0,X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f35495,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X0,X1)),subset_relation) )
| ~ spl0_188
| ~ spl0_1159 ),
inference(forward_demodulation,[],[f35493,f1712]) ).
fof(f35493,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),subset_relation)
| intersection(X0,X1) = x
| ~ subclass(X0,identity_relation) )
| ~ spl0_1159 ),
inference(avatar_component_clause,[],[f35492]) ).
fof(f35690,plain,
( spl0_1188
| ~ spl0_188
| ~ spl0_1158 ),
inference(avatar_split_clause,[],[f35490,f35487,f1710,f35688]) ).
fof(f35688,plain,
( spl0_1188
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f35487,plain,
( spl0_1158
<=> ! [X0] :
( x = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f35490,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_188
| ~ spl0_1158 ),
inference(forward_demodulation,[],[f35488,f1712]) ).
fof(f35488,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ subclass(X0,application_function)
| x = X0 )
| ~ spl0_1158 ),
inference(avatar_component_clause,[],[f35487]) ).
fof(f35686,plain,
( spl0_1187
| ~ spl0_188
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f35485,f35482,f1710,f35684]) ).
fof(f35684,plain,
( spl0_1187
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f35482,plain,
( spl0_1157
<=> ! [X0] :
( x = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f35485,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_188
| ~ spl0_1157 ),
inference(forward_demodulation,[],[f35483,f1712]) ).
fof(f35483,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ subclass(X0,composition_function)
| x = X0 )
| ~ spl0_1157 ),
inference(avatar_component_clause,[],[f35482]) ).
fof(f35682,plain,
( spl0_1186
| ~ spl0_188
| ~ spl0_1156 ),
inference(avatar_split_clause,[],[f35480,f35477,f1710,f35680]) ).
fof(f35680,plain,
( spl0_1186
<=> ! [X2,X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f35477,plain,
( spl0_1156
<=> ! [X2,X0,X1] :
( x = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f35480,plain,
( ! [X2,X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1156 ),
inference(forward_demodulation,[],[f35478,f1712]) ).
fof(f35478,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,compose(X1,X2))
| x = X0
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_1156 ),
inference(avatar_component_clause,[],[f35477]) ).
fof(f35678,plain,
( spl0_1185
| ~ spl0_188
| ~ spl0_1155 ),
inference(avatar_split_clause,[],[f35475,f35472,f1710,f35676]) ).
fof(f35676,plain,
( spl0_1185
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f35472,plain,
( spl0_1155
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f35475,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) )
| ~ spl0_188
| ~ spl0_1155 ),
inference(forward_demodulation,[],[f35473,f1712]) ).
fof(f35473,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = X0
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) )
| ~ spl0_1155 ),
inference(avatar_component_clause,[],[f35472]) ).
fof(f35674,plain,
( spl0_1184
| ~ spl0_188
| ~ spl0_1154 ),
inference(avatar_split_clause,[],[f35470,f35467,f1710,f35672]) ).
fof(f35672,plain,
( spl0_1184
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f35467,plain,
( spl0_1154
<=> ! [X0] :
( ~ subclass(X0,identity_relation)
| x = X0
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f35470,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_188
| ~ spl0_1154 ),
inference(forward_demodulation,[],[f35468,f1712]) ).
fof(f35468,plain,
( ! [X0] :
( member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| x = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_1154 ),
inference(avatar_component_clause,[],[f35467]) ).
fof(f35670,plain,
( spl0_1183
| ~ spl0_188
| ~ spl0_1152 ),
inference(avatar_split_clause,[],[f35460,f35457,f1710,f35668]) ).
fof(f35668,plain,
( spl0_1183
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f35457,plain,
( spl0_1152
<=> ! [X0,X1] :
( x = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f35460,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) )
| ~ spl0_188
| ~ spl0_1152 ),
inference(forward_demodulation,[],[f35458,f1712]) ).
fof(f35458,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,identity_relation)),X1)
| ~ subclass(subset_relation,X1)
| x = intersection(X0,identity_relation) )
| ~ spl0_1152 ),
inference(avatar_component_clause,[],[f35457]) ).
fof(f35666,plain,
( spl0_1182
| ~ spl0_188
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f35455,f35452,f1710,f35664]) ).
fof(f35664,plain,
( spl0_1182
<=> ! [X0,X1] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f35452,plain,
( spl0_1151
<=> ! [X0,X1] :
( x = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f35455,plain,
( ! [X0,X1] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) )
| ~ spl0_188
| ~ spl0_1151 ),
inference(forward_demodulation,[],[f35453,f1712]) ).
fof(f35453,plain,
( ! [X0,X1] :
( member(regular(intersection(identity_relation,X0)),X1)
| ~ subclass(subset_relation,X1)
| x = intersection(identity_relation,X0) )
| ~ spl0_1151 ),
inference(avatar_component_clause,[],[f35452]) ).
fof(f35662,plain,
( ~ spl0_1181
| ~ spl0_188
| spl0_671 ),
inference(avatar_split_clause,[],[f13957,f13593,f1710,f35659]) ).
fof(f13593,plain,
( spl0_671
<=> x = cross_product(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f13957,plain,
( singleton_relation != cross_product(singleton_relation,universal_class)
| ~ spl0_188
| spl0_671 ),
inference(superposition,[],[f13595,f1712]) ).
fof(f13595,plain,
( x != cross_product(x,universal_class)
| spl0_671 ),
inference(avatar_component_clause,[],[f13593]) ).
fof(f35657,plain,
( spl0_1180
| ~ spl0_188
| ~ spl0_1148 ),
inference(avatar_split_clause,[],[f35440,f35437,f1710,f35655]) ).
fof(f35655,plain,
( spl0_1180
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f35437,plain,
( spl0_1148
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f35440,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) )
| ~ spl0_188
| ~ spl0_1148 ),
inference(forward_demodulation,[],[f35438,f1712]) ).
fof(f35438,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| x = X0
| ~ member(regular(X0),universal_class) )
| ~ spl0_1148 ),
inference(avatar_component_clause,[],[f35437]) ).
fof(f35653,plain,
( spl0_1179
| ~ spl0_188
| ~ spl0_1147 ),
inference(avatar_split_clause,[],[f35435,f35432,f1710,f35651]) ).
fof(f35651,plain,
( spl0_1179
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f35432,plain,
( spl0_1147
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f35435,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) )
| ~ spl0_188
| ~ spl0_1147 ),
inference(forward_demodulation,[],[f35433,f1712]) ).
fof(f35433,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| x = X0
| ~ member(regular(X0),universal_class) )
| ~ spl0_1147 ),
inference(avatar_component_clause,[],[f35432]) ).
fof(f35649,plain,
( spl0_1178
| ~ spl0_7
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f18038,f11878,f235,f35647]) ).
fof(f35647,plain,
( spl0_1178
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f18038,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_7
| ~ spl0_639 ),
inference(resolution,[],[f11879,f236]) ).
fof(f35644,plain,
( spl0_1177
| ~ spl0_20
| ~ spl0_607 ),
inference(avatar_split_clause,[],[f11027,f11001,f294,f35642]) ).
fof(f294,plain,
( spl0_20
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f11001,plain,
( spl0_607
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f11027,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,x))),X1) )
| ~ spl0_20
| ~ spl0_607 ),
inference(resolution,[],[f11002,f295]) ).
fof(f295,plain,
( member(x,universal_class)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f11002,plain,
( ! [X2,X0,X1] :
( ~ member(X1,universal_class)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
| ~ spl0_607 ),
inference(avatar_component_clause,[],[f11001]) ).
fof(f35639,plain,
( spl0_1176
| ~ spl0_296
| ~ spl0_486 ),
inference(avatar_split_clause,[],[f7418,f7282,f3204,f35637]) ).
fof(f35637,plain,
( spl0_1176
<=> ! [X2,X0,X1] :
( subclass(intersection(x,X0),X1)
| ~ subclass(intersection(x,X0),complement(X2))
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f7282,plain,
( spl0_486
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f7418,plain,
( ! [X2,X0,X1] :
( subclass(intersection(x,X0),X1)
| ~ subclass(intersection(x,X0),complement(X2))
| x = X2 )
| ~ spl0_296
| ~ spl0_486 ),
inference(duplicate_literal_removal,[],[f7393]) ).
fof(f7393,plain,
( ! [X2,X0,X1] :
( subclass(intersection(x,X0),X1)
| ~ subclass(intersection(x,X0),complement(X2))
| subclass(intersection(x,X0),X1)
| x = X2 )
| ~ spl0_296
| ~ spl0_486 ),
inference(resolution,[],[f7283,f3205]) ).
fof(f7283,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_486 ),
inference(avatar_component_clause,[],[f7282]) ).
fof(f35634,plain,
( spl0_1175
| ~ spl0_297
| ~ spl0_486 ),
inference(avatar_split_clause,[],[f7417,f7282,f3208,f35632]) ).
fof(f35632,plain,
( spl0_1175
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,x),X1)
| ~ subclass(intersection(X0,x),complement(X2))
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f7417,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,x),X1)
| ~ subclass(intersection(X0,x),complement(X2))
| x = X2 )
| ~ spl0_297
| ~ spl0_486 ),
inference(duplicate_literal_removal,[],[f7394]) ).
fof(f7394,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,x),X1)
| ~ subclass(intersection(X0,x),complement(X2))
| subclass(intersection(X0,x),X1)
| x = X2 )
| ~ spl0_297
| ~ spl0_486 ),
inference(resolution,[],[f7283,f3209]) ).
fof(f35630,plain,
( spl0_362
| ~ spl0_1174
| ~ spl0_108
| spl0_364 ),
inference(avatar_split_clause,[],[f4435,f4429,f823,f35627,f4421]) ).
fof(f4421,plain,
( spl0_362
<=> x = domain_of(flip(cross_product(subset_relation,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f35627,plain,
( spl0_1174
<=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f4429,plain,
( spl0_364
<=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f4435,plain,
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
| x = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_108
| spl0_364 ),
inference(resolution,[],[f4431,f824]) ).
fof(f4431,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
| spl0_364 ),
inference(avatar_component_clause,[],[f4429]) ).
fof(f35625,plain,
( spl0_362
| ~ spl0_1173
| ~ spl0_108
| spl0_363 ),
inference(avatar_split_clause,[],[f4433,f4425,f823,f35622,f4421]) ).
fof(f35622,plain,
( spl0_1173
<=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f4425,plain,
( spl0_363
<=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f4433,plain,
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation)
| x = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_108
| spl0_363 ),
inference(resolution,[],[f4426,f824]) ).
fof(f4426,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| spl0_363 ),
inference(avatar_component_clause,[],[f4425]) ).
fof(f35559,plain,
( spl0_359
| ~ spl0_1172
| ~ spl0_108
| spl0_361 ),
inference(avatar_split_clause,[],[f4419,f4413,f823,f35556,f4405]) ).
fof(f4405,plain,
( spl0_359
<=> complement(compose(element_relation,complement(identity_relation))) = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f35556,plain,
( spl0_1172
<=> subclass(complement(compose(element_relation,complement(identity_relation))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f4413,plain,
( spl0_361
<=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f4419,plain,
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),element_relation)
| complement(compose(element_relation,complement(identity_relation))) = x
| ~ spl0_108
| spl0_361 ),
inference(resolution,[],[f4415,f824]) ).
fof(f4415,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
| spl0_361 ),
inference(avatar_component_clause,[],[f4413]) ).
fof(f35554,plain,
( spl0_359
| ~ spl0_1171
| ~ spl0_108
| spl0_360 ),
inference(avatar_split_clause,[],[f4417,f4409,f823,f35551,f4405]) ).
fof(f35551,plain,
( spl0_1171
<=> subclass(complement(compose(element_relation,complement(identity_relation))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f4409,plain,
( spl0_360
<=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f4417,plain,
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),singleton_relation)
| complement(compose(element_relation,complement(identity_relation))) = x
| ~ spl0_108
| spl0_360 ),
inference(resolution,[],[f4410,f824]) ).
fof(f4410,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| spl0_360 ),
inference(avatar_component_clause,[],[f4409]) ).
fof(f35548,plain,
( spl0_1170
| ~ spl0_7
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f3992,f3947,f235,f35546]) ).
fof(f3947,plain,
( spl0_331
<=> ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f3992,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| x = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_7
| ~ spl0_331 ),
inference(resolution,[],[f3948,f236]) ).
fof(f3948,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f3947]) ).
fof(f35543,plain,
( spl0_1169
| ~ spl0_7
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f3987,f3942,f235,f35541]) ).
fof(f3942,plain,
( spl0_330
<=> ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f3987,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_7
| ~ spl0_330 ),
inference(resolution,[],[f3943,f236]) ).
fof(f3943,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f3942]) ).
fof(f35539,plain,
( spl0_222
| ~ spl0_1167
| spl0_237
| spl0_1168
| ~ spl0_223
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3768,f3715,f2217,f35536,f2334,f35532,f2213]) ).
fof(f2213,plain,
( spl0_222
<=> identity_relation = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f35532,plain,
( spl0_1167
<=> subclass(identity_relation,regular(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f35536,plain,
( spl0_1168
<=> member(regular(identity_relation),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f2217,plain,
( spl0_223
<=> member(regular(identity_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f3768,plain,
( member(regular(identity_relation),x)
| subset_relation = x
| ~ subclass(identity_relation,regular(subset_relation))
| identity_relation = x
| ~ spl0_223
| ~ spl0_323 ),
inference(resolution,[],[f3716,f2219]) ).
fof(f2219,plain,
( member(regular(identity_relation),subset_relation)
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f35529,plain,
( spl0_1166
| ~ spl0_246
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3138,f2992,f2410,f35527]) ).
fof(f3138,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| x = cross_product(X1,X2)
| ~ subclass(cross_product(X1,X2),complement(X0)) )
| ~ spl0_246
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f3119]) ).
fof(f3119,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| x = cross_product(X1,X2)
| x = cross_product(X1,X2)
| ~ subclass(cross_product(X1,X2),complement(X0)) )
| ~ spl0_246
| ~ spl0_285 ),
inference(resolution,[],[f2993,f2411]) ).
fof(f35524,plain,
( spl0_1165
| ~ spl0_246
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3091,f2976,f2410,f35522]) ).
fof(f3091,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X2,X0)
| ~ subclass(intersection(X2,X0),complement(X1)) )
| ~ spl0_246
| ~ spl0_281 ),
inference(duplicate_literal_removal,[],[f3066]) ).
fof(f3066,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X2,X0)
| x = intersection(X2,X0)
| ~ subclass(intersection(X2,X0),complement(X1)) )
| ~ spl0_246
| ~ spl0_281 ),
inference(resolution,[],[f2977,f2411]) ).
fof(f35520,plain,
( spl0_1164
| ~ spl0_188
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f13953,f10996,f1710,f35517]) ).
fof(f35517,plain,
( spl0_1164
<=> universal_class = complement(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f10996,plain,
( spl0_606
<=> universal_class = complement(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f13953,plain,
( universal_class = complement(singleton_relation)
| ~ spl0_188
| ~ spl0_606 ),
inference(superposition,[],[f10998,f1712]) ).
fof(f10998,plain,
( universal_class = complement(x)
| ~ spl0_606 ),
inference(avatar_component_clause,[],[f10996]) ).
fof(f35514,plain,
( spl0_1163
| ~ spl0_129
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3083,f2976,f997,f35512]) ).
fof(f3083,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| x = intersection(X1,X0)
| member(regular(intersection(X1,X0)),element_relation) )
| ~ spl0_129
| ~ spl0_281 ),
inference(resolution,[],[f2977,f998]) ).
fof(f35509,plain,
( spl0_1162
| ~ spl0_130
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3081,f2976,f1001,f35507]) ).
fof(f3081,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| x = intersection(X1,X0)
| member(regular(intersection(X1,X0)),subset_relation) )
| ~ spl0_130
| ~ spl0_281 ),
inference(resolution,[],[f2977,f1002]) ).
fof(f35504,plain,
( spl0_1161
| ~ spl0_246
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3038,f2964,f2410,f35502]) ).
fof(f3038,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,X2)
| ~ subclass(intersection(X0,X2),complement(X1)) )
| ~ spl0_246
| ~ spl0_279 ),
inference(duplicate_literal_removal,[],[f3013]) ).
fof(f3013,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,X2)
| x = intersection(X0,X2)
| ~ subclass(intersection(X0,X2),complement(X1)) )
| ~ spl0_246
| ~ spl0_279 ),
inference(resolution,[],[f2965,f2411]) ).
fof(f35499,plain,
( spl0_1160
| ~ spl0_129
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3030,f2964,f997,f35497]) ).
fof(f3030,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| intersection(X0,X1) = x
| member(regular(intersection(X0,X1)),element_relation) )
| ~ spl0_129
| ~ spl0_279 ),
inference(resolution,[],[f2965,f998]) ).
fof(f35494,plain,
( spl0_1159
| ~ spl0_130
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3028,f2964,f1001,f35492]) ).
fof(f3028,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| intersection(X0,X1) = x
| member(regular(intersection(X0,X1)),subset_relation) )
| ~ spl0_130
| ~ spl0_279 ),
inference(resolution,[],[f2965,f1002]) ).
fof(f35489,plain,
( spl0_1158
| ~ spl0_32
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2875,f2797,f345,f35487]) ).
fof(f345,plain,
( spl0_32
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f2875,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_32
| ~ spl0_271 ),
inference(resolution,[],[f2798,f347]) ).
fof(f347,plain,
( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f35484,plain,
( spl0_1157
| ~ spl0_31
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2873,f2797,f339,f35482]) ).
fof(f339,plain,
( spl0_31
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2873,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_31
| ~ spl0_271 ),
inference(resolution,[],[f2798,f341]) ).
fof(f341,plain,
( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f35479,plain,
( spl0_1156
| ~ spl0_29
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2869,f2797,f331,f35477]) ).
fof(f331,plain,
( spl0_29
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f2869,plain,
( ! [X2,X0,X1] :
( x = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_29
| ~ spl0_271 ),
inference(resolution,[],[f2798,f332]) ).
fof(f332,plain,
( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f35474,plain,
( spl0_1155
| ~ spl0_30
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2859,f2797,f335,f35472]) ).
fof(f335,plain,
( spl0_30
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f2859,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) )
| ~ spl0_30
| ~ spl0_271 ),
inference(resolution,[],[f2798,f336]) ).
fof(f336,plain,
( ! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f35469,plain,
( spl0_1154
| ~ spl0_49
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2757,f2714,f434,f35467]) ).
fof(f2714,plain,
( spl0_262
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = X0
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2757,plain,
( ! [X0] :
( ~ subclass(X0,identity_relation)
| x = X0
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_49
| ~ spl0_262 ),
inference(superposition,[],[f2715,f436]) ).
fof(f2715,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = X0
| member(regular(X0),X1) )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2714]) ).
fof(f35464,plain,
( spl0_1153
| ~ spl0_48
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2756,f2714,f429,f35462]) ).
fof(f35462,plain,
( spl0_1153
<=> ! [X0] :
( ~ subclass(X0,singleton_relation)
| x = X0
| member(regular(X0),complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f2756,plain,
( ! [X0] :
( ~ subclass(X0,singleton_relation)
| x = X0
| member(regular(X0),complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_48
| ~ spl0_262 ),
inference(superposition,[],[f2715,f431]) ).
fof(f35459,plain,
( spl0_1152
| ~ spl0_45
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2701,f2506,f417,f35457]) ).
fof(f2701,plain,
( ! [X0,X1] :
( x = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) )
| ~ spl0_45
| ~ spl0_254 ),
inference(resolution,[],[f2507,f418]) ).
fof(f35454,plain,
( spl0_1151
| ~ spl0_45
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2696,f2501,f417,f35452]) ).
fof(f2696,plain,
( ! [X0,X1] :
( x = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) )
| ~ spl0_45
| ~ spl0_253 ),
inference(resolution,[],[f2502,f418]) ).
fof(f35449,plain,
( spl0_1150
| ~ spl0_45
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2691,f2496,f417,f35447]) ).
fof(f35447,plain,
( spl0_1150
<=> ! [X0,X1] :
( x = intersection(X0,singleton_relation)
| ~ subclass(element_relation,X1)
| member(regular(intersection(X0,singleton_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f2691,plain,
( ! [X0,X1] :
( x = intersection(X0,singleton_relation)
| ~ subclass(element_relation,X1)
| member(regular(intersection(X0,singleton_relation)),X1) )
| ~ spl0_45
| ~ spl0_252 ),
inference(resolution,[],[f2497,f418]) ).
fof(f35444,plain,
( spl0_1149
| ~ spl0_45
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2686,f2491,f417,f35442]) ).
fof(f35442,plain,
( spl0_1149
<=> ! [X0,X1] :
( x = intersection(singleton_relation,X0)
| ~ subclass(element_relation,X1)
| member(regular(intersection(singleton_relation,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f2686,plain,
( ! [X0,X1] :
( x = intersection(singleton_relation,X0)
| ~ subclass(element_relation,X1)
| member(regular(intersection(singleton_relation,X0)),X1) )
| ~ spl0_45
| ~ spl0_251 ),
inference(resolution,[],[f2492,f418]) ).
fof(f35439,plain,
( spl0_1148
| ~ spl0_36
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2625,f2410,f366,f35437]) ).
fof(f366,plain,
( spl0_36
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2625,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) )
| ~ spl0_36
| ~ spl0_246 ),
inference(resolution,[],[f2411,f367]) ).
fof(f367,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(X1,universal_class) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f35434,plain,
( spl0_1147
| ~ spl0_35
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2624,f2410,f362,f35432]) ).
fof(f362,plain,
( spl0_35
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f2624,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) )
| ~ spl0_35
| ~ spl0_246 ),
inference(resolution,[],[f2411,f363]) ).
fof(f363,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f35144,plain,
( spl0_1146
| ~ spl0_188
| ~ spl0_1140 ),
inference(avatar_split_clause,[],[f35120,f35115,f1710,f35142]) ).
fof(f35142,plain,
( spl0_1146
<=> ! [X0] :
( singleton_relation = X0
| subclass(regular(X0),singleton_relation)
| ~ member(not_subclass_element(regular(X0),singleton_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f35115,plain,
( spl0_1140
<=> ! [X0] :
( ~ member(not_subclass_element(regular(X0),x),X0)
| subclass(regular(X0),x)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f35120,plain,
( ! [X0] :
( singleton_relation = X0
| subclass(regular(X0),singleton_relation)
| ~ member(not_subclass_element(regular(X0),singleton_relation),X0) )
| ~ spl0_188
| ~ spl0_1140 ),
inference(forward_demodulation,[],[f35119,f1712]) ).
fof(f35119,plain,
( ! [X0] :
( subclass(regular(X0),singleton_relation)
| ~ member(not_subclass_element(regular(X0),singleton_relation),X0)
| x = X0 )
| ~ spl0_188
| ~ spl0_1140 ),
inference(forward_demodulation,[],[f35118,f1712]) ).
fof(f35118,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),singleton_relation),X0)
| subclass(regular(X0),x)
| x = X0 )
| ~ spl0_188
| ~ spl0_1140 ),
inference(forward_demodulation,[],[f35116,f1712]) ).
fof(f35116,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),x),X0)
| subclass(regular(X0),x)
| x = X0 )
| ~ spl0_1140 ),
inference(avatar_component_clause,[],[f35115]) ).
fof(f35140,plain,
( spl0_1145
| ~ spl0_188
| ~ spl0_1139 ),
inference(avatar_split_clause,[],[f35027,f35024,f1710,f35138]) ).
fof(f35138,plain,
( spl0_1145
<=> ! [X0] :
( singleton_relation = intersection(X0,subset_relation)
| member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f35024,plain,
( spl0_1139
<=> ! [X0] :
( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
| x = intersection(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f35027,plain,
( ! [X0] :
( singleton_relation = intersection(X0,subset_relation)
| member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1139 ),
inference(forward_demodulation,[],[f35025,f1712]) ).
fof(f35025,plain,
( ! [X0] :
( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
| x = intersection(X0,subset_relation) )
| ~ spl0_1139 ),
inference(avatar_component_clause,[],[f35024]) ).
fof(f35136,plain,
( spl0_1144
| ~ spl0_188
| ~ spl0_1138 ),
inference(avatar_split_clause,[],[f35022,f35019,f1710,f35134]) ).
fof(f35134,plain,
( spl0_1144
<=> ! [X0] :
( singleton_relation = intersection(subset_relation,X0)
| member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f35019,plain,
( spl0_1138
<=> ! [X0] :
( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
| x = intersection(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f35022,plain,
( ! [X0] :
( singleton_relation = intersection(subset_relation,X0)
| member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1138 ),
inference(forward_demodulation,[],[f35020,f1712]) ).
fof(f35020,plain,
( ! [X0] :
( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
| x = intersection(subset_relation,X0) )
| ~ spl0_1138 ),
inference(avatar_component_clause,[],[f35019]) ).
fof(f35132,plain,
( spl0_1143
| ~ spl0_188
| ~ spl0_1137 ),
inference(avatar_split_clause,[],[f35017,f35014,f1710,f35130]) ).
fof(f35130,plain,
( spl0_1143
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f35014,plain,
( spl0_1137
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f35017,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1137 ),
inference(forward_demodulation,[],[f35015,f1712]) ).
fof(f35015,plain,
( ! [X0,X1] :
( ~ subclass(X0,compose_class(X1))
| x = X0
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_1137 ),
inference(avatar_component_clause,[],[f35014]) ).
fof(f35128,plain,
( spl0_1142
| ~ spl0_188
| ~ spl0_1136 ),
inference(avatar_split_clause,[],[f35012,f35009,f1710,f35126]) ).
fof(f35126,plain,
( spl0_1142
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f35009,plain,
( spl0_1136
<=> ! [X0] :
( x = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f35012,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) )
| ~ spl0_188
| ~ spl0_1136 ),
inference(forward_demodulation,[],[f35010,f1712]) ).
fof(f35010,plain,
( ! [X0] :
( ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| x = X0
| ~ member(regular(X0),subset_relation) )
| ~ spl0_1136 ),
inference(avatar_component_clause,[],[f35009]) ).
fof(f35124,plain,
( spl0_1141
| ~ spl0_188
| ~ spl0_1135 ),
inference(avatar_split_clause,[],[f35007,f35004,f1710,f35122]) ).
fof(f35122,plain,
( spl0_1141
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f35004,plain,
( spl0_1135
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| x = X0
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f35007,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) )
| ~ spl0_188
| ~ spl0_1135 ),
inference(forward_demodulation,[],[f35005,f1712]) ).
fof(f35005,plain,
( ! [X0,X1] :
( member(regular(X0),X1)
| x = X0
| ~ subclass(subset_relation,X1)
| ~ subclass(X0,identity_relation) )
| ~ spl0_1135 ),
inference(avatar_component_clause,[],[f35004]) ).
fof(f35117,plain,
( spl0_1140
| ~ spl0_33
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f3707,f3560,f354,f35115]) ).
fof(f3707,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),x),X0)
| subclass(regular(X0),x)
| x = X0 )
| ~ spl0_33
| ~ spl0_321 ),
inference(duplicate_literal_removal,[],[f3688]) ).
fof(f3688,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),x),X0)
| subclass(regular(X0),x)
| x = X0
| subclass(regular(X0),x) )
| ~ spl0_33
| ~ spl0_321 ),
inference(resolution,[],[f3561,f355]) ).
fof(f35026,plain,
( spl0_1139
| ~ spl0_78
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3325,f3187,f635,f35024]) ).
fof(f635,plain,
( spl0_78
<=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f3325,plain,
( ! [X0] :
( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
| x = intersection(X0,subset_relation) )
| ~ spl0_78
| ~ spl0_292 ),
inference(superposition,[],[f3188,f637]) ).
fof(f637,plain,
( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f35021,plain,
( spl0_1138
| ~ spl0_78
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3262,f3174,f635,f35019]) ).
fof(f3262,plain,
( ! [X0] :
( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
| x = intersection(subset_relation,X0) )
| ~ spl0_78
| ~ spl0_289 ),
inference(superposition,[],[f3175,f637]) ).
fof(f35016,plain,
( spl0_1137
| ~ spl0_25
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2872,f2797,f315,f35014]) ).
fof(f315,plain,
( spl0_25
<=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f2872,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_25
| ~ spl0_271 ),
inference(resolution,[],[f2798,f316]) ).
fof(f316,plain,
( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f35011,plain,
( spl0_1136
| ~ spl0_137
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2627,f2410,f1124,f35009]) ).
fof(f2627,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) )
| ~ spl0_137
| ~ spl0_246 ),
inference(resolution,[],[f2411,f1125]) ).
fof(f35006,plain,
( spl0_1135
| ~ spl0_45
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2399,f2386,f417,f35004]) ).
fof(f2399,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| x = X0
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) )
| ~ spl0_45
| ~ spl0_244 ),
inference(resolution,[],[f2387,f418]) ).
fof(f35001,plain,
( spl0_1134
| ~ spl0_45
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2391,f2382,f417,f34999]) ).
fof(f34999,plain,
( spl0_1134
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| x = X0
| ~ subclass(element_relation,X1)
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f2391,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| x = X0
| ~ subclass(element_relation,X1)
| member(regular(X0),X1) )
| ~ spl0_45
| ~ spl0_243 ),
inference(resolution,[],[f2383,f418]) ).
fof(f34991,plain,
( ~ spl0_1133
| ~ spl0_137
| spl0_391 ),
inference(avatar_split_clause,[],[f5370,f5366,f1124,f34988]) ).
fof(f34988,plain,
( spl0_1133
<=> member(omega,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f5366,plain,
( spl0_391
<=> member(omega,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f5370,plain,
( ~ member(omega,subset_relation)
| ~ spl0_137
| spl0_391 ),
inference(resolution,[],[f5367,f1125]) ).
fof(f5367,plain,
( ~ member(omega,cross_product(universal_class,universal_class))
| spl0_391 ),
inference(avatar_component_clause,[],[f5366]) ).
fof(f34986,plain,
( spl0_1132
| ~ spl0_49
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4165,f4123,f434,f34983]) ).
fof(f34983,plain,
( spl0_1132
<=> subclass(identity_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f4165,plain,
( subclass(identity_relation,subset_relation)
| ~ spl0_49
| ~ spl0_340 ),
inference(superposition,[],[f4124,f436]) ).
fof(f34981,plain,
( ~ spl0_1131
| ~ spl0_188
| spl0_794 ),
inference(avatar_split_clause,[],[f29483,f18709,f1710,f34978]) ).
fof(f34978,plain,
( spl0_1131
<=> subclass(universal_class,flip(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f18709,plain,
( spl0_794
<=> subclass(universal_class,flip(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f29483,plain,
( ~ subclass(universal_class,flip(singleton_relation))
| ~ spl0_188
| spl0_794 ),
inference(superposition,[],[f18711,f1712]) ).
fof(f18711,plain,
( ~ subclass(universal_class,flip(x))
| spl0_794 ),
inference(avatar_component_clause,[],[f18709]) ).
fof(f34423,plain,
( spl0_1130
| ~ spl0_188
| ~ spl0_1120 ),
inference(avatar_split_clause,[],[f34369,f34366,f1710,f34421]) ).
fof(f34369,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(first(regular(cross_product(X0,X1))),X0) )
| ~ spl0_188
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f34367,f1712]) ).
fof(f34419,plain,
( spl0_1129
| ~ spl0_188
| ~ spl0_1119 ),
inference(avatar_split_clause,[],[f34364,f34361,f1710,f34417]) ).
fof(f34364,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(second(regular(cross_product(X0,X1))),X1) )
| ~ spl0_188
| ~ spl0_1119 ),
inference(forward_demodulation,[],[f34362,f1712]) ).
fof(f34404,plain,
( ~ spl0_1128
| ~ spl0_188
| spl0_785 ),
inference(avatar_split_clause,[],[f29481,f17315,f1710,f34401]) ).
fof(f34401,plain,
( spl0_1128
<=> subclass(universal_class,rotate(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f17315,plain,
( spl0_785
<=> subclass(universal_class,rotate(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f29481,plain,
( ~ subclass(universal_class,rotate(singleton_relation))
| ~ spl0_188
| spl0_785 ),
inference(superposition,[],[f17317,f1712]) ).
fof(f17317,plain,
( ~ subclass(universal_class,rotate(x))
| spl0_785 ),
inference(avatar_component_clause,[],[f17315]) ).
fof(f34399,plain,
( spl0_1127
| ~ spl0_188
| ~ spl0_1107 ),
inference(avatar_split_clause,[],[f34306,f34303,f1710,f34397]) ).
fof(f34397,plain,
( spl0_1127
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f34303,plain,
( spl0_1107
<=> ! [X0] :
( x = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f34306,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1107 ),
inference(forward_demodulation,[],[f34304,f1712]) ).
fof(f34304,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,domain_relation)
| x = X0 )
| ~ spl0_1107 ),
inference(avatar_component_clause,[],[f34303]) ).
fof(f34395,plain,
( spl0_1126
| ~ spl0_188
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f34296,f34293,f1710,f34393]) ).
fof(f34393,plain,
( spl0_1126
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f34293,plain,
( spl0_1105
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f34296,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) )
| ~ spl0_188
| ~ spl0_1105 ),
inference(forward_demodulation,[],[f34294,f1712]) ).
fof(f34294,plain,
( ! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,omega)
| x = X0
| ~ inductive(X1) )
| ~ spl0_1105 ),
inference(avatar_component_clause,[],[f34293]) ).
fof(f34391,plain,
( spl0_1125
| ~ spl0_188
| ~ spl0_1104 ),
inference(avatar_split_clause,[],[f34291,f34288,f1710,f34389]) ).
fof(f34389,plain,
( spl0_1125
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f34288,plain,
( spl0_1104
<=> ! [X0] :
( x = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f34291,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1104 ),
inference(forward_demodulation,[],[f34289,f1712]) ).
fof(f34289,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,successor_relation)
| x = X0 )
| ~ spl0_1104 ),
inference(avatar_component_clause,[],[f34288]) ).
fof(f34387,plain,
( spl0_1124
| ~ spl0_188
| ~ spl0_1103 ),
inference(avatar_split_clause,[],[f34286,f34283,f1710,f34385]) ).
fof(f34385,plain,
( spl0_1124
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f34283,plain,
( spl0_1103
<=> ! [X0] :
( x = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f34286,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1103 ),
inference(forward_demodulation,[],[f34284,f1712]) ).
fof(f34284,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,element_relation)
| x = X0 )
| ~ spl0_1103 ),
inference(avatar_component_clause,[],[f34283]) ).
fof(f34383,plain,
( spl0_1123
| ~ spl0_188
| ~ spl0_1100 ),
inference(avatar_split_clause,[],[f34271,f34268,f1710,f34381]) ).
fof(f34381,plain,
( spl0_1123
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,subset_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f34268,plain,
( spl0_1100
<=> ! [X0] :
( ~ subclass(X0,subset_relation)
| x = X0
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f34271,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,subset_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_188
| ~ spl0_1100 ),
inference(forward_demodulation,[],[f34269,f1712]) ).
fof(f34269,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| x = X0
| ~ subclass(X0,subset_relation) )
| ~ spl0_1100 ),
inference(avatar_component_clause,[],[f34268]) ).
fof(f34378,plain,
( spl0_1122
| ~ spl0_296
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f7586,f7354,f3204,f34376]) ).
fof(f34376,plain,
( spl0_1122
<=> ! [X0,X1] :
( subclass(intersection(x,X0),intersection(X1,intersection(x,X0)))
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f7586,plain,
( ! [X0,X1] :
( subclass(intersection(x,X0),intersection(X1,intersection(x,X0)))
| x = X1 )
| ~ spl0_296
| ~ spl0_495 ),
inference(duplicate_literal_removal,[],[f7537]) ).
fof(f7537,plain,
( ! [X0,X1] :
( subclass(intersection(x,X0),intersection(X1,intersection(x,X0)))
| subclass(intersection(x,X0),intersection(X1,intersection(x,X0)))
| x = X1 )
| ~ spl0_296
| ~ spl0_495 ),
inference(resolution,[],[f7355,f3205]) ).
fof(f34373,plain,
( spl0_1121
| ~ spl0_297
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f7585,f7354,f3208,f34371]) ).
fof(f34371,plain,
( spl0_1121
<=> ! [X0,X1] :
( subclass(intersection(X0,x),intersection(X1,intersection(X0,x)))
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f7585,plain,
( ! [X0,X1] :
( subclass(intersection(X0,x),intersection(X1,intersection(X0,x)))
| x = X1 )
| ~ spl0_297
| ~ spl0_495 ),
inference(duplicate_literal_removal,[],[f7538]) ).
fof(f7538,plain,
( ! [X0,X1] :
( subclass(intersection(X0,x),intersection(X1,intersection(X0,x)))
| subclass(intersection(X0,x),intersection(X1,intersection(X0,x)))
| x = X1 )
| ~ spl0_297
| ~ spl0_495 ),
inference(resolution,[],[f7355,f3209]) ).
fof(f34368,plain,
( spl0_1120
| ~ spl0_3
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f4085,f4017,f217,f34366]) ).
fof(f4017,plain,
( spl0_337
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f4085,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = x )
| ~ spl0_3
| ~ spl0_337 ),
inference(duplicate_literal_removal,[],[f4080]) ).
fof(f4080,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = x
| cross_product(X0,X1) = x )
| ~ spl0_3
| ~ spl0_337 ),
inference(resolution,[],[f4018,f218]) ).
fof(f4018,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) = x )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f4017]) ).
fof(f34363,plain,
( spl0_1119
| ~ spl0_3
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f4078,f4013,f217,f34361]) ).
fof(f4013,plain,
( spl0_336
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f4078,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = x )
| ~ spl0_3
| ~ spl0_336 ),
inference(duplicate_literal_removal,[],[f4073]) ).
fof(f4073,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = x
| cross_product(X0,X1) = x )
| ~ spl0_3
| ~ spl0_336 ),
inference(resolution,[],[f4014,f218]) ).
fof(f4014,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) = x )
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f4013]) ).
fof(f34359,plain,
( spl0_1118
| ~ spl0_39
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3963,f3896,f378,f34356]) ).
fof(f34356,plain,
( spl0_1118
<=> 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_1118])]) ).
fof(f3896,plain,
( spl0_328
<=> 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_328])]) ).
fof(f3963,plain,
( member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_39
| ~ spl0_328 ),
inference(resolution,[],[f3898,f379]) ).
fof(f3898,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_328 ),
inference(avatar_component_clause,[],[f3896]) ).
fof(f34354,plain,
( ~ spl0_1117
| ~ spl0_188
| spl0_1114 ),
inference(avatar_split_clause,[],[f34349,f34338,f1710,f34351]) ).
fof(f34351,plain,
( spl0_1117
<=> universal_class = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f34338,plain,
( spl0_1114
<=> universal_class = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f34349,plain,
( universal_class != singleton_relation
| ~ spl0_188
| spl0_1114 ),
inference(forward_demodulation,[],[f34339,f1712]) ).
fof(f34339,plain,
( universal_class != x
| spl0_1114 ),
inference(avatar_component_clause,[],[f34338]) ).
fof(f34348,plain,
( spl0_1114
| ~ spl0_1115
| spl0_1116
| ~ spl0_15
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3661,f3529,f271,f34346,f34342,f34338]) ).
fof(f34342,plain,
( spl0_1115
<=> subclass(universal_class,regular(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f3661,plain,
( ! [X0,X1] :
( member(unordered_pair(X0,X1),x)
| ~ subclass(universal_class,regular(universal_class))
| universal_class = x )
| ~ spl0_15
| ~ spl0_315 ),
inference(resolution,[],[f3530,f272]) ).
fof(f34335,plain,
( spl0_1113
| ~ spl0_108
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2951,f2809,f823,f34333]) ).
fof(f34333,plain,
( spl0_1113
<=> ! [X0,X1] :
( x = intersection(X0,complement(X1))
| ~ subclass(intersection(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f2951,plain,
( ! [X0,X1] :
( x = intersection(X0,complement(X1))
| ~ subclass(intersection(X0,complement(X1)),X1) )
| ~ spl0_108
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2932]) ).
fof(f2932,plain,
( ! [X0,X1] :
( x = intersection(X0,complement(X1))
| ~ subclass(intersection(X0,complement(X1)),X1)
| x = intersection(X0,complement(X1)) )
| ~ spl0_108
| ~ spl0_274 ),
inference(resolution,[],[f2810,f824]) ).
fof(f34330,plain,
( spl0_1112
| ~ spl0_243
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2949,f2809,f2382,f34328]) ).
fof(f2949,plain,
( ! [X0] :
( x = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
| ~ spl0_243
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2935]) ).
fof(f2935,plain,
( ! [X0] :
( x = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation)
| x = intersection(X0,complement(element_relation)) )
| ~ spl0_243
| ~ spl0_274 ),
inference(resolution,[],[f2810,f2383]) ).
fof(f34325,plain,
( spl0_1111
| ~ spl0_244
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2947,f2809,f2386,f34323]) ).
fof(f34323,plain,
( spl0_1111
<=> ! [X0] :
( x = intersection(X0,complement(subset_relation))
| ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f2947,plain,
( ! [X0] :
( x = intersection(X0,complement(subset_relation))
| ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) )
| ~ spl0_244
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2944]) ).
fof(f2944,plain,
( ! [X0] :
( x = intersection(X0,complement(subset_relation))
| ~ subclass(intersection(X0,complement(subset_relation)),identity_relation)
| x = intersection(X0,complement(subset_relation)) )
| ~ spl0_244
| ~ spl0_274 ),
inference(resolution,[],[f2810,f2387]) ).
fof(f34320,plain,
( spl0_1110
| ~ spl0_108
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2926,f2805,f823,f34318]) ).
fof(f34318,plain,
( spl0_1110
<=> ! [X0,X1] :
( x = intersection(complement(X0),X1)
| ~ subclass(intersection(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f2926,plain,
( ! [X0,X1] :
( x = intersection(complement(X0),X1)
| ~ subclass(intersection(complement(X0),X1),X0) )
| ~ spl0_108
| ~ spl0_273 ),
inference(duplicate_literal_removal,[],[f2905]) ).
fof(f2905,plain,
( ! [X0,X1] :
( x = intersection(complement(X0),X1)
| ~ subclass(intersection(complement(X0),X1),X0)
| x = intersection(complement(X0),X1) )
| ~ spl0_108
| ~ spl0_273 ),
inference(resolution,[],[f2806,f824]) ).
fof(f34315,plain,
( spl0_1109
| ~ spl0_243
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2924,f2805,f2382,f34313]) ).
fof(f2924,plain,
( ! [X0] :
( x = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
| ~ spl0_243
| ~ spl0_273 ),
inference(duplicate_literal_removal,[],[f2908]) ).
fof(f2908,plain,
( ! [X0] :
( x = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation)
| x = intersection(complement(element_relation),X0) )
| ~ spl0_243
| ~ spl0_273 ),
inference(resolution,[],[f2806,f2383]) ).
fof(f34310,plain,
( spl0_1108
| ~ spl0_244
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2922,f2805,f2386,f34308]) ).
fof(f34308,plain,
( spl0_1108
<=> ! [X0] :
( x = intersection(complement(subset_relation),X0)
| ~ subclass(intersection(complement(subset_relation),X0),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f2922,plain,
( ! [X0] :
( x = intersection(complement(subset_relation),X0)
| ~ subclass(intersection(complement(subset_relation),X0),identity_relation) )
| ~ spl0_244
| ~ spl0_273 ),
inference(duplicate_literal_removal,[],[f2917]) ).
fof(f2917,plain,
( ! [X0] :
( x = intersection(complement(subset_relation),X0)
| ~ subclass(intersection(complement(subset_relation),X0),identity_relation)
| x = intersection(complement(subset_relation),X0) )
| ~ spl0_244
| ~ spl0_273 ),
inference(resolution,[],[f2806,f2387]) ).
fof(f34305,plain,
( spl0_1107
| ~ spl0_19
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2874,f2797,f289,f34303]) ).
fof(f289,plain,
( spl0_19
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f2874,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_19
| ~ spl0_271 ),
inference(resolution,[],[f2798,f291]) ).
fof(f291,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f34301,plain,
( spl0_1106
| ~ spl0_188
| ~ spl0_564 ),
inference(avatar_split_clause,[],[f13946,f9135,f1710,f34298]) ).
fof(f13946,plain,
( singleton_relation = domain_of(singleton_relation)
| ~ spl0_188
| ~ spl0_564 ),
inference(superposition,[],[f9137,f1712]) ).
fof(f34295,plain,
( spl0_1105
| ~ spl0_18
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2868,f2797,f285,f34293]) ).
fof(f2868,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) )
| ~ spl0_18
| ~ spl0_271 ),
inference(resolution,[],[f2798,f286]) ).
fof(f34290,plain,
( spl0_1104
| ~ spl0_17
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2867,f2797,f280,f34288]) ).
fof(f280,plain,
( spl0_17
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f2867,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_17
| ~ spl0_271 ),
inference(resolution,[],[f2798,f282]) ).
fof(f282,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f34285,plain,
( spl0_1103
| ~ spl0_16
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2862,f2797,f275,f34283]) ).
fof(f275,plain,
( spl0_16
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f2862,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_16
| ~ spl0_271 ),
inference(resolution,[],[f2798,f277]) ).
fof(f277,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f34281,plain,
( spl0_275
| ~ spl0_1102
| ~ spl0_108
| spl0_276 ),
inference(avatar_split_clause,[],[f2835,f2817,f823,f34278,f2813]) ).
fof(f2813,plain,
( spl0_275
<=> x = complement(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f34278,plain,
( spl0_1102
<=> subclass(complement(cross_product(universal_class,universal_class)),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f2817,plain,
( spl0_276
<=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2835,plain,
( ~ subclass(complement(cross_product(universal_class,universal_class)),subset_relation)
| x = complement(cross_product(universal_class,universal_class))
| ~ spl0_108
| spl0_276 ),
inference(resolution,[],[f2819,f824]) ).
fof(f2819,plain,
( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
| spl0_276 ),
inference(avatar_component_clause,[],[f2817]) ).
fof(f34276,plain,
( spl0_275
| ~ spl0_1101
| ~ spl0_244
| spl0_276 ),
inference(avatar_split_clause,[],[f2834,f2817,f2386,f34273,f2813]) ).
fof(f34273,plain,
( spl0_1101
<=> subclass(complement(cross_product(universal_class,universal_class)),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f2834,plain,
( ~ subclass(complement(cross_product(universal_class,universal_class)),identity_relation)
| x = complement(cross_product(universal_class,universal_class))
| ~ spl0_244
| spl0_276 ),
inference(resolution,[],[f2819,f2387]) ).
fof(f34270,plain,
( spl0_1100
| ~ spl0_78
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2755,f2714,f635,f34268]) ).
fof(f2755,plain,
( ! [X0] :
( ~ subclass(X0,subset_relation)
| x = X0
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_78
| ~ spl0_262 ),
inference(superposition,[],[f2715,f637]) ).
fof(f33962,plain,
( spl0_1099
| ~ spl0_188
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f33914,f33910,f1710,f33960]) ).
fof(f33960,plain,
( spl0_1099
<=> ! [X0] :
( singleton_relation = X0
| member(regular(X0),singleton_relation)
| ~ subclass(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f33910,plain,
( spl0_1090
<=> ! [X0] :
( member(regular(X0),x)
| x = X0
| ~ subclass(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f33914,plain,
( ! [X0] :
( singleton_relation = X0
| member(regular(X0),singleton_relation)
| ~ subclass(X0,regular(X0)) )
| ~ spl0_188
| ~ spl0_1090 ),
inference(forward_demodulation,[],[f33913,f1712]) ).
fof(f33913,plain,
( ! [X0] :
( member(regular(X0),singleton_relation)
| x = X0
| ~ subclass(X0,regular(X0)) )
| ~ spl0_188
| ~ spl0_1090 ),
inference(forward_demodulation,[],[f33911,f1712]) ).
fof(f33911,plain,
( ! [X0] :
( ~ subclass(X0,regular(X0))
| x = X0
| member(regular(X0),x) )
| ~ spl0_1090 ),
inference(avatar_component_clause,[],[f33910]) ).
fof(f33958,plain,
( spl0_1098
| ~ spl0_188
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f33908,f33905,f1710,f33956]) ).
fof(f33956,plain,
( spl0_1098
<=> ! [X0] :
( unordered_pair(X0,X0) = singleton_relation
| regular(unordered_pair(X0,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f33905,plain,
( spl0_1089
<=> ! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f33908,plain,
( ! [X0] :
( unordered_pair(X0,X0) = singleton_relation
| regular(unordered_pair(X0,X0)) = X0 )
| ~ spl0_188
| ~ spl0_1089 ),
inference(forward_demodulation,[],[f33906,f1712]) ).
fof(f33906,plain,
( ! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = x )
| ~ spl0_1089 ),
inference(avatar_component_clause,[],[f33905]) ).
fof(f33954,plain,
( spl0_1097
| ~ spl0_188
| ~ spl0_1086 ),
inference(avatar_split_clause,[],[f33855,f33852,f1710,f33952]) ).
fof(f33952,plain,
( spl0_1097
<=> ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f33852,plain,
( spl0_1086
<=> ! [X0] :
( x = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f33855,plain,
( ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
| ~ spl0_188
| ~ spl0_1086 ),
inference(forward_demodulation,[],[f33853,f1712]) ).
fof(f33853,plain,
( ! [X0] :
( ~ subclass(intersection(X0,identity_relation),complement(subset_relation))
| x = intersection(X0,identity_relation) )
| ~ spl0_1086 ),
inference(avatar_component_clause,[],[f33852]) ).
fof(f33950,plain,
( spl0_1096
| ~ spl0_188
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f33850,f33847,f1710,f33948]) ).
fof(f33948,plain,
( spl0_1096
<=> ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f33847,plain,
( spl0_1085
<=> ! [X0] :
( x = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f33850,plain,
( ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
| ~ spl0_188
| ~ spl0_1085 ),
inference(forward_demodulation,[],[f33848,f1712]) ).
fof(f33848,plain,
( ! [X0] :
( ~ subclass(intersection(identity_relation,X0),complement(subset_relation))
| x = intersection(identity_relation,X0) )
| ~ spl0_1085 ),
inference(avatar_component_clause,[],[f33847]) ).
fof(f33941,plain,
( spl0_1095
| ~ spl0_188
| ~ spl0_1080 ),
inference(avatar_split_clause,[],[f33826,f33823,f1710,f33939]) ).
fof(f33939,plain,
( spl0_1095
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f33823,plain,
( spl0_1080
<=> ! [X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(intersection(X0,X1),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f33826,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X0)) )
| ~ spl0_188
| ~ spl0_1080 ),
inference(forward_demodulation,[],[f33824,f1712]) ).
fof(f33824,plain,
( ! [X0,X1] :
( ~ subclass(intersection(X0,X1),complement(X0))
| intersection(X0,X1) = x )
| ~ spl0_1080 ),
inference(avatar_component_clause,[],[f33823]) ).
fof(f33937,plain,
( spl0_1094
| ~ spl0_188
| ~ spl0_576 ),
inference(avatar_split_clause,[],[f13950,f9685,f1710,f33935]) ).
fof(f13950,plain,
( ! [X0] : ~ member(X0,singleton_relation)
| ~ spl0_188
| ~ spl0_576 ),
inference(superposition,[],[f9686,f1712]) ).
fof(f33933,plain,
( spl0_1093
| ~ spl0_188
| ~ spl0_1079 ),
inference(avatar_split_clause,[],[f33821,f33818,f1710,f33931]) ).
fof(f33931,plain,
( spl0_1093
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f33818,plain,
( spl0_1079
<=> ! [X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(intersection(X0,X1),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f33821,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X1)) )
| ~ spl0_188
| ~ spl0_1079 ),
inference(forward_demodulation,[],[f33819,f1712]) ).
fof(f33819,plain,
( ! [X0,X1] :
( ~ subclass(intersection(X0,X1),complement(X1))
| intersection(X0,X1) = x )
| ~ spl0_1079 ),
inference(avatar_component_clause,[],[f33818]) ).
fof(f33923,plain,
( spl0_1092
| ~ spl0_443
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f6519,f6463,f6159,f33921]) ).
fof(f6159,plain,
( spl0_443
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f6519,plain,
( ! [X0] :
( ~ member(not_subclass_element(cross_product(x,x),identity_relation),X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_443
| ~ spl0_454 ),
inference(superposition,[],[f6160,f6465]) ).
fof(f6160,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f6159]) ).
fof(f33918,plain,
( spl0_1091
| ~ spl0_3
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6237,f6167,f217,f33916]) ).
fof(f33916,plain,
( spl0_1091
<=> ! [X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),universal_class)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f6167,plain,
( spl0_445
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f6237,plain,
( ! [X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),universal_class)
| x = X0 )
| ~ spl0_3
| ~ spl0_445 ),
inference(resolution,[],[f6168,f218]) ).
fof(f6168,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f6167]) ).
fof(f33912,plain,
( spl0_1090
| ~ spl0_3
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3798,f3715,f217,f33910]) ).
fof(f3798,plain,
( ! [X0] :
( member(regular(X0),x)
| x = X0
| ~ subclass(X0,regular(X0)) )
| ~ spl0_3
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3734]) ).
fof(f3734,plain,
( ! [X0] :
( member(regular(X0),x)
| x = X0
| ~ subclass(X0,regular(X0))
| x = X0
| x = X0 )
| ~ spl0_3
| ~ spl0_323 ),
inference(resolution,[],[f3716,f218]) ).
fof(f33907,plain,
( spl0_1089
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3117,f2984,f33905]) ).
fof(f2984,plain,
( spl0_283
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3117,plain,
( ! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = x )
| ~ spl0_283 ),
inference(equality_resolution,[],[f2985]) ).
fof(f2985,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2984]) ).
fof(f33883,plain,
( spl0_1088
| spl0_868
| ~ spl0_18
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2751,f2714,f285,f21589,f33881]) ).
fof(f33881,plain,
( spl0_1088
<=> ! [X0,X1] :
( member(regular(omega),X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f2751,plain,
( ! [X0,X1] :
( omega = x
| member(regular(omega),X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl0_18
| ~ spl0_262 ),
inference(resolution,[],[f2715,f286]) ).
fof(f33859,plain,
( spl0_1087
| spl0_868
| ~ spl0_18
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2740,f2710,f285,f21589,f33857]) ).
fof(f33857,plain,
( spl0_1087
<=> ! [X0,X1] :
( member(regular(omega),X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f2710,plain,
( spl0_261
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = X0
| member(regular(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2740,plain,
( ! [X0,X1] :
( omega = x
| member(regular(omega),X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl0_18
| ~ spl0_261 ),
inference(resolution,[],[f2711,f286]) ).
fof(f2711,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = X0
| member(regular(X0),X2) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f2710]) ).
fof(f33854,plain,
( spl0_1086
| ~ spl0_246
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2703,f2506,f2410,f33852]) ).
fof(f2703,plain,
( ! [X0] :
( x = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
| ~ spl0_246
| ~ spl0_254 ),
inference(duplicate_literal_removal,[],[f2699]) ).
fof(f2699,plain,
( ! [X0] :
( x = intersection(X0,identity_relation)
| x = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
| ~ spl0_246
| ~ spl0_254 ),
inference(resolution,[],[f2507,f2411]) ).
fof(f33849,plain,
( spl0_1085
| ~ spl0_246
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2698,f2501,f2410,f33847]) ).
fof(f2698,plain,
( ! [X0] :
( x = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
| ~ spl0_246
| ~ spl0_253 ),
inference(duplicate_literal_removal,[],[f2694]) ).
fof(f2694,plain,
( ! [X0] :
( x = intersection(identity_relation,X0)
| x = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
| ~ spl0_246
| ~ spl0_253 ),
inference(resolution,[],[f2502,f2411]) ).
fof(f33844,plain,
( spl0_1084
| ~ spl0_246
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2693,f2496,f2410,f33842]) ).
fof(f33842,plain,
( spl0_1084
<=> ! [X0] :
( x = intersection(X0,singleton_relation)
| ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f2693,plain,
( ! [X0] :
( x = intersection(X0,singleton_relation)
| ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
| ~ spl0_246
| ~ spl0_252 ),
inference(duplicate_literal_removal,[],[f2689]) ).
fof(f2689,plain,
( ! [X0] :
( x = intersection(X0,singleton_relation)
| x = intersection(X0,singleton_relation)
| ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
| ~ spl0_246
| ~ spl0_252 ),
inference(resolution,[],[f2497,f2411]) ).
fof(f33839,plain,
( spl0_1083
| ~ spl0_246
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2688,f2491,f2410,f33837]) ).
fof(f33837,plain,
( spl0_1083
<=> ! [X0] :
( x = intersection(singleton_relation,X0)
| ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f2688,plain,
( ! [X0] :
( x = intersection(singleton_relation,X0)
| ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
| ~ spl0_246
| ~ spl0_251 ),
inference(duplicate_literal_removal,[],[f2684]) ).
fof(f2684,plain,
( ! [X0] :
( x = intersection(singleton_relation,X0)
| x = intersection(singleton_relation,X0)
| ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
| ~ spl0_246
| ~ spl0_251 ),
inference(resolution,[],[f2492,f2411]) ).
fof(f33835,plain,
( spl0_1082
| ~ spl0_45
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2683,f2436,f417,f33833]) ).
fof(f33833,plain,
( spl0_1082
<=> ! [X0] :
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| member(regular(identity_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f2436,plain,
( spl0_248
<=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2683,plain,
( ! [X0] :
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| member(regular(identity_relation),X0) )
| ~ spl0_45
| ~ spl0_248 ),
inference(resolution,[],[f2438,f418]) ).
fof(f2438,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2436]) ).
fof(f33831,plain,
( ~ spl0_1081
| spl0_222
| ~ spl0_246
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2680,f2436,f2410,f2213,f33828]) ).
fof(f33828,plain,
( spl0_1081
<=> subclass(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f2680,plain,
( identity_relation = x
| ~ subclass(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ spl0_246
| ~ spl0_248 ),
inference(resolution,[],[f2438,f2411]) ).
fof(f33825,plain,
( spl0_1080
| ~ spl0_110
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2648,f2410,f845,f33823]) ).
fof(f845,plain,
( spl0_110
<=> ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2648,plain,
( ! [X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(intersection(X0,X1),complement(X0)) )
| ~ spl0_110
| ~ spl0_246 ),
inference(duplicate_literal_removal,[],[f2621]) ).
fof(f2621,plain,
( ! [X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(intersection(X0,X1),complement(X0))
| intersection(X0,X1) = x )
| ~ spl0_110
| ~ spl0_246 ),
inference(resolution,[],[f2411,f846]) ).
fof(f846,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = x )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f33820,plain,
( spl0_1079
| ~ spl0_111
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2646,f2410,f849,f33818]) ).
fof(f2646,plain,
( ! [X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(intersection(X0,X1),complement(X1)) )
| ~ spl0_111
| ~ spl0_246 ),
inference(duplicate_literal_removal,[],[f2623]) ).
fof(f2623,plain,
( ! [X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(intersection(X0,X1),complement(X1))
| intersection(X0,X1) = x )
| ~ spl0_111
| ~ spl0_246 ),
inference(resolution,[],[f2411,f850]) ).
fof(f33816,plain,
( spl0_1078
| ~ spl0_45
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2471,f2414,f417,f33814]) ).
fof(f33814,plain,
( spl0_1078
<=> ! [X0] :
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),X0)
| member(regular(singleton_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f2471,plain,
( ! [X0] :
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),X0)
| member(regular(singleton_relation),X0) )
| ~ spl0_45
| ~ spl0_247 ),
inference(resolution,[],[f2416,f418]) ).
fof(f33812,plain,
( ~ spl0_1077
| ~ spl0_188
| spl0_754 ),
inference(avatar_split_clause,[],[f29479,f16267,f1710,f33809]) ).
fof(f33809,plain,
( spl0_1077
<=> subclass(element_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f16267,plain,
( spl0_754
<=> subclass(element_relation,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f29479,plain,
( ~ subclass(element_relation,singleton_relation)
| ~ spl0_188
| spl0_754 ),
inference(superposition,[],[f16269,f1712]) ).
fof(f16269,plain,
( ~ subclass(element_relation,x)
| spl0_754 ),
inference(avatar_component_clause,[],[f16267]) ).
fof(f33807,plain,
( ~ spl0_1076
| spl0_275
| ~ spl0_30
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2296,f2286,f335,f2813,f33804]) ).
fof(f33804,plain,
( spl0_1076
<=> function(complement(cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f2286,plain,
( spl0_229
<=> ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2296,plain,
( x = complement(cross_product(universal_class,universal_class))
| ~ function(complement(cross_product(universal_class,universal_class)))
| ~ spl0_30
| ~ spl0_229 ),
inference(resolution,[],[f2287,f336]) ).
fof(f2287,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = x )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2286]) ).
fof(f33650,plain,
( spl0_1075
| ~ spl0_188
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f33621,f33618,f1710,f33648]) ).
fof(f33648,plain,
( spl0_1075
<=> ! [X0] :
( member(not_subclass_element(cross_product(singleton_relation,singleton_relation),identity_relation),X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f33621,plain,
( ! [X0] :
( member(not_subclass_element(cross_product(singleton_relation,singleton_relation),identity_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_188
| ~ spl0_1068 ),
inference(forward_demodulation,[],[f33619,f1712]) ).
fof(f33646,plain,
( spl0_1074
| ~ spl0_188
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f33602,f33599,f1710,f33644]) ).
fof(f33599,plain,
( spl0_1066
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f33602,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,complement(X0))
| ~ subclass(complement(X0),X0) )
| ~ spl0_188
| ~ spl0_1066 ),
inference(forward_demodulation,[],[f33600,f1712]) ).
fof(f33600,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(X1,complement(X0)) )
| ~ spl0_1066 ),
inference(avatar_component_clause,[],[f33599]) ).
fof(f33642,plain,
( spl0_1073
| ~ spl0_188
| ~ spl0_1065 ),
inference(avatar_split_clause,[],[f33548,f33545,f1710,f33640]) ).
fof(f33545,plain,
( spl0_1065
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f33548,plain,
( ! [X0,X1] :
( singleton_relation = intersection(complement(X0),X1)
| ~ subclass(complement(X0),X0) )
| ~ spl0_188
| ~ spl0_1065 ),
inference(forward_demodulation,[],[f33546,f1712]) ).
fof(f33546,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(complement(X0),X1) )
| ~ spl0_1065 ),
inference(avatar_component_clause,[],[f33545]) ).
fof(f33638,plain,
( spl0_1072
| ~ spl0_188
| ~ spl0_1064 ),
inference(avatar_split_clause,[],[f33543,f33540,f1710,f33636]) ).
fof(f33636,plain,
( spl0_1072
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f33540,plain,
( spl0_1064
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f33543,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) )
| ~ spl0_188
| ~ spl0_1064 ),
inference(forward_demodulation,[],[f33541,f1712]) ).
fof(f33541,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = X0
| member(regular(X0),universal_class) )
| ~ spl0_1064 ),
inference(avatar_component_clause,[],[f33540]) ).
fof(f33634,plain,
( spl0_1071
| ~ spl0_188
| ~ spl0_1063 ),
inference(avatar_split_clause,[],[f33538,f33535,f1710,f33632]) ).
fof(f33632,plain,
( spl0_1071
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f33535,plain,
( spl0_1063
<=> ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f33538,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) )
| ~ spl0_188
| ~ spl0_1063 ),
inference(forward_demodulation,[],[f33536,f1712]) ).
fof(f33536,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| x = X0
| ~ subclass(X0,X1) )
| ~ spl0_1063 ),
inference(avatar_component_clause,[],[f33535]) ).
fof(f33630,plain,
( spl0_1070
| ~ spl0_188
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f33528,f33525,f1710,f33628]) ).
fof(f33628,plain,
( spl0_1070
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f33525,plain,
( spl0_1061
<=> ! [X0] :
( x = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f33528,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) )
| ~ spl0_188
| ~ spl0_1061 ),
inference(forward_demodulation,[],[f33526,f1712]) ).
fof(f33526,plain,
( ! [X0] :
( ~ subclass(X0,complement(subset_relation))
| x = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f33525]) ).
fof(f33626,plain,
( ~ spl0_1069
| ~ spl0_188
| spl0_571 ),
inference(avatar_split_clause,[],[f13948,f9571,f1710,f33623]) ).
fof(f33623,plain,
( spl0_1069
<=> singleton_relation = cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f9571,plain,
( spl0_571
<=> x = cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f13948,plain,
( singleton_relation != cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class)
| ~ spl0_188
| spl0_571 ),
inference(superposition,[],[f9572,f1712]) ).
fof(f9572,plain,
( x != cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class)
| spl0_571 ),
inference(avatar_component_clause,[],[f9571]) ).
fof(f33620,plain,
( spl0_1068
| ~ spl0_135
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f6499,f6463,f1116,f33618]) ).
fof(f6499,plain,
( ! [X0] :
( member(not_subclass_element(cross_product(x,x),identity_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_135
| ~ spl0_454 ),
inference(superposition,[],[f1117,f6465]) ).
fof(f33607,plain,
( ~ spl0_238
| spl0_1067
| ~ spl0_198
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3962,f3896,f1814,f33604,f2338]) ).
fof(f2338,plain,
( spl0_238
<=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f33604,plain,
( spl0_1067
<=> member(regular(subset_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f1814,plain,
( spl0_198
<=> ! [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_198])]) ).
fof(f3962,plain,
( member(regular(subset_relation),subset_relation)
| ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_198
| ~ spl0_328 ),
inference(resolution,[],[f3898,f1815]) ).
fof(f1815,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_198 ),
inference(avatar_component_clause,[],[f1814]) ).
fof(f33601,plain,
( spl0_1066
| ~ spl0_274
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3092,f2976,f2809,f33599]) ).
fof(f3092,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(X1,complement(X0)) )
| ~ spl0_274
| ~ spl0_281 ),
inference(duplicate_literal_removal,[],[f3065]) ).
fof(f3065,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(X1,complement(X0))
| x = intersection(X1,complement(X0)) )
| ~ spl0_274
| ~ spl0_281 ),
inference(resolution,[],[f2977,f2810]) ).
fof(f33596,plain,
( spl0_701
| ~ spl0_1050 ),
inference(avatar_contradiction_clause,[],[f33549]) ).
fof(f33549,plain,
( $false
| spl0_701
| ~ spl0_1050 ),
inference(resolution,[],[f33071,f14868]) ).
fof(f14868,plain,
( ~ subclass(singleton_relation,complement(element_relation))
| spl0_701 ),
inference(avatar_component_clause,[],[f14866]) ).
fof(f14866,plain,
( spl0_701
<=> subclass(singleton_relation,complement(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f33071,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_1050 ),
inference(avatar_component_clause,[],[f33070]) ).
fof(f33595,plain,
( spl0_928
| ~ spl0_1050 ),
inference(avatar_contradiction_clause,[],[f33550]) ).
fof(f33550,plain,
( $false
| spl0_928
| ~ spl0_1050 ),
inference(resolution,[],[f33071,f24033]) ).
fof(f24033,plain,
( ~ subclass(singleton_relation,identity_relation)
| spl0_928 ),
inference(avatar_component_clause,[],[f24031]) ).
fof(f33594,plain,
( spl0_929
| ~ spl0_1050 ),
inference(avatar_contradiction_clause,[],[f33551]) ).
fof(f33551,plain,
( $false
| spl0_929
| ~ spl0_1050 ),
inference(resolution,[],[f33071,f24436]) ).
fof(f24436,plain,
( ~ subclass(singleton_relation,subset_relation)
| spl0_929 ),
inference(avatar_component_clause,[],[f24434]) ).
fof(f24434,plain,
( spl0_929
<=> subclass(singleton_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f33547,plain,
( spl0_1065
| ~ spl0_273
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3040,f2964,f2805,f33545]) ).
fof(f3040,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(complement(X0),X1) )
| ~ spl0_273
| ~ spl0_279 ),
inference(duplicate_literal_removal,[],[f3011]) ).
fof(f3011,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| x = intersection(complement(X0),X1)
| x = intersection(complement(X0),X1) )
| ~ spl0_273
| ~ spl0_279 ),
inference(resolution,[],[f2965,f2806]) ).
fof(f33542,plain,
( spl0_1064
| ~ spl0_7
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2857,f2797,f235,f33540]) ).
fof(f2857,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) )
| ~ spl0_7
| ~ spl0_271 ),
inference(resolution,[],[f2798,f236]) ).
fof(f33537,plain,
( spl0_1063
| ~ spl0_108
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2647,f2410,f823,f33535]) ).
fof(f2647,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) )
| ~ spl0_108
| ~ spl0_246 ),
inference(duplicate_literal_removal,[],[f2622]) ).
fof(f2622,plain,
( ! [X0,X1] :
( x = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1)
| x = X0 )
| ~ spl0_108
| ~ spl0_246 ),
inference(resolution,[],[f2411,f824]) ).
fof(f33532,plain,
( spl0_1062
| ~ spl0_243
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2645,f2410,f2382,f33530]) ).
fof(f2645,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_243
| ~ spl0_246 ),
inference(duplicate_literal_removal,[],[f2629]) ).
fof(f2629,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation)
| x = X0 )
| ~ spl0_243
| ~ spl0_246 ),
inference(resolution,[],[f2411,f2383]) ).
fof(f33527,plain,
( spl0_1061
| ~ spl0_244
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2644,f2410,f2386,f33525]) ).
fof(f2644,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) )
| ~ spl0_244
| ~ spl0_246 ),
inference(duplicate_literal_removal,[],[f2639]) ).
fof(f2639,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation)
| x = X0 )
| ~ spl0_244
| ~ spl0_246 ),
inference(resolution,[],[f2411,f2387]) ).
fof(f33522,plain,
( spl0_1060
| ~ spl0_45
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2380,f2369,f417,f33520]) ).
fof(f33520,plain,
( spl0_1060
<=> ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f2380,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),X0)
| member(x,X0) )
| ~ spl0_45
| ~ spl0_241 ),
inference(resolution,[],[f2371,f418]) ).
fof(f33436,plain,
( spl0_1059
| ~ spl0_188
| ~ spl0_1056 ),
inference(avatar_split_clause,[],[f33417,f33414,f1710,f33434]) ).
fof(f33414,plain,
( spl0_1056
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(complement(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f33417,plain,
( ! [X0,X1] :
( singleton_relation = intersection(complement(X1),X0)
| ~ subclass(X0,X1) )
| ~ spl0_188
| ~ spl0_1056 ),
inference(forward_demodulation,[],[f33415,f1712]) ).
fof(f33415,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(complement(X1),X0) )
| ~ spl0_1056 ),
inference(avatar_component_clause,[],[f33414]) ).
fof(f33432,plain,
( spl0_1058
| ~ spl0_188
| ~ spl0_1055 ),
inference(avatar_split_clause,[],[f33412,f33409,f1710,f33430]) ).
fof(f33409,plain,
( spl0_1055
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f33412,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,complement(X1))
| ~ subclass(X0,X1) )
| ~ spl0_188
| ~ spl0_1055 ),
inference(forward_demodulation,[],[f33410,f1712]) ).
fof(f33410,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,complement(X1)) )
| ~ spl0_1055 ),
inference(avatar_component_clause,[],[f33409]) ).
fof(f33428,plain,
( ~ spl0_1057
| ~ spl0_188
| spl0_868 ),
inference(avatar_split_clause,[],[f29488,f21589,f1710,f33425]) ).
fof(f33425,plain,
( spl0_1057
<=> omega = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f29488,plain,
( omega != singleton_relation
| ~ spl0_188
| spl0_868 ),
inference(superposition,[],[f21590,f1712]) ).
fof(f21590,plain,
( omega != x
| spl0_868 ),
inference(avatar_component_clause,[],[f21589]) ).
fof(f33416,plain,
( spl0_1056
| ~ spl0_273
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3093,f2976,f2805,f33414]) ).
fof(f3093,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(complement(X1),X0) )
| ~ spl0_273
| ~ spl0_281 ),
inference(duplicate_literal_removal,[],[f3064]) ).
fof(f3064,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(complement(X1),X0)
| x = intersection(complement(X1),X0) )
| ~ spl0_273
| ~ spl0_281 ),
inference(resolution,[],[f2977,f2806]) ).
fof(f33411,plain,
( spl0_1055
| ~ spl0_274
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f3039,f2964,f2809,f33409]) ).
fof(f3039,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,complement(X1)) )
| ~ spl0_274
| ~ spl0_279 ),
inference(duplicate_literal_removal,[],[f3012]) ).
fof(f3012,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| x = intersection(X0,complement(X1))
| x = intersection(X0,complement(X1)) )
| ~ spl0_274
| ~ spl0_279 ),
inference(resolution,[],[f2965,f2810]) ).
fof(f33405,plain,
( spl0_1054
| ~ spl0_157
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f2855,f2793,f1376,f33403]) ).
fof(f33403,plain,
( spl0_1054
<=> ! [X0,X1] :
( x = X0
| subclass(intersection(x,X1),regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f2793,plain,
( spl0_270
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),x)
| x = X1
| subclass(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2855,plain,
( ! [X0,X1] :
( x = X0
| subclass(intersection(x,X1),regular(X0)) )
| ~ spl0_157
| ~ spl0_270 ),
inference(duplicate_literal_removal,[],[f2844]) ).
fof(f2844,plain,
( ! [X0,X1] :
( x = X0
| subclass(intersection(x,X1),regular(X0))
| subclass(intersection(x,X1),regular(X0)) )
| ~ spl0_157
| ~ spl0_270 ),
inference(resolution,[],[f2794,f1377]) ).
fof(f2794,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),x)
| x = X1
| subclass(X0,regular(X1)) )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f2793]) ).
fof(f33399,plain,
( spl0_1053
| ~ spl0_158
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f2854,f2793,f1380,f33397]) ).
fof(f33397,plain,
( spl0_1053
<=> ! [X0,X1] :
( x = X0
| subclass(intersection(X1,x),regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f2854,plain,
( ! [X0,X1] :
( x = X0
| subclass(intersection(X1,x),regular(X0)) )
| ~ spl0_158
| ~ spl0_270 ),
inference(duplicate_literal_removal,[],[f2845]) ).
fof(f2845,plain,
( ! [X0,X1] :
( x = X0
| subclass(intersection(X1,x),regular(X0))
| subclass(intersection(X1,x),regular(X0)) )
| ~ spl0_158
| ~ spl0_270 ),
inference(resolution,[],[f2794,f1381]) ).
fof(f33395,plain,
( ~ spl0_1052
| spl0_237
| ~ spl0_238
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2626,f2410,f2338,f2334,f33392]) ).
fof(f33392,plain,
( spl0_1052
<=> subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f2626,plain,
( subset_relation = x
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class)))
| ~ spl0_238
| ~ spl0_246 ),
inference(resolution,[],[f2411,f2340]) ).
fof(f2340,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2338]) ).
fof(f33390,plain,
( spl0_1051
| ~ spl0_45
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2364,f2338,f417,f33388]) ).
fof(f33388,plain,
( spl0_1051
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(regular(subset_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f2364,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(regular(subset_relation),X0) )
| ~ spl0_45
| ~ spl0_238 ),
inference(resolution,[],[f2340,f418]) ).
fof(f33072,plain,
( spl0_1050
| ~ spl0_188
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f13935,f5839,f1710,f33070]) ).
fof(f5839,plain,
( spl0_429
<=> ! [X0] : subclass(x,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f13935,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_188
| ~ spl0_429 ),
inference(superposition,[],[f5840,f1712]) ).
fof(f5840,plain,
( ! [X0] : subclass(x,X0)
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f5839]) ).
fof(f32760,plain,
( spl0_1049
| ~ spl0_188
| ~ spl0_1035 ),
inference(avatar_split_clause,[],[f32641,f32638,f1710,f32758]) ).
fof(f32641,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_188
| ~ spl0_1035 ),
inference(forward_demodulation,[],[f32639,f1712]) ).
fof(f32756,plain,
( spl0_1048
| ~ spl0_188
| ~ spl0_1034 ),
inference(avatar_split_clause,[],[f32636,f32633,f1710,f32754]) ).
fof(f32636,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_188
| ~ spl0_1034 ),
inference(forward_demodulation,[],[f32634,f1712]) ).
fof(f32752,plain,
( spl0_1047
| ~ spl0_188
| ~ spl0_1033 ),
inference(avatar_split_clause,[],[f32631,f32628,f1710,f32750]) ).
fof(f32631,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_188
| ~ spl0_1033 ),
inference(forward_demodulation,[],[f32629,f1712]) ).
fof(f32748,plain,
( spl0_1046
| ~ spl0_188
| ~ spl0_1032 ),
inference(avatar_split_clause,[],[f32626,f32623,f1710,f32746]) ).
fof(f32626,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_188
| ~ spl0_1032 ),
inference(forward_demodulation,[],[f32624,f1712]) ).
fof(f32744,plain,
( ~ spl0_9
| spl0_1028 ),
inference(avatar_contradiction_clause,[],[f32743]) ).
fof(f32743,plain,
( $false
| ~ spl0_9
| spl0_1028 ),
inference(resolution,[],[f32599,f245]) ).
fof(f32599,plain,
( ~ subclass(element_relation,element_relation)
| spl0_1028 ),
inference(avatar_component_clause,[],[f32597]) ).
fof(f32597,plain,
( spl0_1028
<=> subclass(element_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f32742,plain,
( ~ spl0_1045
| ~ spl0_188
| spl0_661 ),
inference(avatar_split_clause,[],[f29472,f13255,f1710,f32739]) ).
fof(f32739,plain,
( spl0_1045
<=> singleton_relation = domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f13255,plain,
( spl0_661
<=> x = domain_of(domain_of(flip(cross_product(x,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f29472,plain,
( singleton_relation != domain_of(domain_of(flip(cross_product(singleton_relation,universal_class))))
| ~ spl0_188
| spl0_661 ),
inference(superposition,[],[f13256,f1712]) ).
fof(f13256,plain,
( x != domain_of(domain_of(flip(cross_product(x,universal_class))))
| spl0_661 ),
inference(avatar_component_clause,[],[f13255]) ).
fof(f32717,plain,
( spl0_1043
| spl0_1044
| ~ spl0_328
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f12075,f6167,f3896,f32715,f32711]) ).
fof(f32711,plain,
( spl0_1043
<=> member(regular(subset_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f32715,plain,
( spl0_1044
<=> ! [X0] : ~ member(regular(subset_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f12075,plain,
( ! [X0] :
( ~ member(regular(subset_relation),X0)
| member(regular(subset_relation),universal_class) )
| ~ spl0_328
| ~ spl0_445 ),
inference(resolution,[],[f3898,f6168]) ).
fof(f32688,plain,
( spl0_1041
| spl0_1042
| ~ spl0_248
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6304,f6167,f2436,f32686,f32682]) ).
fof(f32682,plain,
( spl0_1041
<=> member(regular(identity_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f32686,plain,
( spl0_1042
<=> ! [X0] : ~ member(regular(identity_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f6304,plain,
( ! [X0] :
( ~ member(regular(identity_relation),X0)
| member(regular(identity_relation),universal_class) )
| ~ spl0_248
| ~ spl0_445 ),
inference(resolution,[],[f6168,f2438]) ).
fof(f32665,plain,
( spl0_1039
| spl0_1040
| ~ spl0_247
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6300,f6167,f2414,f32663,f32659]) ).
fof(f32659,plain,
( spl0_1039
<=> member(regular(singleton_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f32663,plain,
( spl0_1040
<=> ! [X0] : ~ member(regular(singleton_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f6300,plain,
( ! [X0] :
( ~ member(regular(singleton_relation),X0)
| member(regular(singleton_relation),universal_class) )
| ~ spl0_247
| ~ spl0_445 ),
inference(resolution,[],[f6168,f2416]) ).
fof(f32657,plain,
( ~ spl0_1038
| ~ spl0_188
| spl0_293 ),
inference(avatar_split_clause,[],[f4949,f3191,f1710,f32654]) ).
fof(f32654,plain,
( spl0_1038
<=> inductive(domain_of(regular(cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f3191,plain,
( spl0_293
<=> inductive(domain_of(regular(cross_product(unordered_pair(x,x),universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f4949,plain,
( ~ inductive(domain_of(regular(cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class))))
| ~ spl0_188
| spl0_293 ),
inference(superposition,[],[f3193,f1712]) ).
fof(f3193,plain,
( ~ inductive(domain_of(regular(cross_product(unordered_pair(x,x),universal_class))))
| spl0_293 ),
inference(avatar_component_clause,[],[f3191]) ).
fof(f32651,plain,
( spl0_1037
| ~ spl0_34
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3397,f3208,f358,f32649]) ).
fof(f32649,plain,
( spl0_1037
<=> ! [X0,X1] :
( subclass(intersection(X0,x),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f358,plain,
( spl0_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f3397,plain,
( ! [X0,X1] :
( subclass(intersection(X0,x),X1)
| x = X1 )
| ~ spl0_34
| ~ spl0_297 ),
inference(duplicate_literal_removal,[],[f3369]) ).
fof(f3369,plain,
( ! [X0,X1] :
( subclass(intersection(X0,x),X1)
| x = X1
| subclass(intersection(X0,x),X1) )
| ~ spl0_34
| ~ spl0_297 ),
inference(resolution,[],[f3209,f359]) ).
fof(f359,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f32646,plain,
( spl0_1036
| ~ spl0_34
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3368,f3204,f358,f32644]) ).
fof(f32644,plain,
( spl0_1036
<=> ! [X0,X1] :
( subclass(intersection(x,X0),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f3368,plain,
( ! [X0,X1] :
( subclass(intersection(x,X0),X1)
| x = X1 )
| ~ spl0_34
| ~ spl0_296 ),
inference(duplicate_literal_removal,[],[f3340]) ).
fof(f3340,plain,
( ! [X0,X1] :
( subclass(intersection(x,X0),X1)
| x = X1
| subclass(intersection(x,X0),X1) )
| ~ spl0_34
| ~ spl0_296 ),
inference(resolution,[],[f3205,f359]) ).
fof(f32640,plain,
( spl0_1035
| ~ spl0_273
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3331,f3187,f2805,f32638]) ).
fof(f3331,plain,
( ! [X0,X1] : x = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_273
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f3303]) ).
fof(f3303,plain,
( ! [X0,X1] :
( x = intersection(complement(X0),intersection(X0,X1))
| x = intersection(complement(X0),intersection(X0,X1)) )
| ~ spl0_273
| ~ spl0_292 ),
inference(resolution,[],[f3188,f2806]) ).
fof(f32635,plain,
( spl0_1034
| ~ spl0_273
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3302,f3183,f2805,f32633]) ).
fof(f3302,plain,
( ! [X0,X1] : x = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_273
| ~ spl0_291 ),
inference(duplicate_literal_removal,[],[f3274]) ).
fof(f3274,plain,
( ! [X0,X1] :
( x = intersection(complement(X0),intersection(X1,X0))
| x = intersection(complement(X0),intersection(X1,X0)) )
| ~ spl0_273
| ~ spl0_291 ),
inference(resolution,[],[f3184,f2806]) ).
fof(f32630,plain,
( spl0_1033
| ~ spl0_274
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3268,f3174,f2809,f32628]) ).
fof(f3268,plain,
( ! [X0,X1] : x = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_274
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3240]) ).
fof(f3240,plain,
( ! [X0,X1] :
( x = intersection(intersection(X0,X1),complement(X0))
| x = intersection(intersection(X0,X1),complement(X0)) )
| ~ spl0_274
| ~ spl0_289 ),
inference(resolution,[],[f3175,f2810]) ).
fof(f32625,plain,
( spl0_1032
| ~ spl0_274
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f3239,f3170,f2809,f32623]) ).
fof(f3239,plain,
( ! [X0,X1] : x = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_274
| ~ spl0_288 ),
inference(duplicate_literal_removal,[],[f3211]) ).
fof(f3211,plain,
( ! [X0,X1] :
( x = intersection(intersection(X0,X1),complement(X1))
| x = intersection(intersection(X0,X1),complement(X1)) )
| ~ spl0_274
| ~ spl0_288 ),
inference(resolution,[],[f3171,f2810]) ).
fof(f32614,plain,
( spl0_1031
| ~ spl0_223
| ~ spl0_164
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2681,f2436,f1456,f2217,f32611]) ).
fof(f32611,plain,
( spl0_1031
<=> member(regular(identity_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1456,plain,
( spl0_164
<=> ! [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_164])]) ).
fof(f2681,plain,
( ~ member(regular(identity_relation),subset_relation)
| member(regular(identity_relation),identity_relation)
| ~ spl0_164
| ~ spl0_248 ),
inference(resolution,[],[f2438,f1457]) ).
fof(f1457,plain,
( ! [X0] :
( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,subset_relation)
| member(X0,identity_relation) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1456]) ).
fof(f32609,plain,
( spl0_1030
| ~ spl0_44
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2489,f2303,f398,f32607]) ).
fof(f32607,plain,
( spl0_1030
<=> ! [X0] :
( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f398,plain,
( spl0_44
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f2303,plain,
( spl0_232
<=> ! [X0] :
( ~ inductive(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2489,plain,
( ! [X0] :
( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) )
| ~ spl0_44
| ~ spl0_232 ),
inference(resolution,[],[f2304,f399]) ).
fof(f399,plain,
( ! [X8] :
( function(domain_of(flip(cross_product(X8,universal_class))))
| ~ one_to_one(X8) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f2304,plain,
( ! [X0] :
( ~ function(X0)
| ~ inductive(X0) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2303]) ).
fof(f32605,plain,
( ~ spl0_1029
| spl0_122
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1789,f1710,f966,f32602]) ).
fof(f32602,plain,
( spl0_1029
<=> member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f966,plain,
( spl0_122
<=> member(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1789,plain,
( ~ member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class)
| spl0_122
| ~ spl0_188 ),
inference(superposition,[],[f967,f1712]) ).
fof(f967,plain,
( ~ member(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class)
| spl0_122 ),
inference(avatar_component_clause,[],[f966]) ).
fof(f32600,plain,
( ~ spl0_1028
| spl0_189
| ~ spl0_682 ),
inference(avatar_split_clause,[],[f29496,f13911,f1714,f32597]) ).
fof(f13911,plain,
( spl0_682
<=> ! [X0] :
( ~ subclass(element_relation,X0)
| member(regular(singleton_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f29496,plain,
( ~ subclass(element_relation,element_relation)
| spl0_189
| ~ spl0_682 ),
inference(resolution,[],[f1715,f13912]) ).
fof(f13912,plain,
( ! [X0] :
( member(regular(singleton_relation),X0)
| ~ subclass(element_relation,X0) )
| ~ spl0_682 ),
inference(avatar_component_clause,[],[f13911]) ).
fof(f1715,plain,
( ~ member(regular(singleton_relation),element_relation)
| spl0_189 ),
inference(avatar_component_clause,[],[f1714]) ).
fof(f32590,plain,
( ~ spl0_1027
| ~ spl0_188
| spl0_568 ),
inference(avatar_split_clause,[],[f13947,f9519,f1710,f32587]) ).
fof(f32587,plain,
( spl0_1027
<=> inductive(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f9519,plain,
( spl0_568
<=> inductive(domain_of(domain_of(flip(cross_product(x,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f13947,plain,
( ~ inductive(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))))
| ~ spl0_188
| spl0_568 ),
inference(superposition,[],[f9521,f1712]) ).
fof(f9521,plain,
( ~ inductive(domain_of(domain_of(flip(cross_product(x,universal_class)))))
| spl0_568 ),
inference(avatar_component_clause,[],[f9519]) ).
fof(f32585,plain,
( ~ spl0_1026
| ~ spl0_188
| spl0_294 ),
inference(avatar_split_clause,[],[f4950,f3195,f1710,f32582]) ).
fof(f32582,plain,
( spl0_1026
<=> singleton_relation = cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f3195,plain,
( spl0_294
<=> x = cross_product(unordered_pair(x,x),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f4950,plain,
( singleton_relation != cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)
| ~ spl0_188
| spl0_294 ),
inference(superposition,[],[f3196,f1712]) ).
fof(f3196,plain,
( x != cross_product(unordered_pair(x,x),universal_class)
| spl0_294 ),
inference(avatar_component_clause,[],[f3195]) ).
fof(f32580,plain,
( spl0_1025
| ~ spl0_188
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2431,f2369,f1710,f32577]) ).
fof(f32577,plain,
( spl0_1025
<=> member(singleton_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f2431,plain,
( member(singleton_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_188
| ~ spl0_241 ),
inference(superposition,[],[f2371,f1712]) ).
fof(f32575,plain,
( ~ spl0_1024
| ~ spl0_188
| spl0_235 ),
inference(avatar_split_clause,[],[f2429,f2323,f1710,f32572]) ).
fof(f32572,plain,
( spl0_1024
<=> member(singleton_relation,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f2323,plain,
( spl0_235
<=> member(x,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2429,plain,
( ~ member(singleton_relation,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_188
| spl0_235 ),
inference(superposition,[],[f2324,f1712]) ).
fof(f2324,plain,
( ~ member(x,cross_product(universal_class,cross_product(universal_class,universal_class)))
| spl0_235 ),
inference(avatar_component_clause,[],[f2323]) ).
fof(f32570,plain,
( ~ spl0_1023
| ~ spl0_188
| spl0_862 ),
inference(avatar_split_clause,[],[f29487,f21363,f1710,f32567]) ).
fof(f21363,plain,
( spl0_862
<=> operation(domain_of(flip(cross_product(x,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f29487,plain,
( ~ operation(domain_of(flip(cross_product(singleton_relation,universal_class))))
| ~ spl0_188
| spl0_862 ),
inference(superposition,[],[f21365,f1712]) ).
fof(f21365,plain,
( ~ operation(domain_of(flip(cross_product(x,universal_class))))
| spl0_862 ),
inference(avatar_component_clause,[],[f21363]) ).
fof(f32504,plain,
( ~ spl0_1022
| ~ spl0_188
| spl0_828 ),
inference(avatar_split_clause,[],[f29485,f19988,f1710,f32501]) ).
fof(f32501,plain,
( spl0_1022
<=> member(singleton_relation,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f19988,plain,
( spl0_828
<=> member(x,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f29485,plain,
( ~ member(singleton_relation,composition_function)
| ~ spl0_188
| spl0_828 ),
inference(superposition,[],[f19990,f1712]) ).
fof(f19990,plain,
( ~ member(x,composition_function)
| spl0_828 ),
inference(avatar_component_clause,[],[f19988]) ).
fof(f32498,plain,
( ~ spl0_1021
| spl0_123
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1790,f1710,f971,f32495]) ).
fof(f32495,plain,
( spl0_1021
<=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f971,plain,
( spl0_123
<=> member(x,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1790,plain,
( ~ member(singleton_relation,cross_product(universal_class,universal_class))
| spl0_123
| ~ spl0_188 ),
inference(superposition,[],[f973,f1712]) ).
fof(f973,plain,
( ~ member(x,cross_product(universal_class,universal_class))
| spl0_123 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f32493,plain,
( spl0_1020
| ~ spl0_2
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1783,f1710,f213,f32491]) ).
fof(f213,plain,
( spl0_2
<=> ! [X0] :
( ~ inductive(X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f1783,plain,
( ! [X0] :
( member(singleton_relation,X0)
| ~ inductive(X0) )
| ~ spl0_2
| ~ spl0_188 ),
inference(superposition,[],[f214,f1712]) ).
fof(f214,plain,
( ! [X0] :
( member(x,X0)
| ~ inductive(X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f32489,plain,
( ~ spl0_1019
| spl0_1
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1782,f1710,f208,f32486]) ).
fof(f1782,plain,
( ~ subclass(cross_product(singleton_relation,singleton_relation),identity_relation)
| spl0_1
| ~ spl0_188 ),
inference(superposition,[],[f210,f1712]) ).
fof(f32422,plain,
( spl0_1018
| ~ spl0_90
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1984,f1954,f703,f32420]) ).
fof(f32420,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(f703,plain,
( spl0_90
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1954,plain,
( spl0_211
<=> ! [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_211])]) ).
fof(f1984,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_90
| ~ spl0_211 ),
inference(resolution,[],[f1955,f704]) ).
fof(f704,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| ~ operation(X10) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f1955,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_211 ),
inference(avatar_component_clause,[],[f1954]) ).
fof(f32418,plain,
( spl0_1017
| ~ spl0_90
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1958,f1950,f703,f32416]) ).
fof(f32416,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(f1950,plain,
( spl0_210
<=> ! [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_210])]) ).
fof(f1958,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_90
| ~ spl0_210 ),
inference(resolution,[],[f1951,f704]) ).
fof(f1951,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_210 ),
inference(avatar_component_clause,[],[f1950]) ).
fof(f32374,plain,
( spl0_1016
| ~ spl0_137
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2222,f2209,f1124,f32372]) ).
fof(f32372,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(f2209,plain,
( spl0_221
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2222,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_137
| ~ spl0_221 ),
inference(resolution,[],[f2210,f1125]) ).
fof(f2210,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2209]) ).
fof(f32331,plain,
( spl0_1015
| ~ spl0_102
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2022,f2010,f771,f32329]) ).
fof(f32329,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(f771,plain,
( spl0_102
<=> ! [X10,X11,X0,X9,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f2010,plain,
( spl0_212
<=> ! [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_212])]) ).
fof(f2022,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ homomorphism(X3,X0,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) )
| ~ spl0_102
| ~ spl0_212 ),
inference(resolution,[],[f2011,f772]) ).
fof(f772,plain,
( ! [X10,X0,X11,X1,X9] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
| ~ homomorphism(X9,X10,X11)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f771]) ).
fof(f2011,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_212 ),
inference(avatar_component_clause,[],[f2010]) ).
fof(f32288,plain,
( spl0_1014
| ~ spl0_207
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2146,f2122,f1894,f32286]) ).
fof(f32286,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(f1894,plain,
( spl0_207
<=> ! [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_207])]) ).
fof(f2122,plain,
( spl0_216
<=> ! [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_216])]) ).
fof(f2146,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_207
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1895]) ).
fof(f1895,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_207 ),
inference(avatar_component_clause,[],[f1894]) ).
fof(f2123,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_216 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f32242,plain,
( spl0_1013
| ~ spl0_79
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2221,f2209,f640,f32240]) ).
fof(f32240,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(f640,plain,
( spl0_79
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f2221,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_79
| ~ spl0_221 ),
inference(resolution,[],[f2210,f641]) ).
fof(f641,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f32200,plain,
( spl0_1012
| ~ spl0_212
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2132,f2122,f2010,f32198]) ).
fof(f32198,plain,
( spl0_1012
<=> ! [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_1012])]) ).
fof(f2132,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_212
| ~ spl0_216 ),
inference(resolution,[],[f2123,f2011]) ).
fof(f32158,plain,
( spl0_1011
| ~ spl0_92
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2151,f2122,f712,f32156]) ).
fof(f32156,plain,
( spl0_1011
<=> ! [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_1011])]) ).
fof(f712,plain,
( spl0_92
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f2151,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl0_92
| ~ spl0_216 ),
inference(resolution,[],[f2123,f713]) ).
fof(f713,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f32136,plain,
( spl0_1010
| ~ spl0_102
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1908,f1900,f771,f32134]) ).
fof(f32134,plain,
( spl0_1010
<=> ! [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_1010])]) ).
fof(f1900,plain,
( spl0_208
<=> ! [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_208])]) ).
fof(f1908,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(X3))
| ~ operation(X2)
| ~ homomorphism(X4,X3,X5)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) )
| ~ spl0_102
| ~ spl0_208 ),
inference(resolution,[],[f1901,f772]) ).
fof(f1901,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_208 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f32132,plain,
( spl0_1009
| ~ spl0_102
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1686,f1644,f771,f32130]) ).
fof(f32130,plain,
( spl0_1009
<=> ! [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_1009])]) ).
fof(f1644,plain,
( spl0_186
<=> ! [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_186])]) ).
fof(f1686,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,domain_of(X0))
| ~ member(X1,universal_class)
| ~ homomorphism(X2,X0,X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
| ~ spl0_102
| ~ spl0_186 ),
inference(resolution,[],[f1645,f772]) ).
fof(f1645,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_186 ),
inference(avatar_component_clause,[],[f1644]) ).
fof(f32092,plain,
( spl0_1008
| ~ spl0_56
| ~ spl0_102
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1315,f1294,f771,f493,f32090]) ).
fof(f32090,plain,
( spl0_1008
<=> ! [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_1008])]) ).
fof(f1315,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_56
| ~ spl0_102
| ~ spl0_150 ),
inference(forward_demodulation,[],[f1312,f494]) ).
fof(f1312,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
| ~ spl0_102
| ~ spl0_150 ),
inference(resolution,[],[f1295,f772]) ).
fof(f32088,plain,
( spl0_1007
| ~ spl0_102
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1131,f1116,f771,f32086]) ).
fof(f32086,plain,
( spl0_1007
<=> ! [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_1007])]) ).
fof(f1131,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,domain_of(X0))
| ~ homomorphism(X1,X0,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) )
| ~ spl0_102
| ~ spl0_135 ),
inference(resolution,[],[f1117,f772]) ).
fof(f31919,plain,
( spl0_1006
| ~ spl0_95
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2027,f2010,f739,f31917]) ).
fof(f31917,plain,
( spl0_1006
<=> ! [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_1006])]) ).
fof(f739,plain,
( spl0_95
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f2027,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) )
| ~ spl0_95
| ~ spl0_212 ),
inference(resolution,[],[f2011,f740]) ).
fof(f740,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f31915,plain,
( spl0_1004
| ~ spl0_1005
| ~ spl0_100
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2029,f2010,f760,f31912,f31909]) ).
fof(f31909,plain,
( spl0_1004
<=> ! [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_1004])]) ).
fof(f31912,plain,
( spl0_1005
<=> subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f760,plain,
( spl0_100
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f2029,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),X3) )
| ~ spl0_100
| ~ spl0_212 ),
inference(resolution,[],[f2011,f761]) ).
fof(f761,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f31868,plain,
( spl0_1003
| ~ spl0_199
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2150,f2122,f1847,f31866]) ).
fof(f31866,plain,
( spl0_1003
<=> ! [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_1003])]) ).
fof(f1847,plain,
( spl0_199
<=> ! [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_199])]) ).
fof(f2150,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_199
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1848]) ).
fof(f1848,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_199 ),
inference(avatar_component_clause,[],[f1847]) ).
fof(f31843,plain,
( spl0_1002
| ~ spl0_211
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2041,f2010,f1954,f31841]) ).
fof(f31841,plain,
( spl0_1002
<=> ! [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_1002])]) ).
fof(f2041,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_211
| ~ spl0_212 ),
inference(resolution,[],[f2011,f1955]) ).
fof(f31839,plain,
( ~ spl0_1001
| ~ spl0_188
| spl0_796 ),
inference(avatar_split_clause,[],[f29484,f19041,f1710,f31836]) ).
fof(f31836,plain,
( spl0_1001
<=> member(singleton_relation,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f19041,plain,
( spl0_796
<=> member(x,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f29484,plain,
( ~ member(singleton_relation,domain_relation)
| ~ spl0_188
| spl0_796 ),
inference(superposition,[],[f19043,f1712]) ).
fof(f19043,plain,
( ~ member(x,domain_relation)
| spl0_796 ),
inference(avatar_component_clause,[],[f19041]) ).
fof(f31834,plain,
( spl0_1000
| ~ spl0_210
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2040,f2010,f1950,f31832]) ).
fof(f31832,plain,
( spl0_1000
<=> ! [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_1000])]) ).
fof(f2040,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_210
| ~ spl0_212 ),
inference(resolution,[],[f2011,f1951]) ).
fof(f31830,plain,
( spl0_999
| ~ spl0_93
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2039,f2010,f718,f31828]) ).
fof(f31828,plain,
( spl0_999
<=> ! [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_999])]) ).
fof(f718,plain,
( spl0_93
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2039,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_212 ),
inference(resolution,[],[f2011,f719]) ).
fof(f719,plain,
( ! [X1,X7,X4,X5] :
( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f31756,plain,
( spl0_998
| ~ spl0_212
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2155,f2128,f2010,f31754]) ).
fof(f31754,plain,
( spl0_998
<=> ! [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_998])]) ).
fof(f2128,plain,
( spl0_217
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_217])]) ).
fof(f2155,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_212
| ~ spl0_217 ),
inference(resolution,[],[f2129,f2011]) ).
fof(f2129,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_217 ),
inference(avatar_component_clause,[],[f2128]) ).
fof(f31714,plain,
( spl0_997
| ~ spl0_186
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2131,f2122,f1644,f31712]) ).
fof(f31712,plain,
( spl0_997
<=> ! [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_997])]) ).
fof(f2131,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_186
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1645]) ).
fof(f31640,plain,
( spl0_996
| ~ spl0_92
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2174,f2128,f712,f31638]) ).
fof(f31638,plain,
( spl0_996
<=> ! [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_996])]) ).
fof(f2174,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_92
| ~ spl0_217 ),
inference(resolution,[],[f2129,f713]) ).
fof(f31598,plain,
( spl0_995
| ~ spl0_71
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2152,f2122,f598,f31596]) ).
fof(f31596,plain,
( spl0_995
<=> ! [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_995])]) ).
fof(f598,plain,
( spl0_71
<=> ! [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_71])]) ).
fof(f2152,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_71
| ~ spl0_216 ),
inference(resolution,[],[f2123,f599]) ).
fof(f599,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_71 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f31594,plain,
( ~ spl0_994
| ~ spl0_188
| spl0_787 ),
inference(avatar_split_clause,[],[f29482,f17650,f1710,f31591]) ).
fof(f31591,plain,
( spl0_994
<=> member(singleton_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f17650,plain,
( spl0_787
<=> member(x,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f29482,plain,
( ~ member(singleton_relation,successor_relation)
| ~ spl0_188
| spl0_787 ),
inference(superposition,[],[f17652,f1712]) ).
fof(f17652,plain,
( ~ member(x,successor_relation)
| spl0_787 ),
inference(avatar_component_clause,[],[f17650]) ).
fof(f31569,plain,
( spl0_993
| ~ spl0_208
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2189,f2181,f1900,f31567]) ).
fof(f31567,plain,
( spl0_993
<=> ! [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_993])]) ).
fof(f2181,plain,
( spl0_218
<=> ! [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_218])]) ).
fof(f2189,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_208
| ~ spl0_218 ),
inference(resolution,[],[f2182,f1901]) ).
fof(f2182,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_218 ),
inference(avatar_component_clause,[],[f2181]) ).
fof(f31501,plain,
( spl0_992
| ~ spl0_207
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2178,f2128,f1894,f31499]) ).
fof(f31499,plain,
( spl0_992
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_992])]) ).
fof(f2178,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_207
| ~ spl0_217 ),
inference(duplicate_literal_removal,[],[f2169]) ).
fof(f2169,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_207
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1895]) ).
fof(f31476,plain,
( spl0_991
| ~ spl0_208
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2003,f1954,f1900,f31474]) ).
fof(f31474,plain,
( spl0_991
<=> ! [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_991])]) ).
fof(f2003,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_208
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1901]) ).
fof(f31472,plain,
( spl0_990
| ~ spl0_208
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1977,f1950,f1900,f31470]) ).
fof(f31470,plain,
( spl0_990
<=> ! [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_990])]) ).
fof(f1977,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_208
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1901]) ).
fof(f31468,plain,
( spl0_989
| ~ spl0_93
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1921,f1900,f718,f31466]) ).
fof(f31466,plain,
( spl0_989
<=> ! [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_989])]) ).
fof(f1921,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_208 ),
inference(resolution,[],[f1901,f719]) ).
fof(f31464,plain,
( ~ spl0_988
| ~ spl0_188
| spl0_267 ),
inference(avatar_split_clause,[],[f4943,f2774,f1710,f31461]) ).
fof(f31461,plain,
( spl0_988
<=> member(singleton_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f2774,plain,
( spl0_267
<=> member(x,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f4943,plain,
( ~ member(singleton_relation,identity_relation)
| ~ spl0_188
| spl0_267 ),
inference(superposition,[],[f2775,f1712]) ).
fof(f2775,plain,
( ~ member(x,identity_relation)
| spl0_267 ),
inference(avatar_component_clause,[],[f2774]) ).
fof(f31196,plain,
( spl0_987
| ~ spl0_158
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1992,f1954,f1380,f31194]) ).
fof(f31194,plain,
( spl0_987
<=> ! [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_987])]) ).
fof(f1992,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_158
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1381]) ).
fof(f31192,plain,
( spl0_986
| ~ spl0_157
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1986,f1954,f1376,f31190]) ).
fof(f31190,plain,
( spl0_986
<=> ! [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_986])]) ).
fof(f1986,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_157
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1377]) ).
fof(f31188,plain,
( spl0_985
| ~ spl0_158
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1966,f1950,f1380,f31186]) ).
fof(f31186,plain,
( spl0_985
<=> ! [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_985])]) ).
fof(f1966,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_158
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1381]) ).
fof(f31184,plain,
( spl0_984
| ~ spl0_157
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1960,f1950,f1376,f31182]) ).
fof(f31182,plain,
( spl0_984
<=> ! [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_984])]) ).
fof(f1960,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_157
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1377]) ).
fof(f31180,plain,
( ~ spl0_983
| ~ spl0_188
| spl0_237 ),
inference(avatar_split_clause,[],[f2430,f2334,f1710,f31177]) ).
fof(f31177,plain,
( spl0_983
<=> subset_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f2430,plain,
( subset_relation != singleton_relation
| ~ spl0_188
| spl0_237 ),
inference(superposition,[],[f2335,f1712]) ).
fof(f2335,plain,
( subset_relation != x
| spl0_237 ),
inference(avatar_component_clause,[],[f2334]) ).
fof(f31175,plain,
( spl0_982
| ~ spl0_93
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1427,f1380,f718,f31173]) ).
fof(f31173,plain,
( spl0_982
<=> ! [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_982])]) ).
fof(f1427,plain,
( ! [X2,X3,X0,X1,X4] :
( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_158 ),
inference(resolution,[],[f1381,f719]) ).
fof(f31171,plain,
( spl0_981
| ~ spl0_93
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1406,f1376,f718,f31169]) ).
fof(f31169,plain,
( spl0_981
<=> ! [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_981])]) ).
fof(f1406,plain,
( ! [X2,X3,X0,X1,X4] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_157 ),
inference(resolution,[],[f1377,f719]) ).
fof(f31108,plain,
( spl0_980
| ~ spl0_33
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1985,f1954,f354,f31106]) ).
fof(f31106,plain,
( spl0_980
<=> ! [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_980])]) ).
fof(f1985,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_33
| ~ spl0_211 ),
inference(resolution,[],[f1955,f355]) ).
fof(f31104,plain,
( spl0_979
| ~ spl0_33
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1959,f1950,f354,f31102]) ).
fof(f31102,plain,
( spl0_979
<=> ! [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_979])]) ).
fof(f1959,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_33
| ~ spl0_210 ),
inference(resolution,[],[f1951,f355]) ).
fof(f31056,plain,
( spl0_978
| ~ spl0_137
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2196,f2192,f1124,f31054]) ).
fof(f31054,plain,
( spl0_978
<=> ! [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_978])]) ).
fof(f2192,plain,
( spl0_219
<=> ! [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_219])]) ).
fof(f2196,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_137
| ~ spl0_219 ),
inference(resolution,[],[f2193,f1125]) ).
fof(f2193,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_219 ),
inference(avatar_component_clause,[],[f2192]) ).
fof(f30889,plain,
( spl0_977
| ~ spl0_96
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2028,f2010,f743,f30887]) ).
fof(f30887,plain,
( spl0_977
<=> ! [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_977])]) ).
fof(f743,plain,
( spl0_96
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f2028,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) )
| ~ spl0_96
| ~ spl0_212 ),
inference(resolution,[],[f2011,f744]) ).
fof(f744,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f30874,plain,
( spl0_975
| ~ spl0_976
| ~ spl0_100
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1693,f1644,f760,f30871,f30868]) ).
fof(f30868,plain,
( spl0_975
<=> ! [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_975])]) ).
fof(f30871,plain,
( spl0_976
<=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f1693,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2) )
| ~ spl0_100
| ~ spl0_186 ),
inference(resolution,[],[f1645,f761]) ).
fof(f30499,plain,
( spl0_974
| ~ spl0_55
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2163,f2128,f489,f30497]) ).
fof(f30497,plain,
( spl0_974
<=> ! [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_974])]) ).
fof(f2163,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_55
| ~ spl0_217 ),
inference(resolution,[],[f2129,f490]) ).
fof(f30495,plain,
( spl0_973
| ~ spl0_55
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2140,f2122,f489,f30493]) ).
fof(f30493,plain,
( spl0_973
<=> ! [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_973])]) ).
fof(f2140,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_55
| ~ spl0_216 ),
inference(resolution,[],[f2123,f490]) ).
fof(f30417,plain,
( spl0_972
| ~ spl0_50
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2165,f2128,f465,f30415]) ).
fof(f30415,plain,
( spl0_972
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_972])]) ).
fof(f2165,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_50
| ~ spl0_217 ),
inference(resolution,[],[f2129,f466]) ).
fof(f30413,plain,
( spl0_971
| ~ spl0_50
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2142,f2122,f465,f30411]) ).
fof(f30411,plain,
( spl0_971
<=> ! [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_971])]) ).
fof(f2142,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_50
| ~ spl0_216 ),
inference(resolution,[],[f2123,f466]) ).
fof(f30409,plain,
( ~ spl0_970
| spl0_97
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1786,f1710,f747,f30406]) ).
fof(f30406,plain,
( spl0_970
<=> member(singleton_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f747,plain,
( spl0_97
<=> member(x,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1786,plain,
( ~ member(singleton_relation,subset_relation)
| spl0_97
| ~ spl0_188 ),
inference(superposition,[],[f748,f1712]) ).
fof(f748,plain,
( ~ member(x,subset_relation)
| spl0_97 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f30126,plain,
( spl0_969
| ~ spl0_36
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2159,f2128,f366,f30124]) ).
fof(f30124,plain,
( spl0_969
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_969])]) ).
fof(f2159,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_36
| ~ spl0_217 ),
inference(resolution,[],[f2129,f367]) ).
fof(f30122,plain,
( spl0_968
| ~ spl0_35
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2158,f2128,f362,f30120]) ).
fof(f30120,plain,
( spl0_968
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_968])]) ).
fof(f2158,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_35
| ~ spl0_217 ),
inference(resolution,[],[f2129,f363]) ).
fof(f30118,plain,
( spl0_967
| ~ spl0_36
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2136,f2122,f366,f30116]) ).
fof(f30116,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))),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_967])]) ).
fof(f2136,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_36
| ~ spl0_216 ),
inference(resolution,[],[f2123,f367]) ).
fof(f30114,plain,
( spl0_966
| ~ spl0_35
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2135,f2122,f362,f30112]) ).
fof(f30112,plain,
( spl0_966
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_966])]) ).
fof(f2135,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_35
| ~ spl0_216 ),
inference(resolution,[],[f2123,f363]) ).
fof(f30092,plain,
( spl0_965
| ~ spl0_31
| ~ spl0_101
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2016,f2010,f766,f339,f30090]) ).
fof(f30090,plain,
( spl0_965
<=> ! [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_965])]) ).
fof(f766,plain,
( spl0_101
<=> ! [X4,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f2016,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
| ~ spl0_101
| ~ spl0_212 ),
inference(resolution,[],[f2011,f767]) ).
fof(f767,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f30071,plain,
( spl0_964
| ~ spl0_188
| ~ spl0_963 ),
inference(avatar_split_clause,[],[f30067,f30059,f1710,f30069]) ).
fof(f30069,plain,
( spl0_964
<=> ! [X0,X3,X2,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f30067,plain,
( ! [X2,X3,X0,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) )
| ~ spl0_188
| ~ spl0_963 ),
inference(forward_demodulation,[],[f30066,f1712]) ).
fof(f30066,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_188
| ~ spl0_963 ),
inference(forward_demodulation,[],[f30065,f1712]) ).
fof(f30065,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_188
| ~ spl0_963 ),
inference(forward_demodulation,[],[f30064,f1712]) ).
fof(f30064,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_188
| ~ spl0_963 ),
inference(forward_demodulation,[],[f30063,f1712]) ).
fof(f30063,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_188
| ~ spl0_963 ),
inference(forward_demodulation,[],[f30062,f1712]) ).
fof(f30062,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_188
| ~ spl0_963 ),
inference(forward_demodulation,[],[f30060,f1712]) ).
fof(f30061,plain,
( spl0_963
| ~ spl0_6
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2225,f2209,f231,f30059]) ).
fof(f231,plain,
( spl0_6
<=> ! [X0] :
( x = X0
| intersection(X0,regular(X0)) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f2225,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X2),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_221 ),
inference(superposition,[],[f2210,f232]) ).
fof(f232,plain,
( ! [X0] :
( intersection(X0,regular(X0)) = x
| x = X0 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f29969,plain,
( spl0_962
| ~ spl0_139
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1843,f1814,f1710,f1178,f29967]) ).
fof(f29967,plain,
( spl0_962
<=> ! [X0] :
( singleton_relation = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_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,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| ~ member(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(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,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))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X0,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_962])]) ).
fof(f1178,plain,
( spl0_139
<=> ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1843,plain,
( ! [X0] :
( singleton_relation = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_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,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| ~ member(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(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,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))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class) )
| ~ spl0_139
| ~ spl0_188
| ~ spl0_198 ),
inference(forward_demodulation,[],[f1830,f1712]) ).
fof(f1830,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,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| ~ member(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(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),intersection(X0,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))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
| x = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_139
| ~ spl0_198 ),
inference(resolution,[],[f1815,f1179]) ).
fof(f1179,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f29965,plain,
( spl0_961
| ~ spl0_138
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1839,f1814,f1710,f1174,f29963]) ).
fof(f29963,plain,
( spl0_961
<=> ! [X0] :
( singleton_relation = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_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(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f1174,plain,
( spl0_138
<=> ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1839,plain,
( ! [X0] :
( singleton_relation = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_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(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),universal_class) )
| ~ spl0_138
| ~ spl0_188
| ~ spl0_198 ),
inference(forward_demodulation,[],[f1822,f1712]) ).
fof(f1822,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(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_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(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0),universal_class)
| x = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
| ~ spl0_138
| ~ spl0_198 ),
inference(resolution,[],[f1815,f1175]) ).
fof(f1175,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1174]) ).
fof(f29950,plain,
( ~ spl0_957
| ~ spl0_958
| spl0_959
| spl0_960
| ~ spl0_27
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1838,f1814,f1710,f323,f29947,f29943,f29939,f29935]) ).
fof(f29935,plain,
( spl0_957
<=> member(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_957])]) ).
fof(f29939,plain,
( spl0_958
<=> member(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(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),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))))))),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f29943,plain,
( spl0_959
<=> member(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(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),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_959])]) ).
fof(f29947,plain,
( spl0_960
<=> singleton_relation = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f323,plain,
( spl0_27
<=> ! [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)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1838,plain,
( singleton_relation = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_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(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
| ~ member(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(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),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))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),universal_class)
| ~ spl0_27
| ~ spl0_188
| ~ spl0_198 ),
inference(forward_demodulation,[],[f1821,f1712]) ).
fof(f1821,plain,
( member(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(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)),universal_class))))))),subset_relation)
| ~ member(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(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),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))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),universal_class)
| x = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_27
| ~ spl0_198 ),
inference(resolution,[],[f1815,f324]) ).
fof(f324,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)
| x = X1 )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f29926,plain,
( spl0_956
| ~ spl0_115
| ~ spl0_188
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1777,f1733,f1710,f905,f29924]) ).
fof(f29924,plain,
( spl0_956
<=> ! [X0] :
( singleton_relation = 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)
| ~ 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f905,plain,
( spl0_115
<=> ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1733,plain,
( spl0_193
<=> ! [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_193])]) ).
fof(f1777,plain,
( ! [X0] :
( singleton_relation = 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)
| ~ 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) )
| ~ spl0_115
| ~ spl0_188
| ~ spl0_193 ),
inference(forward_demodulation,[],[f1771,f1712]) ).
fof(f1771,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)
| x = 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_115
| ~ spl0_193 ),
inference(resolution,[],[f1734,f906]) ).
fof(f906,plain,
( ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f905]) ).
fof(f1734,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_193 ),
inference(avatar_component_clause,[],[f1733]) ).
fof(f29897,plain,
( spl0_955
| ~ spl0_132
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1842,f1814,f1710,f1029,f29895]) ).
fof(f29895,plain,
( spl0_955
<=> ! [X0] :
( singleton_relation = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f1029,plain,
( spl0_132
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| ~ member(X0,universal_class)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1842,plain,
( ! [X0] :
( singleton_relation = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class) )
| ~ spl0_132
| ~ spl0_188
| ~ spl0_198 ),
inference(forward_demodulation,[],[f1829,f1712]) ).
fof(f1829,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class)
| x = X0 )
| ~ spl0_132
| ~ spl0_198 ),
inference(resolution,[],[f1815,f1030]) ).
fof(f1030,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| x = X0 )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1029]) ).
fof(f29881,plain,
( spl0_954
| ~ spl0_115
| ~ spl0_188
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1758,f1729,f1710,f905,f29879]) ).
fof(f29879,plain,
( spl0_954
<=> ! [X0,X1] :
( singleton_relation = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class)
| ~ 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1729,plain,
( spl0_192
<=> ! [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_192])]) ).
fof(f1758,plain,
( ! [X0,X1] :
( singleton_relation = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class)
| ~ 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) )
| ~ spl0_115
| ~ spl0_188
| ~ spl0_192 ),
inference(forward_demodulation,[],[f1748,f1712]) ).
fof(f1748,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)
| x = 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_115
| ~ spl0_192 ),
inference(resolution,[],[f1730,f906]) ).
fof(f1730,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_192 ),
inference(avatar_component_clause,[],[f1729]) ).
fof(f29850,plain,
( ~ spl0_953
| ~ spl0_188
| spl0_441 ),
inference(avatar_split_clause,[],[f13937,f6030,f1710,f29847]) ).
fof(f29847,plain,
( spl0_953
<=> function(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f6030,plain,
( spl0_441
<=> function(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f13937,plain,
( ~ function(singleton_relation)
| ~ spl0_188
| spl0_441 ),
inference(superposition,[],[f6031,f1712]) ).
fof(f6031,plain,
( ~ function(x)
| spl0_441 ),
inference(avatar_component_clause,[],[f6030]) ).
fof(f29825,plain,
( spl0_952
| ~ spl0_111
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1845,f1814,f1710,f849,f29823]) ).
fof(f29823,plain,
( spl0_952
<=> ! [X0] :
( singleton_relation = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1845,plain,
( ! [X0] :
( singleton_relation = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_111
| ~ spl0_188
| ~ spl0_198 ),
inference(forward_demodulation,[],[f1833,f1712]) ).
fof(f1833,plain,
( ! [X0] :
( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
| x = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_111
| ~ spl0_198 ),
inference(resolution,[],[f1815,f850]) ).
fof(f29821,plain,
( spl0_951
| ~ spl0_110
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1841,f1814,f1710,f845,f29819]) ).
fof(f29819,plain,
( spl0_951
<=> ! [X0] :
( singleton_relation = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
| member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
| ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1841,plain,
( ! [X0] :
( singleton_relation = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)
| member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
| ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class)) )
| ~ spl0_110
| ~ spl0_188
| ~ spl0_198 ),
inference(forward_demodulation,[],[f1824,f1712]) ).
fof(f1824,plain,
( ! [X0] :
( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
| ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
| x = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
| ~ spl0_110
| ~ spl0_198 ),
inference(resolution,[],[f1815,f846]) ).
fof(f29789,plain,
( spl0_950
| ~ spl0_112
| ~ spl0_188
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1779,f1733,f1710,f881,f29787]) ).
fof(f29787,plain,
( spl0_950
<=> ! [X0,X1] :
( singleton_relation = X0
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),singleton_relation)
| ~ 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))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f881,plain,
( spl0_112
<=> ! [X0,X1] :
( member(X1,x)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1779,plain,
( ! [X0,X1] :
( singleton_relation = X0
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),singleton_relation)
| ~ 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))))),X0) )
| ~ spl0_112
| ~ spl0_188
| ~ spl0_193 ),
inference(forward_demodulation,[],[f1778,f1712]) ).
fof(f1778,plain,
( ! [X0,X1] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),singleton_relation)
| ~ 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))))),X0)
| x = X0 )
| ~ spl0_112
| ~ spl0_188
| ~ spl0_193 ),
inference(forward_demodulation,[],[f1774,f1712]) ).
fof(f1774,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))))),x)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
| x = X0 )
| ~ spl0_112
| ~ spl0_193 ),
inference(resolution,[],[f1734,f882]) ).
fof(f882,plain,
( ! [X0,X1] :
( ~ member(X1,regular(X0))
| member(X1,x)
| ~ member(X1,X0)
| x = X0 )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f29748,plain,
( spl0_949
| ~ spl0_141
| ~ spl0_188
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1794,f1737,f1710,f1229,f29746]) ).
fof(f29746,plain,
( spl0_949
<=> ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1229,plain,
( spl0_141
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1737,plain,
( spl0_194
<=> ! [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_194])]) ).
fof(f1794,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| 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) )
| ~ spl0_141
| ~ spl0_188
| ~ spl0_194 ),
inference(forward_demodulation,[],[f1793,f1712]) ).
fof(f1793,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) = x )
| ~ spl0_141
| ~ spl0_194 ),
inference(superposition,[],[f1738,f1230]) ).
fof(f1230,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) = x )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1229]) ).
fof(f1738,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_194 ),
inference(avatar_component_clause,[],[f1737]) ).
fof(f29744,plain,
( spl0_948
| ~ spl0_112
| ~ spl0_188
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1760,f1729,f1710,f881,f29742]) ).
fof(f29742,plain,
( spl0_948
<=> ! [X2,X0,X1] :
( singleton_relation = X1
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
| ~ 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)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1760,plain,
( ! [X2,X0,X1] :
( singleton_relation = X1
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
| ~ 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)))),X1) )
| ~ spl0_112
| ~ spl0_188
| ~ spl0_192 ),
inference(forward_demodulation,[],[f1759,f1712]) ).
fof(f1759,plain,
( ! [X2,X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
| ~ 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)))),X1)
| x = X1 )
| ~ spl0_112
| ~ spl0_188
| ~ spl0_192 ),
inference(forward_demodulation,[],[f1751,f1712]) ).
fof(f1751,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)))),x)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| x = X1 )
| ~ spl0_112
| ~ spl0_192 ),
inference(resolution,[],[f1730,f882]) ).
fof(f29726,plain,
( ~ spl0_947
| ~ spl0_188
| spl0_440 ),
inference(avatar_split_clause,[],[f13936,f6026,f1710,f29723]) ).
fof(f29723,plain,
( spl0_947
<=> single_valued_class(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f6026,plain,
( spl0_440
<=> single_valued_class(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f13936,plain,
( ~ single_valued_class(singleton_relation)
| ~ spl0_188
| spl0_440 ),
inference(superposition,[],[f6028,f1712]) ).
fof(f6028,plain,
( ~ single_valued_class(x)
| spl0_440 ),
inference(avatar_component_clause,[],[f6026]) ).
fof(f29721,plain,
( spl0_946
| ~ spl0_108
| ~ spl0_188
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1844,f1814,f1710,f823,f29719]) ).
fof(f29719,plain,
( spl0_946
<=> ! [X0] :
( singleton_relation = 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))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1844,plain,
( ! [X0] :
( singleton_relation = 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))))))) )
| ~ spl0_108
| ~ spl0_188
| ~ spl0_198 ),
inference(forward_demodulation,[],[f1832,f1712]) ).
fof(f1832,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)))))))
| x = X0 )
| ~ spl0_108
| ~ spl0_198 ),
inference(resolution,[],[f1815,f824]) ).
fof(f29509,plain,
( spl0_945
| ~ spl0_188
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5004,f5001,f1710,f29507]) ).
fof(f29507,plain,
( spl0_945
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class))
| subclass(intersection(X0,universal_class),domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f5001,plain,
( spl0_378
<=> ! [X0,X1] :
( subclass(intersection(X0,universal_class),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f5004,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class))
| subclass(intersection(X0,universal_class),domain_of(X1)) )
| ~ spl0_188
| ~ spl0_378 ),
inference(forward_demodulation,[],[f5002,f1712]) ).
fof(f5002,plain,
( ! [X0,X1] :
( subclass(intersection(X0,universal_class),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f5001]) ).
fof(f29505,plain,
( spl0_944
| ~ spl0_188
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f4999,f4995,f1710,f29503]) ).
fof(f29503,plain,
( spl0_944
<=> ! [X2,X0,X1] :
( singleton_relation = X1
| member(not_subclass_element(intersection(X0,regular(X1)),X2),singleton_relation)
| subclass(intersection(X0,regular(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f4995,plain,
( spl0_377
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,regular(X1)),X2)
| member(not_subclass_element(intersection(X0,regular(X1)),X2),x)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f4999,plain,
( ! [X2,X0,X1] :
( singleton_relation = X1
| member(not_subclass_element(intersection(X0,regular(X1)),X2),singleton_relation)
| subclass(intersection(X0,regular(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1) )
| ~ spl0_188
| ~ spl0_377 ),
inference(forward_demodulation,[],[f4998,f1712]) ).
fof(f4998,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,regular(X1)),X2),singleton_relation)
| subclass(intersection(X0,regular(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| x = X1 )
| ~ spl0_188
| ~ spl0_377 ),
inference(forward_demodulation,[],[f4996,f1712]) ).
fof(f4996,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| member(not_subclass_element(intersection(X0,regular(X1)),X2),x)
| subclass(intersection(X0,regular(X1)),X2)
| x = X1 )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f4995]) ).
fof(f29501,plain,
( spl0_943
| ~ spl0_188
| ~ spl0_376 ),
inference(avatar_split_clause,[],[f4993,f4990,f1710,f29499]) ).
fof(f29499,plain,
( spl0_943
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class))
| subclass(intersection(universal_class,X0),domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f4990,plain,
( spl0_376
<=> ! [X0,X1] :
( subclass(intersection(universal_class,X0),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f4993,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class))
| subclass(intersection(universal_class,X0),domain_of(X1)) )
| ~ spl0_188
| ~ spl0_376 ),
inference(forward_demodulation,[],[f4991,f1712]) ).
fof(f4991,plain,
( ! [X0,X1] :
( subclass(intersection(universal_class,X0),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) )
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f4990]) ).
fof(f29421,plain,
( spl0_942
| ~ spl0_189
| ~ spl0_163
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2468,f2414,f1452,f1714,f29418]) ).
fof(f1452,plain,
( spl0_163
<=> ! [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_163])]) ).
fof(f2468,plain,
( ~ member(regular(singleton_relation),element_relation)
| member(regular(singleton_relation),singleton_relation)
| ~ spl0_163
| ~ spl0_247 ),
inference(resolution,[],[f2416,f1453]) ).
fof(f1453,plain,
( ! [X0] :
( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,element_relation)
| member(X0,singleton_relation) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f29416,plain,
( spl0_941
| ~ spl0_137
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2185,f2181,f1124,f29414]) ).
fof(f29414,plain,
( spl0_941
<=> ! [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_941])]) ).
fof(f2185,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_137
| ~ spl0_218 ),
inference(resolution,[],[f2182,f1125]) ).
fof(f29385,plain,
( spl0_940
| ~ spl0_79
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2195,f2192,f640,f29383]) ).
fof(f29383,plain,
( spl0_940
<=> ! [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_940])]) ).
fof(f2195,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_79
| ~ spl0_219 ),
inference(resolution,[],[f2193,f641]) ).
fof(f28737,plain,
( spl0_938
| ~ spl0_939
| ~ spl0_105
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2404,f2386,f803,f28734,f28730]) ).
fof(f28730,plain,
( spl0_938
<=> x = complement(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f28734,plain,
( spl0_939
<=> subclass(complement(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f803,plain,
( spl0_105
<=> ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2404,plain,
( ~ subclass(complement(subset_relation),identity_relation)
| x = complement(subset_relation)
| ~ spl0_105
| ~ spl0_244 ),
inference(duplicate_literal_removal,[],[f2397]) ).
fof(f2397,plain,
( ~ subclass(complement(subset_relation),identity_relation)
| x = complement(subset_relation)
| x = complement(subset_relation)
| ~ spl0_105
| ~ spl0_244 ),
inference(resolution,[],[f2387,f804]) ).
fof(f804,plain,
( ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = x )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f27899,plain,
( spl0_936
| ~ spl0_937
| ~ spl0_105
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2396,f2382,f803,f27896,f27892]) ).
fof(f27892,plain,
( spl0_936
<=> complement(element_relation) = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f27896,plain,
( spl0_937
<=> subclass(complement(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f2396,plain,
( ~ subclass(complement(element_relation),singleton_relation)
| complement(element_relation) = x
| ~ spl0_105
| ~ spl0_243 ),
inference(duplicate_literal_removal,[],[f2389]) ).
fof(f2389,plain,
( ~ subclass(complement(element_relation),singleton_relation)
| complement(element_relation) = x
| complement(element_relation) = x
| ~ spl0_105
| ~ spl0_243 ),
inference(resolution,[],[f2383,f804]) ).
fof(f27624,plain,
( spl0_935
| ~ spl0_3
| ~ spl0_520
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f8876,f8637,f8022,f217,f27622]) ).
fof(f27622,plain,
( spl0_935
<=> ! [X0] :
( subclass(X0,complement(x))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f8022,plain,
( spl0_520
<=> ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f8876,plain,
( ! [X0] :
( subclass(X0,complement(x))
| ~ subclass(X0,universal_class) )
| ~ spl0_3
| ~ spl0_520
| ~ spl0_548 ),
inference(forward_demodulation,[],[f8842,f8836]) ).
fof(f8836,plain,
( x = domain_of(x)
| ~ spl0_3
| ~ spl0_548 ),
inference(resolution,[],[f8638,f218]) ).
fof(f8842,plain,
( ! [X0] :
( subclass(X0,complement(domain_of(x)))
| ~ subclass(X0,universal_class) )
| ~ spl0_520
| ~ spl0_548 ),
inference(resolution,[],[f8638,f8023]) ).
fof(f8023,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) )
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f8022]) ).
fof(f26909,plain,
( spl0_222
| ~ spl0_934
| ~ spl0_108
| spl0_930 ),
inference(avatar_split_clause,[],[f25543,f24870,f823,f26906,f2213]) ).
fof(f26906,plain,
( spl0_934
<=> subclass(identity_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f24870,plain,
( spl0_930
<=> member(regular(identity_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f25543,plain,
( ~ subclass(identity_relation,element_relation)
| identity_relation = x
| ~ spl0_108
| spl0_930 ),
inference(resolution,[],[f24871,f824]) ).
fof(f24871,plain,
( ~ member(regular(identity_relation),element_relation)
| spl0_930 ),
inference(avatar_component_clause,[],[f24870]) ).
fof(f26391,plain,
( spl0_222
| ~ spl0_933
| ~ spl0_243
| spl0_930 ),
inference(avatar_split_clause,[],[f25541,f24870,f2382,f26388,f2213]) ).
fof(f26388,plain,
( spl0_933
<=> subclass(identity_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f25541,plain,
( ~ subclass(identity_relation,singleton_relation)
| identity_relation = x
| ~ spl0_243
| spl0_930 ),
inference(resolution,[],[f24871,f2383]) ).
fof(f25779,plain,
( ~ spl0_932
| ~ spl0_692
| spl0_930 ),
inference(avatar_split_clause,[],[f25542,f24870,f14332,f25776]) ).
fof(f25776,plain,
( spl0_932
<=> subclass(subset_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f14332,plain,
( spl0_692
<=> ! [X0] :
( ~ subclass(subset_relation,X0)
| member(regular(identity_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f25542,plain,
( ~ subclass(subset_relation,element_relation)
| ~ spl0_692
| spl0_930 ),
inference(resolution,[],[f24871,f14333]) ).
fof(f14333,plain,
( ! [X0] :
( member(regular(identity_relation),X0)
| ~ subclass(subset_relation,X0) )
| ~ spl0_692 ),
inference(avatar_component_clause,[],[f14332]) ).
fof(f24877,plain,
( spl0_930
| ~ spl0_931
| ~ spl0_129
| ~ spl0_692 ),
inference(avatar_split_clause,[],[f16640,f14332,f997,f24874,f24870]) ).
fof(f24874,plain,
( spl0_931
<=> subclass(subset_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f16640,plain,
( ~ subclass(subset_relation,singleton_relation)
| member(regular(identity_relation),element_relation)
| ~ spl0_129
| ~ spl0_692 ),
inference(resolution,[],[f14333,f998]) ).
fof(f24437,plain,
( spl0_188
| ~ spl0_929
| ~ spl0_108
| spl0_903 ),
inference(avatar_split_clause,[],[f22571,f22325,f823,f24434,f1710]) ).
fof(f22325,plain,
( spl0_903
<=> member(regular(singleton_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f22571,plain,
( ~ subclass(singleton_relation,subset_relation)
| singleton_relation = x
| ~ spl0_108
| spl0_903 ),
inference(resolution,[],[f22326,f824]) ).
fof(f22326,plain,
( ~ member(regular(singleton_relation),subset_relation)
| spl0_903 ),
inference(avatar_component_clause,[],[f22325]) ).
fof(f24034,plain,
( spl0_188
| ~ spl0_928
| ~ spl0_244
| spl0_903 ),
inference(avatar_split_clause,[],[f22569,f22325,f2386,f24031,f1710]) ).
fof(f22569,plain,
( ~ subclass(singleton_relation,identity_relation)
| singleton_relation = x
| ~ spl0_244
| spl0_903 ),
inference(resolution,[],[f22326,f2387]) ).
fof(f22827,plain,
( ~ spl0_727
| ~ spl0_926 ),
inference(avatar_contradiction_clause,[],[f22784]) ).
fof(f22784,plain,
( $false
| ~ spl0_727
| ~ spl0_926 ),
inference(resolution,[],[f22779,f15643]) ).
fof(f15643,plain,
( member(not_subclass_element(cross_product(x,x),identity_relation),universal_class)
| ~ spl0_727 ),
inference(avatar_component_clause,[],[f15641]) ).
fof(f15641,plain,
( spl0_727
<=> member(not_subclass_element(cross_product(x,x),identity_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f22779,plain,
( ! [X2] : ~ member(X2,universal_class)
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f22778]) ).
fof(f22778,plain,
( spl0_926
<=> ! [X2] : ~ member(X2,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f22826,plain,
( ~ spl0_15
| ~ spl0_926 ),
inference(avatar_contradiction_clause,[],[f22785]) ).
fof(f22785,plain,
( $false
| ~ spl0_15
| ~ spl0_926 ),
inference(resolution,[],[f22779,f272]) ).
fof(f22825,plain,
( ~ spl0_8
| ~ spl0_926 ),
inference(avatar_contradiction_clause,[],[f22786]) ).
fof(f22786,plain,
( $false
| ~ spl0_8
| ~ spl0_926 ),
inference(resolution,[],[f22779,f241]) ).
fof(f241,plain,
( member(omega,universal_class)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f239,plain,
( spl0_8
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f22824,plain,
( ~ spl0_20
| ~ spl0_926 ),
inference(avatar_contradiction_clause,[],[f22788]) ).
fof(f22788,plain,
( $false
| ~ spl0_20
| ~ spl0_926 ),
inference(resolution,[],[f22779,f295]) ).
fof(f22783,plain,
( spl0_926
| spl0_927
| ~ spl0_79
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2184,f2181,f640,f22781,f22778]) ).
fof(f22781,plain,
( spl0_927
<=> ! [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_927])]) ).
fof(f2184,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(X0,universal_class)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) )
| ~ spl0_79
| ~ spl0_218 ),
inference(resolution,[],[f2182,f641]) ).
fof(f22776,plain,
( spl0_925
| ~ spl0_95
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1691,f1644,f739,f22774]) ).
fof(f22774,plain,
( spl0_925
<=> ! [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_925])]) ).
fof(f1691,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,rotate(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) )
| ~ spl0_95
| ~ spl0_186 ),
inference(resolution,[],[f1645,f740]) ).
fof(f22772,plain,
( ~ spl0_923
| spl0_924
| ~ spl0_90
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1485,f1456,f703,f22770,f22766]) ).
fof(f22766,plain,
( spl0_923
<=> operation(flip(cross_product(subset_relation,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f22770,plain,
( spl0_924
<=> ! [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_924])]) ).
fof(f1485,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation)
| ~ operation(X1)
| ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
| homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
| ~ operation(flip(cross_product(subset_relation,universal_class))) )
| ~ spl0_90
| ~ spl0_164 ),
inference(resolution,[],[f1457,f704]) ).
fof(f22764,plain,
( spl0_921
| ~ spl0_922
| ~ spl0_198
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2036,f2010,f1814,f22761,f22758]) ).
fof(f22758,plain,
( spl0_921
<=> ! [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_921])]) ).
fof(f22761,plain,
( spl0_922
<=> 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_922])]) ).
fof(f2036,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_198
| ~ spl0_212 ),
inference(resolution,[],[f2011,f1815]) ).
fof(f22705,plain,
( spl0_920
| ~ spl0_183
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2164,f2128,f1625,f22703]) ).
fof(f22703,plain,
( spl0_920
<=> ! [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_920])]) ).
fof(f1625,plain,
( spl0_183
<=> ! [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_183])]) ).
fof(f2164,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_183
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1626]) ).
fof(f1626,plain,
( ! [X0] :
( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,subset_relation) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1625]) ).
fof(f22701,plain,
( ~ spl0_919
| ~ spl0_682
| spl0_903 ),
inference(avatar_split_clause,[],[f22570,f22325,f13911,f22698]) ).
fof(f22698,plain,
( spl0_919
<=> subclass(element_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f22570,plain,
( ~ subclass(element_relation,subset_relation)
| ~ spl0_682
| spl0_903 ),
inference(resolution,[],[f22326,f13912]) ).
fof(f22696,plain,
( spl0_918
| ~ spl0_183
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2141,f2122,f1625,f22694]) ).
fof(f22694,plain,
( spl0_918
<=> ! [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_918])]) ).
fof(f2141,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_183
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1626]) ).
fof(f22671,plain,
( spl0_917
| ~ spl0_193
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1994,f1954,f1733,f22669]) ).
fof(f22669,plain,
( spl0_917
<=> ! [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_917])]) ).
fof(f1994,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_193
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1734]) ).
fof(f22667,plain,
( spl0_916
| ~ spl0_193
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1968,f1950,f1733,f22665]) ).
fof(f22665,plain,
( spl0_916
<=> ! [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_916])]) ).
fof(f1968,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_193
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1734]) ).
fof(f22663,plain,
( spl0_915
| ~ spl0_93
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1770,f1733,f718,f22661]) ).
fof(f22661,plain,
( spl0_915
<=> ! [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_915])]) ).
fof(f1770,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_193 ),
inference(resolution,[],[f1734,f719]) ).
fof(f22619,plain,
( spl0_914
| ~ spl0_199
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2177,f2128,f1847,f22617]) ).
fof(f22617,plain,
( spl0_914
<=> ! [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_914])]) ).
fof(f2177,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_199
| ~ spl0_217 ),
inference(duplicate_literal_removal,[],[f2173]) ).
fof(f2173,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_199
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1848]) ).
fof(f22568,plain,
( spl0_913
| ~ spl0_186
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2154,f2128,f1644,f22566]) ).
fof(f22566,plain,
( spl0_913
<=> ! [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_913])]) ).
fof(f2154,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_186
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1645]) ).
fof(f22540,plain,
( spl0_912
| ~ spl0_186
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1993,f1954,f1644,f22538]) ).
fof(f22538,plain,
( spl0_912
<=> ! [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_912])]) ).
fof(f1993,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_186
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1645]) ).
fof(f22536,plain,
( spl0_911
| ~ spl0_186
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1967,f1950,f1644,f22534]) ).
fof(f22534,plain,
( spl0_911
<=> ! [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_911])]) ).
fof(f1967,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_186
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1645]) ).
fof(f22532,plain,
( spl0_910
| ~ spl0_93
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1702,f1644,f718,f22530]) ).
fof(f22530,plain,
( spl0_910
<=> ! [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_910])]) ).
fof(f1702,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_186 ),
inference(resolution,[],[f1645,f719]) ).
fof(f22522,plain,
( spl0_909
| ~ spl0_141
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2120,f2112,f1229,f22520]) ).
fof(f22520,plain,
( spl0_909
<=> ! [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)
| x = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f2112,plain,
( spl0_215
<=> ! [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)
| x = 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_215])]) ).
fof(f2120,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)
| x = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
| cross_product(X0,X1) = x )
| ~ spl0_141
| ~ spl0_215 ),
inference(superposition,[],[f2113,f1230]) ).
fof(f2113,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)
| x = 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_215 ),
inference(avatar_component_clause,[],[f2112]) ).
fof(f22416,plain,
( spl0_908
| ~ spl0_150
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2168,f2128,f1294,f22414]) ).
fof(f22414,plain,
( spl0_908
<=> ! [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_908])]) ).
fof(f2168,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_150
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1295]) ).
fof(f22412,plain,
( spl0_907
| ~ spl0_149
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2166,f2128,f1290,f22410]) ).
fof(f22410,plain,
( spl0_907
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_907])]) ).
fof(f2166,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_149
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1291]) ).
fof(f22408,plain,
( spl0_906
| ~ spl0_150
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2145,f2122,f1294,f22406]) ).
fof(f22406,plain,
( spl0_906
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_906])]) ).
fof(f2145,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_150
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1295]) ).
fof(f22404,plain,
( spl0_905
| ~ spl0_149
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2143,f2122,f1290,f22402]) ).
fof(f22402,plain,
( spl0_905
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(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_905])]) ).
fof(f2143,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_149
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1291]) ).
fof(f22332,plain,
( spl0_903
| ~ spl0_904
| ~ spl0_130
| ~ spl0_682 ),
inference(avatar_split_clause,[],[f16095,f13911,f1001,f22329,f22325]) ).
fof(f22329,plain,
( spl0_904
<=> subclass(element_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f16095,plain,
( ~ subclass(element_relation,identity_relation)
| member(regular(singleton_relation),subset_relation)
| ~ spl0_130
| ~ spl0_682 ),
inference(resolution,[],[f13912,f1002]) ).
fof(f22311,plain,
( spl0_902
| ~ spl0_71
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2175,f2128,f598,f22309]) ).
fof(f22309,plain,
( spl0_902
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),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_902])]) ).
fof(f2175,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_71
| ~ spl0_217 ),
inference(resolution,[],[f2129,f599]) ).
fof(f22306,plain,
( spl0_900
| ~ spl0_901
| ~ spl0_164
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2043,f2010,f1456,f22303,f22300]) ).
fof(f22300,plain,
( spl0_900
<=> ! [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_900])]) ).
fof(f22303,plain,
( spl0_901
<=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2043,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_164
| ~ spl0_212 ),
inference(resolution,[],[f2011,f1457]) ).
fof(f22298,plain,
( spl0_898
| ~ spl0_899
| ~ spl0_163
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2038,f2010,f1452,f22295,f22292]) ).
fof(f22292,plain,
( spl0_898
<=> ! [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_898])]) ).
fof(f22295,plain,
( spl0_899
<=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2038,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_163
| ~ spl0_212 ),
inference(resolution,[],[f2011,f1453]) ).
fof(f22290,plain,
( spl0_897
| ~ spl0_192
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2002,f1954,f1729,f22288]) ).
fof(f22288,plain,
( spl0_897
<=> ! [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_897])]) ).
fof(f2002,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_192
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1730]) ).
fof(f22286,plain,
( spl0_896
| ~ spl0_192
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1976,f1950,f1729,f22284]) ).
fof(f22284,plain,
( spl0_896
<=> ! [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_896])]) ).
fof(f1976,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_192
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1730]) ).
fof(f22282,plain,
( spl0_895
| ~ spl0_93
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1747,f1729,f718,f22280]) ).
fof(f22280,plain,
( spl0_895
<=> ! [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_895])]) ).
fof(f1747,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X4,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_192 ),
inference(resolution,[],[f1730,f719]) ).
fof(f22225,plain,
( spl0_894
| ~ spl0_137
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2161,f2128,f1124,f22223]) ).
fof(f22223,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(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_894])]) ).
fof(f2161,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_137
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1125]) ).
fof(f22221,plain,
( spl0_893
| ~ spl0_137
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2138,f2122,f1124,f22219]) ).
fof(f22219,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(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_893])]) ).
fof(f2138,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_137
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1125]) ).
fof(f22190,plain,
( spl0_892
| ~ spl0_54
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2032,f2010,f485,f22188]) ).
fof(f22188,plain,
( spl0_892
<=> ! [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_892])]) ).
fof(f485,plain,
( spl0_54
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f2032,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_54
| ~ spl0_212 ),
inference(resolution,[],[f2011,f486]) ).
fof(f486,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f485]) ).
fof(f22174,plain,
( spl0_891
| ~ spl0_102
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1249,f1229,f771,f22172]) ).
fof(f22172,plain,
( spl0_891
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f1249,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) = x )
| ~ spl0_102
| ~ spl0_141 ),
inference(superposition,[],[f772,f1230]) ).
fof(f22164,plain,
( spl0_890
| ~ spl0_198
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1918,f1900,f1814,f22162]) ).
fof(f22162,plain,
( spl0_890
<=> ! [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_890])]) ).
fof(f1918,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_198
| ~ spl0_208 ),
inference(resolution,[],[f1901,f1815]) ).
fof(f22139,plain,
( spl0_222
| spl0_889
| ~ spl0_260
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f14570,f3544,f2675,f22136,f2213]) ).
fof(f22136,plain,
( spl0_889
<=> member(regular(x),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f2675,plain,
( spl0_260
<=> ! [X0] :
( identity_relation = intersection(singleton_relation,X0)
| member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f3544,plain,
( spl0_318
<=> x = intersection(singleton_relation,complement(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f14570,plain,
( member(regular(x),element_relation)
| identity_relation = x
| ~ spl0_260
| ~ spl0_318 ),
inference(superposition,[],[f2676,f3546]) ).
fof(f3546,plain,
( x = intersection(singleton_relation,complement(element_relation))
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3544]) ).
fof(f2676,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| identity_relation = intersection(singleton_relation,X0) )
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f2675]) ).
fof(f22034,plain,
( spl0_888
| ~ spl0_139
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1996,f1954,f1178,f22032]) ).
fof(f22032,plain,
( spl0_888
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class)
| x = 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_888])]) ).
fof(f1996,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class)
| x = 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_139
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1179]) ).
fof(f22030,plain,
( spl0_887
| ~ spl0_138
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1988,f1954,f1174,f22028]) ).
fof(f22028,plain,
( spl0_887
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class)
| x = 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_887])]) ).
fof(f1988,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class)
| x = 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_138
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1175]) ).
fof(f22026,plain,
( spl0_886
| ~ spl0_139
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1970,f1950,f1178,f22024]) ).
fof(f22024,plain,
( spl0_886
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| x = 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_886])]) ).
fof(f1970,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| x = 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_139
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1179]) ).
fof(f22022,plain,
( spl0_885
| ~ spl0_138
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1962,f1950,f1174,f22020]) ).
fof(f22020,plain,
( spl0_885
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| x = 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_885])]) ).
fof(f1962,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| x = 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_138
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1175]) ).
fof(f22018,plain,
( spl0_884
| ~ spl0_93
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1204,f1178,f718,f22016]) ).
fof(f22016,plain,
( spl0_884
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| x = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f1204,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| x = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_139 ),
inference(resolution,[],[f1179,f719]) ).
fof(f22000,plain,
( spl0_883
| ~ spl0_93
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1187,f1174,f718,f21998]) ).
fof(f21998,plain,
( spl0_883
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| x = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f1187,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| x = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_138 ),
inference(resolution,[],[f1175,f719]) ).
fof(f21966,plain,
( spl0_882
| ~ spl0_194
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2139,f2122,f1737,f21964]) ).
fof(f21964,plain,
( spl0_882
<=> ! [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_882])]) ).
fof(f2139,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(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_194
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1738]) ).
fof(f21962,plain,
( spl0_881
| ~ spl0_15
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f2115,f2112,f271,f21960]) ).
fof(f21960,plain,
( spl0_881
<=> ! [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)
| x = 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_881])]) ).
fof(f2115,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)
| x = 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_15
| ~ spl0_215 ),
inference(resolution,[],[f2113,f272]) ).
fof(f21928,plain,
( spl0_880
| ~ spl0_194
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2179,f2128,f1737,f21926]) ).
fof(f21926,plain,
( spl0_880
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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_880])]) ).
fof(f2179,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_194
| ~ spl0_217 ),
inference(duplicate_literal_removal,[],[f2162]) ).
fof(f2162,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(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_194
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1738]) ).
fof(f21892,plain,
( spl0_879
| ~ spl0_27
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1987,f1954,f323,f21890]) ).
fof(f21890,plain,
( spl0_879
<=> ! [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)
| x = domain_of(domain_of(flip(cross_product(intersection(X1,cross_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_879])]) ).
fof(f1987,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)
| x = domain_of(domain_of(flip(cross_product(intersection(X1,cross_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_27
| ~ spl0_211 ),
inference(resolution,[],[f1955,f324]) ).
fof(f21888,plain,
( spl0_878
| ~ spl0_27
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1961,f1950,f323,f21886]) ).
fof(f21886,plain,
( spl0_878
<=> ! [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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_878])]) ).
fof(f1961,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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_27
| ~ spl0_210 ),
inference(resolution,[],[f1951,f324]) ).
fof(f21856,plain,
( spl0_877
| ~ spl0_137
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2103,f2099,f1124,f21854]) ).
fof(f21854,plain,
( spl0_877
<=> ! [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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_877])]) ).
fof(f2099,plain,
( spl0_214
<=> ! [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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_214])]) ).
fof(f2103,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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_137
| ~ spl0_214 ),
inference(resolution,[],[f2100,f1125]) ).
fof(f2100,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_214 ),
inference(avatar_component_clause,[],[f2099]) ).
fof(f21813,plain,
( spl0_876
| ~ spl0_174
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1997,f1954,f1542,f21811]) ).
fof(f21811,plain,
( spl0_876
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,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_876])]) ).
fof(f1542,plain,
( spl0_174
<=> ! [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_174])]) ).
fof(f1997,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_174
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1543]) ).
fof(f1543,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1542]) ).
fof(f21809,plain,
( spl0_875
| ~ spl0_174
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1971,f1950,f1542,f21807]) ).
fof(f21807,plain,
( spl0_875
<=> ! [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_875])]) ).
fof(f1971,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_174
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1543]) ).
fof(f21805,plain,
( spl0_874
| ~ spl0_164
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1923,f1900,f1456,f21803]) ).
fof(f21803,plain,
( spl0_874
<=> ! [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_874])]) ).
fof(f1923,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_164
| ~ spl0_208 ),
inference(resolution,[],[f1901,f1457]) ).
fof(f21801,plain,
( spl0_873
| ~ spl0_163
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1920,f1900,f1452,f21799]) ).
fof(f21799,plain,
( spl0_873
<=> ! [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_873])]) ).
fof(f1920,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_163
| ~ spl0_208 ),
inference(resolution,[],[f1901,f1453]) ).
fof(f21797,plain,
( spl0_872
| ~ spl0_93
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1562,f1542,f718,f21795]) ).
fof(f21795,plain,
( spl0_872
<=> ! [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_872])]) ).
fof(f1562,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_174 ),
inference(resolution,[],[f1543,f719]) ).
fof(f21774,plain,
( spl0_871
| ~ spl0_54
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1914,f1900,f485,f21772]) ).
fof(f21772,plain,
( spl0_871
<=> ! [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_871])]) ).
fof(f1914,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_54
| ~ spl0_208 ),
inference(resolution,[],[f1901,f486]) ).
fof(f21600,plain,
( spl0_870
| ~ spl0_79
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2160,f2128,f640,f21598]) ).
fof(f21598,plain,
( spl0_870
<=> ! [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_870])]) ).
fof(f2160,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
| ~ spl0_79
| ~ spl0_217 ),
inference(resolution,[],[f2129,f641]) ).
fof(f21596,plain,
( spl0_869
| ~ spl0_79
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2137,f2122,f640,f21594]) ).
fof(f21594,plain,
( spl0_869
<=> ! [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_869])]) ).
fof(f2137,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
| ~ spl0_79
| ~ spl0_216 ),
inference(resolution,[],[f2123,f641]) ).
fof(f21592,plain,
( ~ spl0_867
| spl0_868
| ~ spl0_18
| ~ spl0_721 ),
inference(avatar_split_clause,[],[f21308,f15466,f285,f21589,f21585]) ).
fof(f21585,plain,
( spl0_867
<=> inductive(complement(omega)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f15466,plain,
( spl0_721
<=> ! [X0] :
( x = X0
| ~ subclass(X0,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f21308,plain,
( omega = x
| ~ inductive(complement(omega))
| ~ spl0_18
| ~ spl0_721 ),
inference(resolution,[],[f15467,f286]) ).
fof(f15467,plain,
( ! [X0] :
( ~ subclass(X0,complement(X0))
| x = X0 )
| ~ spl0_721 ),
inference(avatar_component_clause,[],[f15466]) ).
fof(f21583,plain,
( spl0_866
| ~ spl0_96
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1692,f1644,f743,f21581]) ).
fof(f21581,plain,
( spl0_866
<=> ! [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_866])]) ).
fof(f1692,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,flip(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) )
| ~ spl0_96
| ~ spl0_186 ),
inference(resolution,[],[f1645,f744]) ).
fof(f21377,plain,
( spl0_865
| ~ spl0_179
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1936,f1929,f1598,f21375]) ).
fof(f21375,plain,
( spl0_865
<=> ! [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_865])]) ).
fof(f1598,plain,
( spl0_179
<=> ! [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_179])]) ).
fof(f1929,plain,
( spl0_209
<=> ! [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_209])]) ).
fof(f1936,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_179
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1599]) ).
fof(f1599,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_179 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f1930,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_209 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f21373,plain,
( spl0_864
| ~ spl0_178
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1935,f1929,f1594,f21371]) ).
fof(f21371,plain,
( spl0_864
<=> ! [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_864])]) ).
fof(f1594,plain,
( spl0_178
<=> ! [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_178])]) ).
fof(f1935,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_178
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1595]) ).
fof(f1595,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_178 ),
inference(avatar_component_clause,[],[f1594]) ).
fof(f21369,plain,
( ~ spl0_862
| spl0_863
| ~ spl0_6
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2228,f2209,f231,f21367,f21363]) ).
fof(f21367,plain,
( spl0_863
<=> ! [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(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3))))))),cross_product(universal_class,universal_class))
| x = 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(x,universal_class))),X3)
| ~ compatible(X2,domain_of(flip(cross_product(x,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(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,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_863])]) ).
fof(f2228,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(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,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(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(x,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(x,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(x,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(x,universal_class))),X3)
| homomorphism(X2,domain_of(flip(cross_product(x,universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(x,universal_class))))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_6
| ~ spl0_221 ),
inference(superposition,[],[f2210,f232]) ).
fof(f21345,plain,
( spl0_861
| ~ spl0_6
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2106,f2099,f231,f21343]) ).
fof(f21343,plain,
( spl0_861
<=> ! [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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),universal_class)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2106,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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))),universal_class)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_214 ),
inference(superposition,[],[f2100,f232]) ).
fof(f21244,plain,
( spl0_860
| ~ spl0_151
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2001,f1954,f1317,f21242]) ).
fof(f21242,plain,
( spl0_860
<=> ! [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_860])]) ).
fof(f2001,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_151
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1318]) ).
fof(f21240,plain,
( spl0_859
| ~ spl0_151
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1975,f1950,f1317,f21238]) ).
fof(f21238,plain,
( spl0_859
<=> ! [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_859])]) ).
fof(f1975,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_151
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1318]) ).
fof(f21236,plain,
( spl0_858
| ~ spl0_140
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1946,f1929,f1216,f21234]) ).
fof(f21234,plain,
( spl0_858
<=> ! [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_858])]) ).
fof(f1216,plain,
( spl0_140
<=> ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1946,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_140
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1217]) ).
fof(f1217,plain,
( ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f21232,plain,
( spl0_857
| ~ spl0_93
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1341,f1317,f718,f21230]) ).
fof(f21230,plain,
( spl0_857
<=> ! [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_857])]) ).
fof(f1341,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X0,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_151 ),
inference(resolution,[],[f1318,f719]) ).
fof(f21042,plain,
( spl0_856
| ~ spl0_168
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1938,f1929,f1516,f21040]) ).
fof(f21040,plain,
( spl0_856
<=> ! [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_856])]) ).
fof(f1516,plain,
( spl0_168
<=> ! [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_168])]) ).
fof(f1938,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_168
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1517]) ).
fof(f1517,plain,
( ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1516]) ).
fof(f21038,plain,
( spl0_855
| ~ spl0_81
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1423,f1380,f658,f21036]) ).
fof(f21036,plain,
( spl0_855
<=> ! [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_855])]) ).
fof(f1423,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_81
| ~ spl0_158 ),
inference(resolution,[],[f1381,f659]) ).
fof(f21034,plain,
( spl0_854
| ~ spl0_81
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1402,f1376,f658,f21032]) ).
fof(f21032,plain,
( spl0_854
<=> ! [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_854])]) ).
fof(f1402,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_81
| ~ spl0_157 ),
inference(resolution,[],[f1377,f659]) ).
fof(f21001,plain,
( spl0_853
| ~ spl0_79
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2102,f2099,f640,f20999]) ).
fof(f20999,plain,
( spl0_853
<=> ! [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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_853])]) ).
fof(f2102,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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_79
| ~ spl0_214 ),
inference(resolution,[],[f2100,f641]) ).
fof(f20797,plain,
( spl0_852
| ~ spl0_135
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2000,f1954,f1116,f20795]) ).
fof(f20795,plain,
( spl0_852
<=> ! [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_852])]) ).
fof(f2000,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_135
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1117]) ).
fof(f20793,plain,
( ~ spl0_851
| ~ spl0_682
| spl0_697 ),
inference(avatar_split_clause,[],[f20659,f14699,f13911,f20790]) ).
fof(f20790,plain,
( spl0_851
<=> subclass(element_relation,compose(element_relation,complement(identity_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f14699,plain,
( spl0_697
<=> member(regular(singleton_relation),compose(element_relation,complement(identity_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f20659,plain,
( ~ subclass(element_relation,compose(element_relation,complement(identity_relation)))
| ~ spl0_682
| spl0_697 ),
inference(resolution,[],[f14701,f13912]) ).
fof(f14701,plain,
( ~ member(regular(singleton_relation),compose(element_relation,complement(identity_relation)))
| spl0_697 ),
inference(avatar_component_clause,[],[f14699]) ).
fof(f20788,plain,
( spl0_850
| ~ spl0_135
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1974,f1950,f1116,f20786]) ).
fof(f20786,plain,
( spl0_850
<=> ! [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_850])]) ).
fof(f1974,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_135
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1117]) ).
fof(f20784,plain,
( spl0_849
| ~ spl0_197
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1933,f1929,f1807,f20782]) ).
fof(f20782,plain,
( spl0_849
<=> ! [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_849])]) ).
fof(f1807,plain,
( spl0_197
<=> ! [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_197])]) ).
fof(f1933,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_197
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1808]) ).
fof(f1808,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_197 ),
inference(avatar_component_clause,[],[f1807]) ).
fof(f20780,plain,
( spl0_848
| ~ spl0_93
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1152,f1116,f718,f20778]) ).
fof(f20778,plain,
( spl0_848
<=> ! [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_848])]) ).
fof(f1152,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_135 ),
inference(resolution,[],[f1117,f719]) ).
fof(f20764,plain,
( spl0_847
| ~ spl0_184
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1874,f1871,f1636,f20762]) ).
fof(f20762,plain,
( spl0_847
<=> ! [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_847])]) ).
fof(f1636,plain,
( spl0_184
<=> ! [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_184])]) ).
fof(f1871,plain,
( spl0_204
<=> ! [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_204])]) ).
fof(f1874,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_184
| ~ spl0_204 ),
inference(resolution,[],[f1872,f1637]) ).
fof(f1637,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_184 ),
inference(avatar_component_clause,[],[f1636]) ).
fof(f1872,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_204 ),
inference(avatar_component_clause,[],[f1871]) ).
fof(f20668,plain,
( spl0_846
| ~ spl0_135
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2156,f2128,f1116,f20666]) ).
fof(f20666,plain,
( spl0_846
<=> ! [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_846])]) ).
fof(f2156,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_135
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1117]) ).
fof(f20664,plain,
( spl0_845
| ~ spl0_135
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2133,f2122,f1116,f20662]) ).
fof(f20662,plain,
( spl0_845
<=> ! [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_845])]) ).
fof(f2133,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_135
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1117]) ).
fof(f20657,plain,
( spl0_844
| ~ spl0_183
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1664,f1640,f1625,f20655]) ).
fof(f20655,plain,
( spl0_844
<=> ! [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_844])]) ).
fof(f1640,plain,
( spl0_185
<=> ! [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_185])]) ).
fof(f1664,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_183
| ~ spl0_185 ),
inference(resolution,[],[f1641,f1626]) ).
fof(f1641,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_185 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f20630,plain,
( spl0_843
| ~ spl0_45
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2031,f2010,f417,f20628]) ).
fof(f20628,plain,
( spl0_843
<=> ! [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_843])]) ).
fof(f2031,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_45
| ~ spl0_212 ),
inference(resolution,[],[f2011,f418]) ).
fof(f20625,plain,
( spl0_842
| spl0_748
| ~ spl0_81
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1557,f1542,f658,f16108,f20623]) ).
fof(f20623,plain,
( spl0_842
<=> ! [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_842])]) ).
fof(f16108,plain,
( spl0_748
<=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f1557,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_81
| ~ spl0_174 ),
inference(resolution,[],[f1543,f659]) ).
fof(f20544,plain,
( spl0_841
| ~ spl0_38
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2035,f2010,f374,f20542]) ).
fof(f20542,plain,
( spl0_841
<=> ! [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_841])]) ).
fof(f2035,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_38
| ~ spl0_212 ),
inference(resolution,[],[f2011,f375]) ).
fof(f20540,plain,
( spl0_840
| ~ spl0_39
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2034,f2010,f378,f20538]) ).
fof(f20538,plain,
( spl0_840
<=> ! [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_840])]) ).
fof(f2034,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_39
| ~ spl0_212 ),
inference(resolution,[],[f2011,f379]) ).
fof(f20536,plain,
( spl0_839
| ~ spl0_89
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2024,f2010,f699,f20534]) ).
fof(f20534,plain,
( spl0_839
<=> ! [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_839])]) ).
fof(f699,plain,
( spl0_89
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f2024,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,compose(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_89
| ~ spl0_212 ),
inference(resolution,[],[f2011,f700]) ).
fof(f700,plain,
( ! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f20532,plain,
( spl0_838
| ~ spl0_84
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1906,f1900,f676,f20530]) ).
fof(f20530,plain,
( spl0_838
<=> ! [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_838])]) ).
fof(f676,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(f1906,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_208 ),
inference(resolution,[],[f1901,f677]) ).
fof(f677,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,[],[f676]) ).
fof(f20147,plain,
( spl0_837
| ~ spl0_15
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2157,f2128,f271,f20145]) ).
fof(f20145,plain,
( spl0_837
<=> ! [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_837])]) ).
fof(f2157,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_15
| ~ spl0_217 ),
inference(resolution,[],[f2129,f272]) ).
fof(f20143,plain,
( spl0_237
| ~ spl0_836
| ~ spl0_108
| spl0_789 ),
inference(avatar_split_clause,[],[f18480,f17661,f823,f20140,f2334]) ).
fof(f20140,plain,
( spl0_836
<=> subclass(subset_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f17661,plain,
( spl0_789
<=> member(regular(subset_relation),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f18480,plain,
( ~ subclass(subset_relation,successor_relation)
| subset_relation = x
| ~ spl0_108
| spl0_789 ),
inference(resolution,[],[f17662,f824]) ).
fof(f17662,plain,
( ~ member(regular(subset_relation),successor_relation)
| spl0_789 ),
inference(avatar_component_clause,[],[f17661]) ).
fof(f20138,plain,
( spl0_835
| ~ spl0_15
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2134,f2122,f271,f20136]) ).
fof(f20136,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))),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_835])]) ).
fof(f2134,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_15
| ~ spl0_216 ),
inference(resolution,[],[f2123,f272]) ).
fof(f20134,plain,
( spl0_834
| ~ spl0_28
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2037,f2010,f327,f20132]) ).
fof(f20132,plain,
( spl0_834
<=> ! [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_834])]) ).
fof(f2037,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_28
| ~ spl0_212 ),
inference(resolution,[],[f2011,f328]) ).
fof(f20130,plain,
( spl0_833
| ~ spl0_649
| ~ spl0_91
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2013,f2010,f708,f12699,f20128]) ).
fof(f20128,plain,
( spl0_833
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| compose(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))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f12699,plain,
( spl0_649
<=> subclass(composition_function,application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f708,plain,
( spl0_91
<=> ! [X4,X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f2013,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))
| compose(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))))))) )
| ~ spl0_91
| ~ spl0_212 ),
inference(resolution,[],[f2011,f709]) ).
fof(f709,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4 )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f20105,plain,
( spl0_832
| ~ spl0_56
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f20022,f1529,f493,f20103]) ).
fof(f20103,plain,
( spl0_832
<=> ! [X0] : intersection(X0,application_function) = intersection(application_function,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f1529,plain,
( spl0_171
<=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f20022,plain,
( ! [X0] : intersection(X0,application_function) = intersection(application_function,X0)
| ~ spl0_56
| ~ spl0_171 ),
inference(superposition,[],[f494,f1531]) ).
fof(f1531,plain,
( cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f20101,plain,
( ~ spl0_831
| spl0_169
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f20014,f1529,f1520,f20098]) ).
fof(f20098,plain,
( spl0_831
<=> composition_function = application_function ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f1520,plain,
( spl0_169
<=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f20014,plain,
( composition_function != application_function
| spl0_169
| ~ spl0_171 ),
inference(superposition,[],[f1521,f1531]) ).
fof(f1521,plain,
( composition_function != cross_product(universal_class,cross_product(universal_class,universal_class))
| spl0_169 ),
inference(avatar_component_clause,[],[f1520]) ).
fof(f20091,plain,
( spl0_649
| ~ spl0_31
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f20011,f1529,f339,f12699]) ).
fof(f20011,plain,
( subclass(composition_function,application_function)
| ~ spl0_31
| ~ spl0_171 ),
inference(superposition,[],[f341,f1531]) ).
fof(f20010,plain,
( spl0_830
| spl0_172
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1943,f1929,f1533,f20007]) ).
fof(f20007,plain,
( spl0_830
<=> 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_830])]) ).
fof(f1533,plain,
( spl0_172
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1943,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_172
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1535]) ).
fof(f1535,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| spl0_172 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f20004,plain,
( spl0_829
| ~ spl0_32
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f19916,f1520,f345,f20001]) ).
fof(f20001,plain,
( spl0_829
<=> subclass(application_function,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f19916,plain,
( subclass(application_function,composition_function)
| ~ spl0_32
| ~ spl0_169 ),
inference(superposition,[],[f347,f1522]) ).
fof(f1522,plain,
( composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1520]) ).
fof(f19991,plain,
( ~ spl0_828
| ~ spl0_169
| spl0_235 ),
inference(avatar_split_clause,[],[f19920,f2323,f1520,f19988]) ).
fof(f19920,plain,
( ~ member(x,composition_function)
| ~ spl0_169
| spl0_235 ),
inference(superposition,[],[f2324,f1522]) ).
fof(f19914,plain,
( spl0_827
| spl0_170
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1941,f1929,f1524,f19911]) ).
fof(f19911,plain,
( spl0_827
<=> 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_827])]) ).
fof(f1524,plain,
( spl0_170
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1941,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_170
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1526]) ).
fof(f1526,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| spl0_170 ),
inference(avatar_component_clause,[],[f1524]) ).
fof(f19909,plain,
( spl0_826
| ~ spl0_160
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1940,f1929,f1388,f19907]) ).
fof(f19907,plain,
( spl0_826
<=> ! [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_826])]) ).
fof(f1388,plain,
( spl0_160
<=> ! [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_160])]) ).
fof(f1940,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_160
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1389]) ).
fof(f1389,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1388]) ).
fof(f19905,plain,
( spl0_824
| ~ spl0_825
| ~ spl0_129
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2046,f2010,f997,f19902,f19899]) ).
fof(f19899,plain,
( spl0_824
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f19902,plain,
( spl0_825
<=> subclass(composition_function,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2046,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,singleton_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) )
| ~ spl0_129
| ~ spl0_212 ),
inference(resolution,[],[f2011,f998]) ).
fof(f19897,plain,
( spl0_822
| ~ spl0_823
| ~ spl0_130
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2044,f2010,f1001,f19894,f19891]) ).
fof(f19891,plain,
( spl0_822
<=> ! [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_822])]) ).
fof(f19894,plain,
( spl0_823
<=> subclass(composition_function,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2044,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_130
| ~ spl0_212 ),
inference(resolution,[],[f2011,f1002]) ).
fof(f19842,plain,
( spl0_239
| ~ spl0_586
| ~ spl0_606
| ~ spl0_640 ),
inference(avatar_split_clause,[],[f19720,f12197,f10996,f10475,f2358]) ).
fof(f2358,plain,
( spl0_239
<=> member(subset_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f10475,plain,
( spl0_586
<=> subclass(universal_class,complement(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f12197,plain,
( spl0_640
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f19720,plain,
( member(subset_relation,universal_class)
| ~ spl0_586
| ~ spl0_606
| ~ spl0_640 ),
inference(forward_demodulation,[],[f19715,f10998]) ).
fof(f19715,plain,
( member(subset_relation,complement(x))
| ~ spl0_586
| ~ spl0_640 ),
inference(resolution,[],[f12198,f10477]) ).
fof(f10477,plain,
( subclass(universal_class,complement(x))
| ~ spl0_586 ),
inference(avatar_component_clause,[],[f10475]) ).
fof(f12198,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(subset_relation,X0) )
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f12197]) ).
fof(f19841,plain,
( spl0_821
| ~ spl0_46
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1945,f1929,f421,f19839]) ).
fof(f19839,plain,
( spl0_821
<=> ! [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_821])]) ).
fof(f421,plain,
( spl0_46
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1945,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_46
| ~ spl0_209 ),
inference(resolution,[],[f1930,f422]) ).
fof(f422,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f19837,plain,
( spl0_820
| ~ spl0_89
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1910,f1900,f699,f19835]) ).
fof(f19835,plain,
( spl0_820
<=> ! [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_820])]) ).
fof(f1910,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_89
| ~ spl0_208 ),
inference(resolution,[],[f1901,f700]) ).
fof(f19833,plain,
( spl0_819
| ~ spl0_94
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1168,f1124,f734,f19831]) ).
fof(f19831,plain,
( spl0_819
<=> ! [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_819])]) ).
fof(f734,plain,
( spl0_94
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1168,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| ~ spl0_94
| ~ spl0_137 ),
inference(resolution,[],[f1125,f735]) ).
fof(f735,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f734]) ).
fof(f19752,plain,
( spl0_818
| ~ spl0_56
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1980,f1950,f493,f19750]) ).
fof(f19750,plain,
( spl0_818
<=> ! [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_818])]) ).
fof(f1980,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_56
| ~ spl0_210 ),
inference(superposition,[],[f1951,f494]) ).
fof(f19746,plain,
( spl0_817
| ~ spl0_159
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1932,f1929,f1384,f19744]) ).
fof(f19744,plain,
( spl0_817
<=> ! [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_817])]) ).
fof(f1384,plain,
( spl0_159
<=> ! [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_159])]) ).
fof(f1932,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_159
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1385]) ).
fof(f1385,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1384]) ).
fof(f19742,plain,
( ~ spl0_815
| spl0_816
| ~ spl0_186
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1827,f1814,f1644,f19740,f19736]) ).
fof(f19736,plain,
( spl0_815
<=> 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_815])]) ).
fof(f19740,plain,
( spl0_816
<=> ! [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_816])]) ).
fof(f1827,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_186
| ~ spl0_198 ),
inference(resolution,[],[f1815,f1645]) ).
fof(f19713,plain,
( spl0_814
| ~ spl0_101
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1248,f1229,f766,f19711]) ).
fof(f19711,plain,
( spl0_814
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f1248,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) = x )
| ~ spl0_101
| ~ spl0_141 ),
inference(superposition,[],[f767,f1230]) ).
fof(f19706,plain,
( spl0_813
| ~ spl0_45
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1913,f1900,f417,f19704]) ).
fof(f19704,plain,
( spl0_813
<=> ! [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_813])]) ).
fof(f1913,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_45
| ~ spl0_208 ),
inference(resolution,[],[f1901,f418]) ).
fof(f19662,plain,
( spl0_812
| ~ spl0_38
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1917,f1900,f374,f19660]) ).
fof(f19660,plain,
( spl0_812
<=> ! [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_812])]) ).
fof(f1917,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_38
| ~ spl0_208 ),
inference(resolution,[],[f1901,f375]) ).
fof(f19658,plain,
( spl0_811
| ~ spl0_39
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1916,f1900,f378,f19656]) ).
fof(f19656,plain,
( spl0_811
<=> ! [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_811])]) ).
fof(f1916,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_39
| ~ spl0_208 ),
inference(resolution,[],[f1901,f379]) ).
fof(f19637,plain,
( spl0_238
| ~ spl0_38
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f3964,f3896,f374,f2338]) ).
fof(f3964,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_38
| ~ spl0_328 ),
inference(resolution,[],[f3898,f375]) ).
fof(f19636,plain,
( spl0_810
| ~ spl0_81
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1200,f1178,f658,f19634]) ).
fof(f19634,plain,
( spl0_810
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
| x = intersection(X0,cross_product(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f1200,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
| x = intersection(X0,cross_product(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) )
| ~ spl0_81
| ~ spl0_139 ),
inference(resolution,[],[f1179,f659]) ).
fof(f19632,plain,
( spl0_809
| ~ spl0_81
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1183,f1174,f658,f19630]) ).
fof(f19630,plain,
( spl0_809
<=> ! [X2,X0,X1] :
( ~ member(intersection(cross_product(X0,X1),X2),universal_class)
| x = intersection(cross_product(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f1183,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(cross_product(X0,X1),X2),universal_class)
| x = intersection(cross_product(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) )
| ~ spl0_81
| ~ spl0_138 ),
inference(resolution,[],[f1175,f659]) ).
fof(f19590,plain,
( spl0_808
| ~ spl0_28
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1919,f1900,f327,f19588]) ).
fof(f19588,plain,
( spl0_808
<=> ! [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_808])]) ).
fof(f1919,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_28
| ~ spl0_208 ),
inference(resolution,[],[f1901,f328]) ).
fof(f19572,plain,
( spl0_807
| ~ spl0_141
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2190,f2181,f1229,f19570]) ).
fof(f19570,plain,
( spl0_807
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2190,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) = x )
| ~ spl0_141
| ~ spl0_218 ),
inference(superposition,[],[f2182,f1230]) ).
fof(f19550,plain,
( spl0_806
| ~ spl0_129
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1926,f1900,f997,f19548]) ).
fof(f19548,plain,
( spl0_806
<=> ! [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_806])]) ).
fof(f1926,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_129
| ~ spl0_208 ),
inference(resolution,[],[f1901,f998]) ).
fof(f19546,plain,
( spl0_805
| ~ spl0_130
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1924,f1900,f1001,f19544]) ).
fof(f19544,plain,
( spl0_805
<=> ! [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_805])]) ).
fof(f1924,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_130
| ~ spl0_208 ),
inference(resolution,[],[f1901,f1002]) ).
fof(f19465,plain,
( spl0_804
| ~ spl0_45
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f1898,f1894,f417,f19463]) ).
fof(f19463,plain,
( spl0_804
<=> ! [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_804])]) ).
fof(f1898,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_45
| ~ spl0_207 ),
inference(resolution,[],[f1895,f418]) ).
fof(f19353,plain,
( spl0_803
| ~ spl0_176
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2171,f2128,f1579,f19351]) ).
fof(f19351,plain,
( spl0_803
<=> ! [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(x,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))
| x = 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_803])]) ).
fof(f1579,plain,
( spl0_176
<=> ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(x,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))
| x = 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_176])]) ).
fof(f2171,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(x,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))
| x = 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_176
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1580]) ).
fof(f1580,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(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1579]) ).
fof(f19349,plain,
( spl0_802
| ~ spl0_11
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2167,f2128,f254,f19347]) ).
fof(f19347,plain,
( spl0_802
<=> ! [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)
| x = 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_802])]) ).
fof(f254,plain,
( spl0_11
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| x = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f2167,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)
| x = 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_11
| ~ spl0_217 ),
inference(resolution,[],[f2129,f255]) ).
fof(f255,plain,
( ! [X0,X4] :
( member(X4,domain_of(X0))
| ~ member(X4,universal_class)
| x = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f19345,plain,
( spl0_801
| ~ spl0_176
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2148,f2122,f1579,f19343]) ).
fof(f19343,plain,
( spl0_801
<=> ! [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(x,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))
| x = 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_801])]) ).
fof(f2148,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(x,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))
| x = 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_176
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1580]) ).
fof(f19341,plain,
( spl0_800
| ~ spl0_11
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2144,f2122,f254,f19339]) ).
fof(f19339,plain,
( spl0_800
<=> ! [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)
| x = 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_800])]) ).
fof(f2144,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)
| x = 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_11
| ~ spl0_216 ),
inference(resolution,[],[f2123,f255]) ).
fof(f19060,plain,
( spl0_799
| ~ spl0_16
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f18843,f1281,f275,f19057]) ).
fof(f19057,plain,
( spl0_799
<=> subclass(element_relation,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f1281,plain,
( spl0_147
<=> cross_product(universal_class,universal_class) = domain_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f18843,plain,
( subclass(element_relation,domain_relation)
| ~ spl0_16
| ~ spl0_147 ),
inference(superposition,[],[f277,f1283]) ).
fof(f1283,plain,
( cross_product(universal_class,universal_class) = domain_relation
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1281]) ).
fof(f19055,plain,
( ~ spl0_798
| spl0_125
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f18861,f1281,f979,f19052]) ).
fof(f19052,plain,
( spl0_798
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(domain_relation,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f979,plain,
( spl0_125
<=> 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_125])]) ).
fof(f18861,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(domain_relation,universal_class)),universal_class)))))
| spl0_125
| ~ spl0_147 ),
inference(superposition,[],[f981,f1283]) ).
fof(f981,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
| spl0_125 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f19049,plain,
( ~ spl0_797
| ~ spl0_147
| spl0_227 ),
inference(avatar_split_clause,[],[f18886,f2270,f1281,f19046]) ).
fof(f19046,plain,
( spl0_797
<=> member(identity_relation,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2270,plain,
( spl0_227
<=> member(identity_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f18886,plain,
( ~ member(identity_relation,domain_relation)
| ~ spl0_147
| spl0_227 ),
inference(superposition,[],[f2271,f1283]) ).
fof(f2271,plain,
( ~ member(identity_relation,cross_product(universal_class,universal_class))
| spl0_227 ),
inference(avatar_component_clause,[],[f2270]) ).
fof(f19044,plain,
( ~ spl0_796
| spl0_123
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f18860,f1281,f971,f19041]) ).
fof(f18860,plain,
( ~ member(x,domain_relation)
| spl0_123
| ~ spl0_147 ),
inference(superposition,[],[f973,f1283]) ).
fof(f18842,plain,
( spl0_795
| spl0_148
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1942,f1929,f1285,f18839]) ).
fof(f18839,plain,
( spl0_795
<=> 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_795])]) ).
fof(f1285,plain,
( spl0_148
<=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1942,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_148
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1287]) ).
fof(f1287,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| spl0_148 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f18712,plain,
( ~ spl0_794
| ~ spl0_548
| ~ spl0_564
| ~ spl0_778 ),
inference(avatar_split_clause,[],[f17041,f16831,f9135,f8637,f18709]) ).
fof(f16831,plain,
( spl0_778
<=> ! [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_778])]) ).
fof(f17041,plain,
( ~ subclass(universal_class,flip(x))
| ~ spl0_548
| ~ spl0_564
| ~ spl0_778 ),
inference(forward_demodulation,[],[f17025,f9137]) ).
fof(f17025,plain,
( ~ subclass(universal_class,flip(domain_of(x)))
| ~ spl0_548
| ~ spl0_778 ),
inference(resolution,[],[f16832,f8638]) ).
fof(f16832,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_778 ),
inference(avatar_component_clause,[],[f16831]) ).
fof(f18174,plain,
( spl0_237
| ~ spl0_239
| spl0_793
| ~ spl0_78
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1212,f1178,f635,f18171,f2358,f2334]) ).
fof(f18171,plain,
( spl0_793
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1212,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(subset_relation,universal_class)
| subset_relation = x
| ~ spl0_78
| ~ spl0_139 ),
inference(superposition,[],[f1179,f637]) ).
fof(f17789,plain,
( spl0_792
| ~ spl0_237
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f3950,f3947,f2334,f17787]) ).
fof(f17787,plain,
( spl0_792
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f3950,plain,
( ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_237
| ~ spl0_331 ),
inference(forward_demodulation,[],[f3948,f2336]) ).
fof(f2336,plain,
( subset_relation = x
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2334]) ).
fof(f17766,plain,
( spl0_791
| ~ spl0_16
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f17452,f1272,f275,f17763]) ).
fof(f17763,plain,
( spl0_791
<=> subclass(element_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f1272,plain,
( spl0_145
<=> cross_product(universal_class,universal_class) = successor_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f17452,plain,
( subclass(element_relation,successor_relation)
| ~ spl0_16
| ~ spl0_145 ),
inference(superposition,[],[f277,f1274]) ).
fof(f1274,plain,
( cross_product(universal_class,universal_class) = successor_relation
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1272]) ).
fof(f17761,plain,
( ~ spl0_790
| spl0_125
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f17470,f1272,f979,f17758]) ).
fof(f17758,plain,
( spl0_790
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(successor_relation,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f17470,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(successor_relation,universal_class)),universal_class)))))
| spl0_125
| ~ spl0_145 ),
inference(superposition,[],[f981,f1274]) ).
fof(f17664,plain,
( spl0_789
| ~ spl0_145
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f17497,f2338,f1272,f17661]) ).
fof(f17497,plain,
( member(regular(subset_relation),successor_relation)
| ~ spl0_145
| ~ spl0_238 ),
inference(superposition,[],[f2340,f1274]) ).
fof(f17658,plain,
( ~ spl0_788
| ~ spl0_145
| spl0_227 ),
inference(avatar_split_clause,[],[f17495,f2270,f1272,f17655]) ).
fof(f17655,plain,
( spl0_788
<=> member(identity_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f17495,plain,
( ~ member(identity_relation,successor_relation)
| ~ spl0_145
| spl0_227 ),
inference(superposition,[],[f2271,f1274]) ).
fof(f17653,plain,
( ~ spl0_787
| spl0_123
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f17469,f1272,f971,f17650]) ).
fof(f17469,plain,
( ~ member(x,successor_relation)
| spl0_123
| ~ spl0_145 ),
inference(superposition,[],[f973,f1274]) ).
fof(f17451,plain,
( spl0_786
| spl0_146
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1937,f1929,f1276,f17448]) ).
fof(f17448,plain,
( spl0_786
<=> not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1276,plain,
( spl0_146
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1937,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_146
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1278]) ).
fof(f1278,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| spl0_146 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f17318,plain,
( ~ spl0_785
| ~ spl0_548
| ~ spl0_564
| ~ spl0_777 ),
inference(avatar_split_clause,[],[f16937,f16827,f9135,f8637,f17315]) ).
fof(f16827,plain,
( spl0_777
<=> ! [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_777])]) ).
fof(f16937,plain,
( ~ subclass(universal_class,rotate(x))
| ~ spl0_548
| ~ spl0_564
| ~ spl0_777 ),
inference(forward_demodulation,[],[f16921,f9137]) ).
fof(f16921,plain,
( ~ subclass(universal_class,rotate(domain_of(x)))
| ~ spl0_548
| ~ spl0_777 ),
inference(resolution,[],[f16828,f8638]) ).
fof(f16828,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_777 ),
inference(avatar_component_clause,[],[f16827]) ).
fof(f17288,plain,
( spl0_784
| ~ spl0_17
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f17072,f1263,f280,f17285]) ).
fof(f17285,plain,
( spl0_784
<=> subclass(successor_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1263,plain,
( spl0_143
<=> element_relation = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f17072,plain,
( subclass(successor_relation,element_relation)
| ~ spl0_17
| ~ spl0_143 ),
inference(superposition,[],[f282,f1265]) ).
fof(f1265,plain,
( element_relation = cross_product(universal_class,universal_class)
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f17283,plain,
( ~ spl0_783
| spl0_125
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f17089,f1263,f979,f17280]) ).
fof(f17280,plain,
( spl0_783
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f17089,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class)))))
| spl0_125
| ~ spl0_143 ),
inference(superposition,[],[f981,f1265]) ).
fof(f17278,plain,
( ~ spl0_782
| ~ spl0_143
| spl0_227 ),
inference(avatar_split_clause,[],[f17114,f2270,f1263,f17275]) ).
fof(f17275,plain,
( spl0_782
<=> member(identity_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f17114,plain,
( ~ member(identity_relation,element_relation)
| ~ spl0_143
| spl0_227 ),
inference(superposition,[],[f2271,f1265]) ).
fof(f17272,plain,
( spl0_69
| ~ spl0_123
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f17088,f1263,f971,f584]) ).
fof(f584,plain,
( spl0_69
<=> member(x,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f17088,plain,
( member(x,element_relation)
| ~ spl0_123
| ~ spl0_143 ),
inference(superposition,[],[f972,f1265]) ).
fof(f972,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f17070,plain,
( spl0_781
| spl0_144
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1934,f1929,f1267,f17067]) ).
fof(f17067,plain,
( spl0_781
<=> 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_781])]) ).
fof(f1267,plain,
( spl0_144
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1934,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_144
| ~ spl0_209 ),
inference(resolution,[],[f1930,f1269]) ).
fof(f1269,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| spl0_144 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f17049,plain,
( spl0_780
| ~ spl0_141
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2176,f2128,f1229,f17047]) ).
fof(f17047,plain,
( spl0_780
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f2176,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) = x )
| ~ spl0_141
| ~ spl0_217 ),
inference(superposition,[],[f2129,f1230]) ).
fof(f17045,plain,
( spl0_779
| ~ spl0_115
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2042,f2010,f905,f17043]) ).
fof(f17043,plain,
( spl0_779
<=> ! [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))
| x = 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_779])]) ).
fof(f2042,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))
| x = 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_115
| ~ spl0_212 ),
inference(resolution,[],[f2011,f906]) ).
fof(f16833,plain,
( spl0_778
| ~ spl0_96
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1143,f1116,f743,f16831]) ).
fof(f1143,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
| ~ spl0_96
| ~ spl0_135 ),
inference(resolution,[],[f1117,f744]) ).
fof(f16829,plain,
( spl0_777
| ~ spl0_95
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1142,f1116,f739,f16827]) ).
fof(f1142,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
| ~ spl0_95
| ~ spl0_135 ),
inference(resolution,[],[f1117,f740]) ).
fof(f16822,plain,
( spl0_775
| ~ spl0_776
| ~ spl0_80
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2023,f2010,f654,f16819,f16816]) ).
fof(f16816,plain,
( spl0_775
<=> ! [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_775])]) ).
fof(f16819,plain,
( spl0_776
<=> subclass(composition_function,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f654,plain,
( spl0_80
<=> ! [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_80])]) ).
fof(f2023,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_80
| ~ spl0_212 ),
inference(resolution,[],[f2011,f655]) ).
fof(f655,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_80 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f16814,plain,
( spl0_774
| ~ spl0_80
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1909,f1900,f654,f16812]) ).
fof(f16812,plain,
( spl0_774
<=> ! [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_774])]) ).
fof(f1909,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_80
| ~ spl0_208 ),
inference(resolution,[],[f1901,f655]) ).
fof(f16760,plain,
( spl0_773
| ~ spl0_166
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2170,f2128,f1502,f16758]) ).
fof(f16758,plain,
( spl0_773
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),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(x,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))
| x = 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_773])]) ).
fof(f1502,plain,
( spl0_166
<=> ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2170,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(x,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))
| x = 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_166
| ~ spl0_217 ),
inference(resolution,[],[f2129,f1503]) ).
fof(f1503,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(x,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))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f16756,plain,
( spl0_772
| ~ spl0_166
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2147,f2122,f1502,f16754]) ).
fof(f16754,plain,
( spl0_772
<=> ! [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(x,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))
| x = 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_772])]) ).
fof(f2147,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(x,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))
| x = 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_166
| ~ spl0_216 ),
inference(resolution,[],[f2123,f1503]) ).
fof(f16752,plain,
( ~ spl0_771
| ~ spl0_548
| ~ spl0_564
| ~ spl0_692 ),
inference(avatar_split_clause,[],[f16642,f14332,f9135,f8637,f16749]) ).
fof(f16749,plain,
( spl0_771
<=> subclass(subset_relation,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f16642,plain,
( ~ subclass(subset_relation,x)
| ~ spl0_548
| ~ spl0_564
| ~ spl0_692 ),
inference(forward_demodulation,[],[f16632,f9137]) ).
fof(f16632,plain,
( ~ subclass(subset_relation,domain_of(x))
| ~ spl0_548
| ~ spl0_692 ),
inference(resolution,[],[f14333,f8638]) ).
fof(f16698,plain,
( spl0_770
| ~ spl0_100
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1247,f1229,f760,f16696]) ).
fof(f16696,plain,
( spl0_770
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f1247,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) = x )
| ~ spl0_100
| ~ spl0_141 ),
inference(superposition,[],[f761,f1230]) ).
fof(f16667,plain,
( spl0_769
| ~ spl0_54
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1764,f1733,f485,f16665]) ).
fof(f16665,plain,
( spl0_769
<=> ! [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_769])]) ).
fof(f1764,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_54
| ~ spl0_193 ),
inference(resolution,[],[f1734,f486]) ).
fof(f16662,plain,
( spl0_767
| ~ spl0_768
| ~ spl0_164
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1704,f1644,f1456,f16659,f16656]) ).
fof(f16656,plain,
( spl0_767
<=> ! [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_767])]) ).
fof(f16659,plain,
( spl0_768
<=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f1704,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_164
| ~ spl0_186 ),
inference(resolution,[],[f1645,f1457]) ).
fof(f16654,plain,
( spl0_765
| ~ spl0_766
| ~ spl0_163
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1701,f1644,f1452,f16651,f16648]) ).
fof(f16648,plain,
( spl0_765
<=> ! [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_765])]) ).
fof(f16651,plain,
( spl0_766
<=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f1701,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_163
| ~ spl0_186 ),
inference(resolution,[],[f1645,f1453]) ).
fof(f16646,plain,
( spl0_764
| ~ spl0_81
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1337,f1317,f658,f16644]) ).
fof(f16644,plain,
( spl0_764
<=> ! [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_764])]) ).
fof(f1337,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_81
| ~ spl0_151 ),
inference(resolution,[],[f1318,f659]) ).
fof(f16454,plain,
( spl0_763
| ~ spl0_111
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1999,f1954,f849,f16452]) ).
fof(f16452,plain,
( spl0_763
<=> ! [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))
| x = 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_763])]) ).
fof(f1999,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))
| x = 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_111
| ~ spl0_211 ),
inference(resolution,[],[f1955,f850]) ).
fof(f16450,plain,
( spl0_762
| ~ spl0_110
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1990,f1954,f845,f16448]) ).
fof(f16448,plain,
( spl0_762
<=> ! [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))
| x = 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_762])]) ).
fof(f1990,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))
| x = 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_110
| ~ spl0_211 ),
inference(resolution,[],[f1955,f846]) ).
fof(f16446,plain,
( spl0_761
| ~ spl0_111
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1973,f1950,f849,f16444]) ).
fof(f16444,plain,
( spl0_761
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(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))
| x = 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_761])]) ).
fof(f1973,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))
| x = 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_111
| ~ spl0_210 ),
inference(resolution,[],[f1951,f850]) ).
fof(f16442,plain,
( spl0_760
| ~ spl0_110
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1964,f1950,f845,f16440]) ).
fof(f16440,plain,
( spl0_760
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(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))
| x = 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_760])]) ).
fof(f1964,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))
| x = 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_110
| ~ spl0_210 ),
inference(resolution,[],[f1951,f846]) ).
fof(f16438,plain,
( spl0_759
| ~ spl0_93
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f872,f849,f718,f16436]) ).
fof(f16436,plain,
( spl0_759
<=> ! [X0,X3,X2,X1] :
( x = 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_759])]) ).
fof(f872,plain,
( ! [X2,X3,X0,X1] :
( x = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_111 ),
inference(resolution,[],[f850,f719]) ).
fof(f16434,plain,
( spl0_758
| ~ spl0_93
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f858,f845,f718,f16432]) ).
fof(f16432,plain,
( spl0_758
<=> ! [X0,X3,X2,X1] :
( x = 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_758])]) ).
fof(f858,plain,
( ! [X2,X3,X0,X1] :
( x = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_110 ),
inference(resolution,[],[f846,f719]) ).
fof(f16282,plain,
( spl0_757
| ~ spl0_75
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2025,f2010,f618,f16280]) ).
fof(f16280,plain,
( spl0_757
<=> ! [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_757])]) ).
fof(f618,plain,
( spl0_75
<=> ! [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_75])]) ).
fof(f2025,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_75
| ~ spl0_212 ),
inference(resolution,[],[f2011,f619]) ).
fof(f619,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_75 ),
inference(avatar_component_clause,[],[f618]) ).
fof(f16278,plain,
( spl0_756
| ~ spl0_54
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1741,f1729,f485,f16276]) ).
fof(f16276,plain,
( spl0_756
<=> ! [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_756])]) ).
fof(f1741,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_54
| ~ spl0_192 ),
inference(resolution,[],[f1730,f486]) ).
fof(f16274,plain,
( spl0_755
| ~ spl0_54
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1696,f1644,f485,f16272]) ).
fof(f16272,plain,
( spl0_755
<=> ! [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_755])]) ).
fof(f1696,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_54
| ~ spl0_186 ),
inference(resolution,[],[f1645,f486]) ).
fof(f16270,plain,
( ~ spl0_754
| ~ spl0_548
| ~ spl0_564
| ~ spl0_682 ),
inference(avatar_split_clause,[],[f16103,f13911,f9135,f8637,f16267]) ).
fof(f16103,plain,
( ~ subclass(element_relation,x)
| ~ spl0_548
| ~ spl0_564
| ~ spl0_682 ),
inference(forward_demodulation,[],[f16093,f9137]) ).
fof(f16093,plain,
( ~ subclass(element_relation,domain_of(x))
| ~ spl0_548
| ~ spl0_682 ),
inference(resolution,[],[f13912,f8638]) ).
fof(f16265,plain,
( spl0_753
| ~ spl0_55
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1663,f1640,f489,f16263]) ).
fof(f16263,plain,
( spl0_753
<=> ! [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_753])]) ).
fof(f1663,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_55
| ~ spl0_185 ),
inference(resolution,[],[f1641,f490]) ).
fof(f16261,plain,
( spl0_752
| ~ spl0_142
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1632,f1625,f1259,f16259]) ).
fof(f16259,plain,
( spl0_752
<=> ! [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_752])]) ).
fof(f1259,plain,
( spl0_142
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1632,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
| subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
| ~ spl0_142
| ~ spl0_183 ),
inference(resolution,[],[f1626,f1260]) ).
fof(f1260,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f16225,plain,
( spl0_751
| ~ spl0_56
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1886,f1877,f493,f16223]) ).
fof(f16223,plain,
( spl0_751
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X1))
| x = domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f1877,plain,
( spl0_205
<=> ! [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))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_205])]) ).
fof(f1886,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X1))
| x = domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_56
| ~ spl0_205 ),
inference(superposition,[],[f1878,f494]) ).
fof(f1878,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))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_205 ),
inference(avatar_component_clause,[],[f1877]) ).
fof(f16221,plain,
( spl0_750
| ~ spl0_56
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1883,f1877,f493,f16219]) ).
fof(f16219,plain,
( spl0_750
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_750])]) ).
fof(f1883,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_56
| ~ spl0_205 ),
inference(superposition,[],[f1878,f494]) ).
fof(f16201,plain,
( spl0_749
| ~ spl0_72
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2018,f2010,f602,f16199]) ).
fof(f16199,plain,
( spl0_749
<=> ! [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_749])]) ).
fof(f602,plain,
( spl0_72
<=> ! [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_72])]) ).
fof(f2018,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_72
| ~ spl0_212 ),
inference(resolution,[],[f2011,f603]) ).
fof(f603,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_72 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f16110,plain,
( spl0_747
| spl0_748
| ~ spl0_81
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1148,f1116,f658,f16108,f16105]) ).
fof(f16105,plain,
( spl0_747
<=> ! [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_747])]) ).
fof(f1148,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_81
| ~ spl0_135 ),
inference(resolution,[],[f1117,f659]) ).
fof(f16030,plain,
( spl0_746
| ~ spl0_137
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1881,f1877,f1124,f16028]) ).
fof(f16028,plain,
( spl0_746
<=> ! [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))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_746])]) ).
fof(f1881,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))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_137
| ~ spl0_205 ),
inference(resolution,[],[f1878,f1125]) ).
fof(f15995,plain,
( spl0_745
| ~ spl0_99
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1246,f1229,f756,f15993]) ).
fof(f15993,plain,
( spl0_745
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f756,plain,
( spl0_99
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1246,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) = x )
| ~ spl0_99
| ~ spl0_141 ),
inference(superposition,[],[f757,f1230]) ).
fof(f757,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f15930,plain,
( spl0_743
| ~ spl0_744
| ~ spl0_67
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2026,f2010,f576,f15927,f15924]) ).
fof(f15924,plain,
( spl0_743
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| 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_743])]) ).
fof(f15927,plain,
( spl0_744
<=> subclass(composition_function,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f576,plain,
( spl0_67
<=> ! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f2026,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,domain_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
| ~ spl0_67
| ~ spl0_212 ),
inference(resolution,[],[f2011,f577]) ).
fof(f577,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
| domain_of(X0) = X1 )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f15922,plain,
( spl0_742
| ~ spl0_89
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1688,f1644,f699,f15920]) ).
fof(f15920,plain,
( spl0_742
<=> ! [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_742])]) ).
fof(f1688,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,compose(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_89
| ~ spl0_186 ),
inference(resolution,[],[f1645,f700]) ).
fof(f15918,plain,
( spl0_741
| ~ spl0_34
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1631,f1625,f358,f15916]) ).
fof(f15916,plain,
( spl0_741
<=> ! [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_741])]) ).
fof(f1631,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
| subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_34
| ~ spl0_183 ),
inference(resolution,[],[f1626,f359]) ).
fof(f15719,plain,
( spl0_739
| ~ spl0_740
| ~ spl0_64
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2021,f2010,f562,f15716,f15713]) ).
fof(f15713,plain,
( spl0_739
<=> ! [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_739])]) ).
fof(f15716,plain,
( spl0_740
<=> subclass(composition_function,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f562,plain,
( spl0_64
<=> ! [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_64])]) ).
fof(f2021,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_64
| ~ spl0_212 ),
inference(resolution,[],[f2011,f563]) ).
fof(f563,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X0,X1) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f15711,plain,
( spl0_738
| ~ spl0_150
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1668,f1640,f1294,f15709]) ).
fof(f15709,plain,
( spl0_738
<=> ! [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_738])]) ).
fof(f1668,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_150
| ~ spl0_185 ),
inference(resolution,[],[f1641,f1295]) ).
fof(f15707,plain,
( ~ spl0_737
| ~ spl0_30
| spl0_729 ),
inference(avatar_split_clause,[],[f15653,f15649,f335,f15704]) ).
fof(f15704,plain,
( spl0_737
<=> function(composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f15649,plain,
( spl0_729
<=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f15653,plain,
( ~ function(composition_function)
| ~ spl0_30
| spl0_729 ),
inference(resolution,[],[f15651,f336]) ).
fof(f15651,plain,
( ~ subclass(composition_function,cross_product(universal_class,universal_class))
| spl0_729 ),
inference(avatar_component_clause,[],[f15649]) ).
fof(f15702,plain,
( spl0_736
| ~ spl0_149
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1666,f1640,f1290,f15700]) ).
fof(f15700,plain,
( spl0_736
<=> ! [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_736])]) ).
fof(f1666,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_149
| ~ spl0_185 ),
inference(resolution,[],[f1641,f1291]) ).
fof(f15698,plain,
( spl0_735
| ~ spl0_158
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1497,f1456,f1380,f15696]) ).
fof(f15696,plain,
( spl0_735
<=> ! [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_735])]) ).
fof(f1497,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_158
| ~ spl0_164 ),
inference(resolution,[],[f1457,f1381]) ).
fof(f15694,plain,
( spl0_734
| ~ spl0_157
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1487,f1456,f1376,f15692]) ).
fof(f15692,plain,
( spl0_734
<=> ! [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_734])]) ).
fof(f1487,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_157
| ~ spl0_164 ),
inference(resolution,[],[f1457,f1377]) ).
fof(f15690,plain,
( spl0_733
| ~ spl0_158
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1475,f1452,f1380,f15688]) ).
fof(f15688,plain,
( spl0_733
<=> ! [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_733])]) ).
fof(f1475,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_158
| ~ spl0_163 ),
inference(resolution,[],[f1453,f1381]) ).
fof(f15686,plain,
( spl0_732
| ~ spl0_157
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1465,f1452,f1376,f15684]) ).
fof(f15684,plain,
( spl0_732
<=> ! [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_732])]) ).
fof(f1465,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_157
| ~ spl0_163 ),
inference(resolution,[],[f1453,f1377]) ).
fof(f15682,plain,
( spl0_731
| ~ spl0_88
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1169,f1124,f694,f15680]) ).
fof(f15680,plain,
( spl0_731
<=> ! [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_731])]) ).
fof(f694,plain,
( spl0_88
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1169,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) )
| ~ spl0_88
| ~ spl0_137 ),
inference(resolution,[],[f1125,f695]) ).
fof(f695,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f15657,plain,
( spl0_730
| ~ spl0_81
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1086,f1029,f658,f15655]) ).
fof(f15655,plain,
( spl0_730
<=> ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f1086,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) )
| ~ spl0_81
| ~ spl0_132 ),
inference(resolution,[],[f1030,f659]) ).
fof(f15652,plain,
( spl0_728
| ~ spl0_729
| ~ spl0_175
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2019,f2010,f1570,f15649,f15646]) ).
fof(f15646,plain,
( spl0_728
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| x = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),compose(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f1570,plain,
( spl0_175
<=> ! [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)
| x = 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_175])]) ).
fof(f2019,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),universal_class)
| x = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_175
| ~ spl0_212 ),
inference(resolution,[],[f2011,f1571]) ).
fof(f1571,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)
| x = 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_175 ),
inference(avatar_component_clause,[],[f1570]) ).
fof(f15644,plain,
( spl0_727
| ~ spl0_15
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f6492,f6463,f271,f15641]) ).
fof(f6492,plain,
( member(not_subclass_element(cross_product(x,x),identity_relation),universal_class)
| ~ spl0_15
| ~ spl0_454 ),
inference(superposition,[],[f272,f6465]) ).
fof(f15535,plain,
( spl0_726
| ~ spl0_141
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2153,f2122,f1229,f15533]) ).
fof(f15533,plain,
( spl0_726
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2153,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) = x )
| ~ spl0_141
| ~ spl0_216 ),
inference(superposition,[],[f2123,f1230]) ).
fof(f15531,plain,
( spl0_725
| ~ spl0_115
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1922,f1900,f905,f15529]) ).
fof(f15529,plain,
( spl0_725
<=> ! [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)
| x = 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_725])]) ).
fof(f1922,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)
| x = 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_115
| ~ spl0_208 ),
inference(resolution,[],[f1901,f906]) ).
fof(f15527,plain,
( spl0_724
| ~ spl0_96
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1245,f1229,f743,f15525]) ).
fof(f15525,plain,
( spl0_724
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1245,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) = x )
| ~ spl0_96
| ~ spl0_141 ),
inference(superposition,[],[f744,f1230]) ).
fof(f15476,plain,
( spl0_723
| ~ spl0_151
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1835,f1814,f1317,f15474]) ).
fof(f15474,plain,
( spl0_723
<=> ! [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_723])]) ).
fof(f1835,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_151
| ~ spl0_198 ),
inference(resolution,[],[f1815,f1318]) ).
fof(f15472,plain,
( spl0_722
| ~ spl0_50
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1665,f1640,f465,f15470]) ).
fof(f15470,plain,
( spl0_722
<=> ! [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_722])]) ).
fof(f1665,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_50
| ~ spl0_185 ),
inference(resolution,[],[f1641,f466]) ).
fof(f15468,plain,
( spl0_721
| ~ spl0_3
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2649,f2410,f217,f15466]) ).
fof(f2649,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(X0)) )
| ~ spl0_3
| ~ spl0_246 ),
inference(duplicate_literal_removal,[],[f2620]) ).
fof(f2620,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,complement(X0))
| x = X0 )
| ~ spl0_3
| ~ spl0_246 ),
inference(resolution,[],[f2411,f218]) ).
fof(f15422,plain,
( spl0_720
| ~ spl0_6
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2199,f2192,f231,f15420]) ).
fof(f15420,plain,
( spl0_720
<=> ! [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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X1),universal_class)))),X2)
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2199,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(x,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X1),universal_class)))),X2)
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_219 ),
inference(superposition,[],[f2193,f232]) ).
fof(f15418,plain,
( spl0_719
| ~ spl0_132
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1995,f1954,f1029,f15416]) ).
fof(f15416,plain,
( spl0_719
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f1995,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class)
| x = X1 )
| ~ spl0_132
| ~ spl0_211 ),
inference(resolution,[],[f1955,f1030]) ).
fof(f15414,plain,
( spl0_718
| ~ spl0_132
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1969,f1950,f1029,f15412]) ).
fof(f15412,plain,
( spl0_718
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(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)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1969,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class)
| x = X1 )
| ~ spl0_132
| ~ spl0_210 ),
inference(resolution,[],[f1951,f1030]) ).
fof(f15410,plain,
( spl0_717
| ~ spl0_93
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1090,f1029,f718,f15408]) ).
fof(f15408,plain,
( spl0_717
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X0,universal_class)
| x = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1090,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X0,universal_class)
| x = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_132 ),
inference(resolution,[],[f1030,f719]) ).
fof(f15361,plain,
( spl0_716
| ~ spl0_45
| ~ spl0_122 ),
inference(avatar_split_clause,[],[f15357,f966,f417,f15359]) ).
fof(f15359,plain,
( spl0_716
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(domain_of(domain_of(flip(cross_product(x,universal_class)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f15357,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(domain_of(domain_of(flip(cross_product(x,universal_class)))),X0) )
| ~ spl0_45
| ~ spl0_122 ),
inference(resolution,[],[f968,f418]) ).
fof(f968,plain,
( member(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f966]) ).
fof(f15344,plain,
( spl0_715
| ~ spl0_661
| ~ spl0_714 ),
inference(avatar_split_clause,[],[f15340,f15335,f13255,f15342]) ).
fof(f15342,plain,
( spl0_715
<=> ! [X0,X1] :
( x = domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f15335,plain,
( spl0_714
<=> ! [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(x,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(x,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(x,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(x,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f15340,plain,
( ! [X0,X1] :
( x = domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_661
| ~ spl0_714 ),
inference(forward_demodulation,[],[f15339,f13257]) ).
fof(f13257,plain,
( x = domain_of(domain_of(flip(cross_product(x,universal_class))))
| ~ spl0_661 ),
inference(avatar_component_clause,[],[f13255]) ).
fof(f15339,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(x,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_661
| ~ spl0_714 ),
inference(forward_demodulation,[],[f15338,f13257]) ).
fof(f15338,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(x,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(x,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(x,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(x,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_661
| ~ spl0_714 ),
inference(forward_demodulation,[],[f15336,f13257]) ).
fof(f15336,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(x,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(x,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_714 ),
inference(avatar_component_clause,[],[f15335]) ).
fof(f15337,plain,
( spl0_714
| ~ spl0_6
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1884,f1877,f231,f15335]) ).
fof(f1884,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(x,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(x,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(x,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(x,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_205 ),
inference(superposition,[],[f1878,f232]) ).
fof(f15255,plain,
( spl0_713
| ~ spl0_75
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1911,f1900,f618,f15253]) ).
fof(f15253,plain,
( spl0_713
<=> ! [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_713])]) ).
fof(f1911,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_75
| ~ spl0_208 ),
inference(resolution,[],[f1901,f619]) ).
fof(f15251,plain,
( ~ spl0_712
| spl0_222
| ~ spl0_223
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2638,f2410,f2217,f2213,f15248]) ).
fof(f15248,plain,
( spl0_712
<=> subclass(identity_relation,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f2638,plain,
( identity_relation = x
| ~ subclass(identity_relation,complement(subset_relation))
| ~ spl0_223
| ~ spl0_246 ),
inference(resolution,[],[f2411,f2219]) ).
fof(f15246,plain,
( spl0_711
| ~ spl0_89
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1133,f1116,f699,f15244]) ).
fof(f15244,plain,
( spl0_711
<=> ! [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_711])]) ).
fof(f1133,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,compose(X0,X1))
| member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_89
| ~ spl0_135 ),
inference(resolution,[],[f1117,f700]) ).
fof(f15132,plain,
( spl0_710
| ~ spl0_45
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1856,f1847,f417,f15130]) ).
fof(f15130,plain,
( spl0_710
<=> ! [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_710])]) ).
fof(f1856,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_45
| ~ spl0_199 ),
inference(resolution,[],[f1848,f418]) ).
fof(f15128,plain,
( ~ spl0_708
| spl0_709
| ~ spl0_135
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1834,f1814,f1116,f15126,f15122]) ).
fof(f15122,plain,
( spl0_708
<=> 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_708])]) ).
fof(f15126,plain,
( spl0_709
<=> ! [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_709])]) ).
fof(f1834,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_135
| ~ spl0_198 ),
inference(resolution,[],[f1815,f1117]) ).
fof(f15120,plain,
( spl0_707
| ~ spl0_78
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1673,f1640,f635,f15118]) ).
fof(f15118,plain,
( spl0_707
<=> ! [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_707])]) ).
fof(f1673,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
| subclass(X0,subset_relation) )
| ~ spl0_78
| ~ spl0_185 ),
inference(superposition,[],[f1641,f637]) ).
fof(f15006,plain,
( spl0_706
| ~ spl0_79
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1880,f1877,f640,f15004]) ).
fof(f15004,plain,
( spl0_706
<=> ! [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))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_706])]) ).
fof(f1880,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))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_79
| ~ spl0_205 ),
inference(resolution,[],[f1878,f641]) ).
fof(f15002,plain,
( spl0_705
| ~ spl0_95
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1244,f1229,f739,f15000]) ).
fof(f15000,plain,
( spl0_705
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f1244,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) = x )
| ~ spl0_95
| ~ spl0_141 ),
inference(superposition,[],[f740,f1230]) ).
fof(f14932,plain,
( spl0_704
| ~ spl0_67
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1912,f1900,f576,f14930]) ).
fof(f14930,plain,
( spl0_704
<=> ! [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_704])]) ).
fof(f1912,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) )
| ~ spl0_67
| ~ spl0_208 ),
inference(resolution,[],[f1901,f577]) ).
fof(f14928,plain,
( spl0_703
| ~ spl0_140
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1656,f1636,f1216,f14926]) ).
fof(f14926,plain,
( spl0_703
<=> ! [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_703])]) ).
fof(f1656,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_140
| ~ spl0_184 ),
inference(resolution,[],[f1637,f1217]) ).
fof(f14924,plain,
( spl0_702
| ~ spl0_78
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1551,f1538,f635,f14922]) ).
fof(f14922,plain,
( spl0_702
<=> ! [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_702])]) ).
fof(f1538,plain,
( spl0_173
<=> ! [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_173])]) ).
fof(f1551,plain,
( ! [X0,X1] :
( ~ subclass(subset_relation,X0)
| ~ member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(X1,X0) )
| ~ spl0_78
| ~ spl0_173 ),
inference(superposition,[],[f1539,f637]) ).
fof(f1539,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1538]) ).
fof(f14869,plain,
( ~ spl0_701
| spl0_188
| ~ spl0_189
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2628,f2410,f1714,f1710,f14866]) ).
fof(f2628,plain,
( singleton_relation = x
| ~ subclass(singleton_relation,complement(element_relation))
| ~ spl0_189
| ~ spl0_246 ),
inference(resolution,[],[f2411,f1716]) ).
fof(f14762,plain,
( spl0_700
| ~ spl0_64
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1907,f1900,f562,f14760]) ).
fof(f14760,plain,
( spl0_700
<=> ! [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_700])]) ).
fof(f1907,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_64
| ~ spl0_208 ),
inference(resolution,[],[f1901,f563]) ).
fof(f14740,plain,
( spl0_699
| ~ spl0_19
| ~ spl0_84
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1684,f1644,f676,f289,f14738]) ).
fof(f14738,plain,
( spl0_699
<=> ! [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_699])]) ).
fof(f1684,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_186 ),
inference(resolution,[],[f1645,f677]) ).
fof(f14736,plain,
( spl0_698
| ~ spl0_137
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1662,f1640,f1124,f14734]) ).
fof(f14734,plain,
( spl0_698
<=> ! [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_698])]) ).
fof(f1662,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_137
| ~ spl0_185 ),
inference(resolution,[],[f1641,f1125]) ).
fof(f14702,plain,
( ~ spl0_697
| ~ spl0_28
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2469,f2414,f327,f14699]) ).
fof(f2469,plain,
( ~ member(regular(singleton_relation),compose(element_relation,complement(identity_relation)))
| ~ spl0_28
| ~ spl0_247 ),
inference(resolution,[],[f2416,f328]) ).
fof(f14601,plain,
( spl0_222
| ~ spl0_371
| spl0_696
| ~ spl0_49
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1197,f1174,f434,f14598,f4963,f2213]) ).
fof(f4963,plain,
( spl0_371
<=> member(identity_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f14598,plain,
( spl0_696
<=> 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_696])]) ).
fof(f1197,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(identity_relation,universal_class)
| identity_relation = x
| ~ spl0_49
| ~ spl0_138 ),
inference(superposition,[],[f1175,f436]) ).
fof(f14582,plain,
( spl0_227
| ~ spl0_9
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f14394,f2478,f244,f2270]) ).
fof(f2478,plain,
( spl0_250
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f14394,plain,
( member(identity_relation,cross_product(universal_class,universal_class))
| ~ spl0_9
| ~ spl0_250 ),
inference(resolution,[],[f2479,f245]) ).
fof(f2479,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(identity_relation,X0) )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2478]) ).
fof(f14580,plain,
( spl0_695
| ~ spl0_81
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2441,f2270,f658,f14577]) ).
fof(f14577,plain,
( spl0_695
<=> identity_relation = unordered_pair(unordered_pair(first(identity_relation),first(identity_relation)),unordered_pair(first(identity_relation),unordered_pair(second(identity_relation),second(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f2441,plain,
( identity_relation = unordered_pair(unordered_pair(first(identity_relation),first(identity_relation)),unordered_pair(first(identity_relation),unordered_pair(second(identity_relation),second(identity_relation))))
| ~ spl0_81
| ~ spl0_227 ),
inference(resolution,[],[f2272,f659]) ).
fof(f2272,plain,
( member(identity_relation,cross_product(universal_class,universal_class))
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2270]) ).
fof(f14552,plain,
( spl0_230
| ~ spl0_45
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f2276,f971,f417,f2290]) ).
fof(f2290,plain,
( spl0_230
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2276,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(x,X0) )
| ~ spl0_45
| ~ spl0_123 ),
inference(resolution,[],[f972,f418]) ).
fof(f14527,plain,
( spl0_371
| ~ spl0_7
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f14395,f2478,f235,f4963]) ).
fof(f14395,plain,
( member(identity_relation,universal_class)
| ~ spl0_7
| ~ spl0_250 ),
inference(resolution,[],[f2479,f236]) ).
fof(f14402,plain,
( spl0_694
| ~ spl0_222
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2499,f2496,f2213,f14400]) ).
fof(f14400,plain,
( spl0_694
<=> ! [X0] :
( identity_relation = intersection(X0,singleton_relation)
| member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2499,plain,
( ! [X0] :
( identity_relation = intersection(X0,singleton_relation)
| member(regular(intersection(X0,singleton_relation)),element_relation) )
| ~ spl0_222
| ~ spl0_252 ),
inference(forward_demodulation,[],[f2497,f2215]) ).
fof(f2215,plain,
( identity_relation = x
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2213]) ).
fof(f14383,plain,
( spl0_693
| spl0_123
| ~ spl0_29
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f795,f782,f331,f971,f14381]) ).
fof(f14381,plain,
( spl0_693
<=> ! [X0,X1] : ~ inductive(compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f782,plain,
( spl0_104
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(x,X1)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f795,plain,
( ! [X0,X1] :
( member(x,cross_product(universal_class,universal_class))
| ~ inductive(compose(X0,X1)) )
| ~ spl0_29
| ~ spl0_104 ),
inference(resolution,[],[f783,f332]) ).
fof(f783,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(x,X1)
| ~ inductive(X0) )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f782]) ).
fof(f14334,plain,
( spl0_692
| ~ spl0_45
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2284,f2217,f417,f14332]) ).
fof(f2284,plain,
( ! [X0] :
( ~ subclass(subset_relation,X0)
| member(regular(identity_relation),X0) )
| ~ spl0_45
| ~ spl0_223 ),
inference(resolution,[],[f2219,f418]) ).
fof(f14330,plain,
( spl0_691
| ~ spl0_33
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1486,f1456,f354,f14328]) ).
fof(f14328,plain,
( spl0_691
<=> ! [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_691])]) ).
fof(f1486,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_33
| ~ spl0_164 ),
inference(resolution,[],[f1457,f355]) ).
fof(f14326,plain,
( spl0_690
| ~ spl0_33
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1464,f1452,f354,f14324]) ).
fof(f14324,plain,
( spl0_690
<=> ! [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_690])]) ).
fof(f1464,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_33
| ~ spl0_163 ),
inference(resolution,[],[f1453,f355]) ).
fof(f14322,plain,
( spl0_689
| ~ spl0_54
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1422,f1380,f485,f14320]) ).
fof(f14320,plain,
( spl0_689
<=> ! [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_689])]) ).
fof(f1422,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_54
| ~ spl0_158 ),
inference(resolution,[],[f1381,f486]) ).
fof(f14318,plain,
( spl0_688
| ~ spl0_54
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1401,f1376,f485,f14316]) ).
fof(f14316,plain,
( spl0_688
<=> ! [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_688])]) ).
fof(f1401,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_54
| ~ spl0_157 ),
inference(resolution,[],[f1377,f486]) ).
fof(f14314,plain,
( spl0_687
| ~ spl0_84
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1165,f1124,f676,f14312]) ).
fof(f14312,plain,
( spl0_687
<=> ! [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_687])]) ).
fof(f1165,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_137 ),
inference(resolution,[],[f1125,f677]) ).
fof(f14310,plain,
( ~ spl0_4
| ~ spl0_685
| spl0_686
| ~ spl0_66
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1159,f1120,f570,f14307,f14303,f221]) ).
fof(f221,plain,
( spl0_4
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f14303,plain,
( spl0_685
<=> 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_685])]) ).
fof(f14307,plain,
( spl0_686
<=> 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_686])]) ).
fof(f570,plain,
( spl0_66
<=> ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1120,plain,
( spl0_136
<=> ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1159,plain,
( omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))))
| ~ inductive(omega)
| ~ spl0_66
| ~ spl0_136 ),
inference(resolution,[],[f1121,f571]) ).
fof(f571,plain,
( ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f1121,plain,
( ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f14124,plain,
( spl0_188
| ~ spl0_200
| spl0_684
| ~ spl0_48
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1196,f1174,f429,f14121,f1851,f1710]) ).
fof(f14121,plain,
( spl0_684
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1196,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),complement(compose(element_relation,complement(identity_relation))))
| ~ member(singleton_relation,universal_class)
| singleton_relation = x
| ~ spl0_48
| ~ spl0_138 ),
inference(superposition,[],[f1175,f431]) ).
fof(f13963,plain,
( spl0_683
| ~ spl0_188
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f4988,f4984,f1710,f13961]) ).
fof(f13961,plain,
( spl0_683
<=> ! [X2,X0,X1] :
( singleton_relation = X0
| member(not_subclass_element(intersection(regular(X0),X1),X2),singleton_relation)
| subclass(intersection(regular(X0),X1),X2)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f4984,plain,
( spl0_375
<=> ! [X2,X0,X1] :
( subclass(intersection(regular(X0),X1),X2)
| member(not_subclass_element(intersection(regular(X0),X1),X2),x)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f4988,plain,
( ! [X2,X0,X1] :
( singleton_relation = X0
| member(not_subclass_element(intersection(regular(X0),X1),X2),singleton_relation)
| subclass(intersection(regular(X0),X1),X2)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0) )
| ~ spl0_188
| ~ spl0_375 ),
inference(forward_demodulation,[],[f4987,f1712]) ).
fof(f4987,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(regular(X0),X1),X2),singleton_relation)
| subclass(intersection(regular(X0),X1),X2)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| x = X0 )
| ~ spl0_188
| ~ spl0_375 ),
inference(forward_demodulation,[],[f4985,f1712]) ).
fof(f4985,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| member(not_subclass_element(intersection(regular(X0),X1),X2),x)
| subclass(intersection(regular(X0),X1),X2)
| x = X0 )
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f4984]) ).
fof(f13913,plain,
( spl0_682
| ~ spl0_45
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f2126,f1714,f417,f13911]) ).
fof(f2126,plain,
( ! [X0] :
( ~ subclass(element_relation,X0)
| member(regular(singleton_relation),X0) )
| ~ spl0_45
| ~ spl0_189 ),
inference(resolution,[],[f1716,f418]) ).
fof(f13878,plain,
( spl0_681
| ~ spl0_72
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1904,f1900,f602,f13876]) ).
fof(f13876,plain,
( spl0_681
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f1904,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_72
| ~ spl0_208 ),
inference(resolution,[],[f1901,f603]) ).
fof(f13874,plain,
( spl0_680
| ~ spl0_73
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1903,f1900,f606,f13872]) ).
fof(f13872,plain,
( spl0_680
<=> ! [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_680])]) ).
fof(f606,plain,
( spl0_73
<=> ! [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_73])]) ).
fof(f1903,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_73
| ~ spl0_208 ),
inference(resolution,[],[f1901,f607]) ).
fof(f607,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_73 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f13870,plain,
( spl0_679
| ~ spl0_46
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1654,f1636,f421,f13868]) ).
fof(f13868,plain,
( spl0_679
<=> ! [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_679])]) ).
fof(f1654,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_46
| ~ spl0_184 ),
inference(resolution,[],[f1637,f422]) ).
fof(f13866,plain,
( spl0_678
| ~ spl0_54
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1556,f1542,f485,f13864]) ).
fof(f13864,plain,
( spl0_678
<=> ! [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_678])]) ).
fof(f1556,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_54
| ~ spl0_174 ),
inference(resolution,[],[f1543,f486]) ).
fof(f13636,plain,
( spl0_677
| ~ spl0_30
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1812,f1807,f335,f13634]) ).
fof(f13634,plain,
( spl0_677
<=> ! [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_677])]) ).
fof(f1812,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_30
| ~ spl0_197 ),
inference(resolution,[],[f1808,f336]) ).
fof(f13632,plain,
( spl0_676
| ~ spl0_45
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1792,f1737,f417,f13630]) ).
fof(f13630,plain,
( spl0_676
<=> ! [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_676])]) ).
fof(f1792,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_45
| ~ spl0_194 ),
inference(resolution,[],[f1738,f418]) ).
fof(f13628,plain,
( spl0_675
| ~ spl0_45
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1763,f1733,f417,f13626]) ).
fof(f13626,plain,
( spl0_675
<=> ! [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_675])]) ).
fof(f1763,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_45
| ~ spl0_193 ),
inference(resolution,[],[f1734,f418]) ).
fof(f13624,plain,
( spl0_674
| ~ spl0_45
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1740,f1729,f417,f13622]) ).
fof(f13622,plain,
( spl0_674
<=> ! [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_674])]) ).
fof(f1740,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_45
| ~ spl0_192 ),
inference(resolution,[],[f1730,f418]) ).
fof(f13620,plain,
( spl0_673
| ~ spl0_136
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1655,f1636,f1120,f13618]) ).
fof(f13618,plain,
( spl0_673
<=> ! [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_673])]) ).
fof(f1655,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_136
| ~ spl0_184 ),
inference(resolution,[],[f1637,f1121]) ).
fof(f13600,plain,
( spl0_672
| ~ spl0_6
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2202,f2192,f231,f13598]) ).
fof(f13598,plain,
( spl0_672
<=> ! [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(x,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),X2)
| x = 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_672])]) ).
fof(f2202,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(x,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(x,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(x,universal_class)))),X2)
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_6
| ~ spl0_219 ),
inference(superposition,[],[f2193,f232]) ).
fof(f13596,plain,
( ~ spl0_671
| spl0_571
| ~ spl0_661 ),
inference(avatar_split_clause,[],[f13265,f13255,f9571,f13593]) ).
fof(f13265,plain,
( x != cross_product(x,universal_class)
| spl0_571
| ~ spl0_661 ),
inference(superposition,[],[f9572,f13257]) ).
fof(f13591,plain,
( spl0_670
| ~ spl0_175
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1905,f1900,f1570,f13589]) ).
fof(f13589,plain,
( spl0_670
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
| ~ member(not_homomorphism2(X0,X1,X2),universal_class)
| x = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1905,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
| ~ member(not_homomorphism2(X0,X1,X2),universal_class)
| x = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_175
| ~ spl0_208 ),
inference(resolution,[],[f1901,f1571]) ).
fof(f13549,plain,
( spl0_669
| ~ spl0_112
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2045,f2010,f881,f13547]) ).
fof(f13547,plain,
( spl0_669
<=> ! [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))))))),x)
| ~ 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)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f2045,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))))))),x)
| ~ 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)
| x = X0 )
| ~ spl0_112
| ~ spl0_212 ),
inference(resolution,[],[f2011,f882]) ).
fof(f13362,plain,
( spl0_668
| ~ spl0_38
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1767,f1733,f374,f13360]) ).
fof(f13360,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1767,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_38
| ~ spl0_193 ),
inference(resolution,[],[f1734,f375]) ).
fof(f13356,plain,
( ~ spl0_20
| spl0_122
| ~ spl0_661 ),
inference(avatar_split_clause,[],[f13262,f13255,f966,f294]) ).
fof(f13262,plain,
( ~ member(x,universal_class)
| spl0_122
| ~ spl0_661 ),
inference(superposition,[],[f967,f13257]) ).
fof(f13355,plain,
( spl0_667
| ~ spl0_39
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1766,f1733,f378,f13353]) ).
fof(f13353,plain,
( spl0_667
<=> ! [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_667])]) ).
fof(f1766,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_39
| ~ spl0_193 ),
inference(resolution,[],[f1734,f379]) ).
fof(f13351,plain,
( spl0_666
| ~ spl0_38
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1744,f1729,f374,f13349]) ).
fof(f13349,plain,
( spl0_666
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1744,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_38
| ~ spl0_192 ),
inference(resolution,[],[f1730,f375]) ).
fof(f13347,plain,
( spl0_665
| ~ spl0_39
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1743,f1729,f378,f13345]) ).
fof(f13345,plain,
( spl0_665
<=> ! [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_665])]) ).
fof(f1743,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_39
| ~ spl0_192 ),
inference(resolution,[],[f1730,f379]) ).
fof(f13343,plain,
( spl0_664
| ~ spl0_45
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1695,f1644,f417,f13341]) ).
fof(f13341,plain,
( spl0_664
<=> ! [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_664])]) ).
fof(f1695,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_45
| ~ spl0_186 ),
inference(resolution,[],[f1645,f418]) ).
fof(f13339,plain,
( spl0_663
| ~ spl0_55
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1298,f1259,f489,f13337]) ).
fof(f13337,plain,
( spl0_663
<=> ! [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_663])]) ).
fof(f1298,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_55
| ~ spl0_142 ),
inference(resolution,[],[f1260,f490]) ).
fof(f13261,plain,
( spl0_661
| spl0_662
| ~ spl0_6
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f1887,f1877,f231,f13259,f13255]) ).
fof(f13259,plain,
( spl0_662
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(x,universal_class))))),regular(domain_of(domain_of(flip(cross_product(x,universal_class)))))))),cross_product(universal_class,universal_class))
| x = 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(x,universal_class))))),regular(domain_of(domain_of(flip(cross_product(x,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_662])]) ).
fof(f1887,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(x,universal_class))))),regular(domain_of(domain_of(flip(cross_product(x,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(x,universal_class))))),regular(domain_of(domain_of(flip(cross_product(x,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))
| x = domain_of(domain_of(flip(cross_product(x,universal_class))))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_6
| ~ spl0_205 ),
inference(superposition,[],[f1878,f232]) ).
fof(f13240,plain,
( spl0_660
| ~ spl0_115
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1091,f1029,f905,f13238]) ).
fof(f13238,plain,
( spl0_660
<=> ! [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)
| x = X0
| x = 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_660])]) ).
fof(f1091,plain,
( ! [X0] :
( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
| ~ member(X0,universal_class)
| x = X0
| x = 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_115
| ~ spl0_132 ),
inference(resolution,[],[f1030,f906]) ).
fof(f13127,plain,
( spl0_659
| ~ spl0_73
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2017,f2010,f606,f13125]) ).
fof(f13125,plain,
( spl0_659
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2017,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_73
| ~ spl0_212 ),
inference(resolution,[],[f2011,f607]) ).
fof(f13123,plain,
( spl0_658
| ~ spl0_28
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1768,f1733,f327,f13121]) ).
fof(f13121,plain,
( spl0_658
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1768,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_28
| ~ spl0_193 ),
inference(resolution,[],[f1734,f328]) ).
fof(f13119,plain,
( spl0_657
| ~ spl0_28
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1745,f1729,f327,f13117]) ).
fof(f13117,plain,
( spl0_657
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,complement(X1))
| ~ member(X2,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1745,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_28
| ~ spl0_192 ),
inference(resolution,[],[f1730,f328]) ).
fof(f13115,plain,
( spl0_656
| ~ spl0_38
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1699,f1644,f374,f13113]) ).
fof(f13113,plain,
( spl0_656
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f1699,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_38
| ~ spl0_186 ),
inference(resolution,[],[f1645,f375]) ).
fof(f13111,plain,
( spl0_655
| ~ spl0_39
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1698,f1644,f378,f13109]) ).
fof(f13109,plain,
( spl0_655
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f1698,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_39
| ~ spl0_186 ),
inference(resolution,[],[f1645,f379]) ).
fof(f13106,plain,
( spl0_654
| ~ spl0_3
| ~ spl0_548
| ~ spl0_549 ),
inference(avatar_split_clause,[],[f8951,f8641,f8637,f217,f13104]) ).
fof(f13104,plain,
( spl0_654
<=> ! [X0] : subclass(intersection(universal_class,X0),complement(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f8641,plain,
( spl0_549
<=> ! [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_549])]) ).
fof(f8951,plain,
( ! [X0] : subclass(intersection(universal_class,X0),complement(x))
| ~ spl0_3
| ~ spl0_548
| ~ spl0_549 ),
inference(forward_demodulation,[],[f8931,f8836]) ).
fof(f8931,plain,
( ! [X0] : subclass(intersection(universal_class,X0),complement(domain_of(x)))
| ~ spl0_548
| ~ spl0_549 ),
inference(resolution,[],[f8642,f8638]) ).
fof(f8642,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_549 ),
inference(avatar_component_clause,[],[f8641]) ).
fof(f13102,plain,
( spl0_653
| ~ spl0_45
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1630,f1625,f417,f13100]) ).
fof(f13100,plain,
( spl0_653
<=> ! [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_653])]) ).
fof(f1630,plain,
( ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
| member(X0,X1) )
| ~ spl0_45
| ~ spl0_183 ),
inference(resolution,[],[f1626,f418]) ).
fof(f12967,plain,
( spl0_652
| ~ spl0_3
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2056,f2049,f217,f12965]) ).
fof(f12965,plain,
( spl0_652
<=> ! [X2,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))))))
| ~ member(X0,X2)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2049,plain,
( spl0_213
<=> ! [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_213])]) ).
fof(f2056,plain,
( ! [X2,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))))))
| ~ member(X0,X2)
| x = X1 )
| ~ spl0_3
| ~ spl0_213 ),
inference(resolution,[],[f2050,f218]) ).
fof(f2050,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X1,X2)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X0,X3) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f12963,plain,
( spl0_651
| ~ spl0_11
| ~ spl0_56
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1114,f1104,f493,f254,f12961]) ).
fof(f12961,plain,
( spl0_651
<=> ! [X0] :
( x = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
| ~ member(complement(domain_of(X0)),universal_class)
| x = complement(domain_of(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1104,plain,
( spl0_134
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1114,plain,
( ! [X0] :
( x = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
| ~ member(complement(domain_of(X0)),universal_class)
| x = complement(domain_of(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) )
| ~ spl0_11
| ~ spl0_56
| ~ spl0_134 ),
inference(forward_demodulation,[],[f1111,f494]) ).
fof(f1111,plain,
( ! [X0] :
( ~ member(complement(domain_of(X0)),universal_class)
| x = complement(domain_of(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class)
| x = 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_11
| ~ spl0_134 ),
inference(resolution,[],[f1105,f255]) ).
fof(f1105,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = x )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f12734,plain,
( spl0_650
| ~ spl0_3
| ~ spl0_151
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f8894,f8637,f1317,f217,f12732]) ).
fof(f12732,plain,
( spl0_650
<=> ! [X0,X1] :
( ~ subclass(X0,x)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f8894,plain,
( ! [X0,X1] :
( ~ subclass(X0,x)
| subclass(X0,X1) )
| ~ spl0_3
| ~ spl0_151
| ~ spl0_548 ),
inference(forward_demodulation,[],[f8854,f8836]) ).
fof(f8854,plain,
( ! [X0,X1] :
( ~ subclass(X0,domain_of(x))
| subclass(X0,X1) )
| ~ spl0_151
| ~ spl0_548 ),
inference(resolution,[],[f8638,f1318]) ).
fof(f12702,plain,
( spl0_648
| ~ spl0_649
| ~ spl0_86
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2014,f2010,f686,f12699,f12696]) ).
fof(f12696,plain,
( spl0_648
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f686,plain,
( spl0_86
<=> ! [X4,X0,X1] :
( member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f2014,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X1,domain_of(X0)) )
| ~ spl0_86
| ~ spl0_212 ),
inference(resolution,[],[f2011,f687]) ).
fof(f687,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
| member(X1,domain_of(X0)) )
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f686]) ).
fof(f12694,plain,
( spl0_647
| ~ spl0_28
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1700,f1644,f327,f12692]) ).
fof(f12692,plain,
( spl0_647
<=> ! [X0,X1] :
( ~ subclass(domain_relation,complement(X0))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1700,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_28
| ~ spl0_186 ),
inference(resolution,[],[f1645,f328]) ).
fof(f12690,plain,
( spl0_646
| ~ spl0_152
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1652,f1636,f1321,f12688]) ).
fof(f12688,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X0,X2)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1321,plain,
( spl0_152
<=> ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1652,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_152
| ~ spl0_184 ),
inference(resolution,[],[f1637,f1322]) ).
fof(f1322,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f12686,plain,
( spl0_645
| ~ spl0_153
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1651,f1636,f1325,f12684]) ).
fof(f12684,plain,
( spl0_645
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X1,X2)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1325,plain,
( spl0_153
<=> ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1651,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_153
| ~ spl0_184 ),
inference(resolution,[],[f1637,f1326]) ).
fof(f1326,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1325]) ).
fof(f12682,plain,
( spl0_644
| ~ spl0_45
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1621,f1618,f417,f12680]) ).
fof(f12680,plain,
( spl0_644
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f1618,plain,
( spl0_182
<=> ! [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_182])]) ).
fof(f1621,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) )
| ~ spl0_45
| ~ spl0_182 ),
inference(resolution,[],[f1619,f418]) ).
fof(f1619,plain,
( ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X1) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1618]) ).
fof(f12678,plain,
( spl0_643
| ~ spl0_151
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1499,f1456,f1317,f12676]) ).
fof(f12676,plain,
( spl0_643
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),subset_relation)
| member(not_subclass_element(X0,X1),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f1499,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_151
| ~ spl0_164 ),
inference(resolution,[],[f1457,f1318]) ).
fof(f12674,plain,
( spl0_642
| ~ spl0_151
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1477,f1452,f1317,f12672]) ).
fof(f12672,plain,
( spl0_642
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1477,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_151
| ~ spl0_163 ),
inference(resolution,[],[f1453,f1318]) ).
fof(f12669,plain,
( spl0_641
| ~ spl0_3
| ~ spl0_547
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f8875,f8637,f8633,f217,f12667]) ).
fof(f12667,plain,
( spl0_641
<=> ! [X0] : subclass(intersection(X0,universal_class),complement(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f8633,plain,
( spl0_547
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f8875,plain,
( ! [X0] : subclass(intersection(X0,universal_class),complement(x))
| ~ spl0_3
| ~ spl0_547
| ~ spl0_548 ),
inference(forward_demodulation,[],[f8841,f8836]) ).
fof(f8841,plain,
( ! [X0] : subclass(intersection(X0,universal_class),complement(domain_of(x)))
| ~ spl0_547
| ~ spl0_548 ),
inference(resolution,[],[f8638,f8634]) ).
fof(f8634,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_547 ),
inference(avatar_component_clause,[],[f8633]) ).
fof(f12199,plain,
( spl0_640
| ~ spl0_45
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f3968,f2358,f417,f12197]) ).
fof(f3968,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(subset_relation,X0) )
| ~ spl0_45
| ~ spl0_239 ),
inference(resolution,[],[f2360,f418]) ).
fof(f2360,plain,
( member(subset_relation,universal_class)
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2358]) ).
fof(f11880,plain,
( spl0_639
| ~ spl0_237
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f3945,f3942,f2334,f11878]) ).
fof(f3945,plain,
( ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_237
| ~ spl0_330 ),
inference(forward_demodulation,[],[f3943,f2336]) ).
fof(f11830,plain,
( spl0_638
| ~ spl0_328
| ~ spl0_505 ),
inference(avatar_split_clause,[],[f11729,f7625,f3896,f11827]) ).
fof(f11827,plain,
( spl0_638
<=> member(regular(subset_relation),x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f7625,plain,
( spl0_505
<=> x = 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_505])]) ).
fof(f11729,plain,
( member(regular(subset_relation),x)
| ~ spl0_328
| ~ spl0_505 ),
inference(superposition,[],[f3898,f7627]) ).
fof(f7627,plain,
( x = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f7625]) ).
fof(f11722,plain,
( spl0_637
| ~ spl0_110
| spl0_506
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f11718,f11715,f7629,f845,f11720]) ).
fof(f11720,plain,
( spl0_637
<=> ! [X0] :
( member(not_subclass_element(subset_relation,X0),x)
| subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f7629,plain,
( spl0_506
<=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f11715,plain,
( spl0_636
<=> ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f11718,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),x)
| subclass(subset_relation,X0) )
| ~ spl0_110
| spl0_506
| ~ spl0_636 ),
inference(forward_demodulation,[],[f11716,f7642]) ).
fof(f7642,plain,
( x = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_110
| spl0_506 ),
inference(resolution,[],[f7631,f846]) ).
fof(f7631,plain,
( ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
| spl0_506 ),
inference(avatar_component_clause,[],[f7629]) ).
fof(f11716,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) )
| ~ spl0_636 ),
inference(avatar_component_clause,[],[f11715]) ).
fof(f11717,plain,
( spl0_636
| ~ spl0_78
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1435,f1380,f635,f11715]) ).
fof(f1435,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) )
| ~ spl0_78
| ~ spl0_158 ),
inference(superposition,[],[f1381,f637]) ).
fof(f11619,plain,
( spl0_635
| ~ spl0_139
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1496,f1456,f1178,f11617]) ).
fof(f11617,plain,
( spl0_635
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| x = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1496,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| x = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_139
| ~ spl0_164 ),
inference(resolution,[],[f1457,f1179]) ).
fof(f11613,plain,
( spl0_634
| ~ spl0_157
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f8831,f8637,f1376,f11611]) ).
fof(f11611,plain,
( spl0_634
<=> ! [X0,X1] : subclass(intersection(domain_of(x),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f8831,plain,
( ! [X0,X1] : subclass(intersection(domain_of(x),X0),X1)
| ~ spl0_157
| ~ spl0_548 ),
inference(resolution,[],[f8638,f1377]) ).
fof(f11609,plain,
( spl0_633
| ~ spl0_138
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1489,f1456,f1174,f11607]) ).
fof(f11607,plain,
( spl0_633
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| x = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1489,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| x = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
| ~ spl0_138
| ~ spl0_164 ),
inference(resolution,[],[f1457,f1175]) ).
fof(f11605,plain,
( spl0_632
| ~ spl0_139
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1474,f1452,f1178,f11603]) ).
fof(f11603,plain,
( spl0_632
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| x = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f1474,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| x = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_139
| ~ spl0_163 ),
inference(resolution,[],[f1453,f1179]) ).
fof(f11601,plain,
( spl0_631
| ~ spl0_138
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1467,f1452,f1174,f11599]) ).
fof(f11599,plain,
( spl0_631
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| x = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1467,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| x = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
| ~ spl0_138
| ~ spl0_163 ),
inference(resolution,[],[f1453,f1175]) ).
fof(f11584,plain,
( spl0_630
| ~ spl0_141
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1589,f1579,f1229,f11582]) ).
fof(f11582,plain,
( spl0_630
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| x = 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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1589,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(x,universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| x = 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) = x )
| ~ spl0_141
| ~ spl0_176 ),
inference(superposition,[],[f1580,f1230]) ).
fof(f11577,plain,
( ~ spl0_629
| ~ spl0_110
| spl0_506
| ~ spl0_606
| spl0_628 ),
inference(avatar_split_clause,[],[f11570,f11565,f10996,f7629,f845,f11574]) ).
fof(f11574,plain,
( spl0_629
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f11565,plain,
( spl0_628
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f11570,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation)
| ~ spl0_110
| spl0_506
| ~ spl0_606
| spl0_628 ),
inference(forward_demodulation,[],[f11569,f10998]) ).
fof(f11569,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(x),complement(x)),universal_class)),universal_class))))))),subset_relation)
| ~ spl0_110
| spl0_506
| spl0_628 ),
inference(forward_demodulation,[],[f11567,f7642]) ).
fof(f11567,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| spl0_628 ),
inference(avatar_component_clause,[],[f11565]) ).
fof(f11568,plain,
( spl0_427
| ~ spl0_627
| ~ spl0_628
| ~ spl0_134
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1633,f1625,f1104,f11565,f11561,f5830]) ).
fof(f5830,plain,
( spl0_427
<=> x = 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_427])]) ).
fof(f11561,plain,
( spl0_627
<=> member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1633,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
| x = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_134
| ~ spl0_183 ),
inference(resolution,[],[f1626,f1105]) ).
fof(f11497,plain,
( spl0_626
| ~ spl0_459
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f8832,f8637,f6538,f11494]) ).
fof(f11494,plain,
( spl0_626
<=> subclass(universal_class,complement(domain_of(x))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f6538,plain,
( spl0_459
<=> ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f8832,plain,
( subclass(universal_class,complement(domain_of(x)))
| ~ spl0_459
| ~ spl0_548 ),
inference(resolution,[],[f8638,f6539]) ).
fof(f6539,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl0_459 ),
inference(avatar_component_clause,[],[f6538]) ).
fof(f11432,plain,
( spl0_625
| ~ spl0_55
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1837,f1814,f489,f11430]) ).
fof(f11430,plain,
( spl0_625
<=> ! [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_625])]) ).
fof(f1837,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_55
| ~ spl0_198 ),
inference(duplicate_literal_removal,[],[f1818]) ).
fof(f1818,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_55
| ~ spl0_198 ),
inference(resolution,[],[f1815,f490]) ).
fof(f11428,plain,
( spl0_623
| ~ spl0_624
| ~ spl0_129
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1707,f1644,f997,f11425,f11422]) ).
fof(f11422,plain,
( spl0_623
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f11425,plain,
( spl0_624
<=> subclass(domain_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f1707,plain,
( ! [X0] :
( ~ subclass(domain_relation,singleton_relation)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) )
| ~ spl0_129
| ~ spl0_186 ),
inference(resolution,[],[f1645,f998]) ).
fof(f11420,plain,
( spl0_621
| ~ spl0_622
| ~ spl0_130
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1705,f1644,f1001,f11417,f11414]) ).
fof(f11414,plain,
( spl0_621
<=> ! [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_621])]) ).
fof(f11417,plain,
( spl0_622
<=> subclass(domain_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f1705,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_130
| ~ spl0_186 ),
inference(resolution,[],[f1645,f1002]) ).
fof(f11412,plain,
( spl0_620
| ~ spl0_50
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1299,f1259,f465,f11410]) ).
fof(f11410,plain,
( spl0_620
<=> ! [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_620])]) ).
fof(f1299,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_50
| ~ spl0_142 ),
inference(resolution,[],[f1260,f466]) ).
fof(f11408,plain,
( spl0_619
| ~ spl0_81
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1162,f1124,f658,f11406]) ).
fof(f11406,plain,
( spl0_619
<=> ! [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_619])]) ).
fof(f1162,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_81
| ~ spl0_137 ),
inference(resolution,[],[f1125,f659]) ).
fof(f11393,plain,
( spl0_618
| ~ spl0_89
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1587,f1579,f699,f11391]) ).
fof(f11391,plain,
( spl0_618
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| x = 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_618])]) ).
fof(f1587,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
| ~ spl0_89
| ~ spl0_176 ),
inference(resolution,[],[f1580,f700]) ).
fof(f11246,plain,
( spl0_617
| ~ spl0_54
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1336,f1317,f485,f11244]) ).
fof(f11244,plain,
( spl0_617
<=> ! [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_617])]) ).
fof(f1336,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_54
| ~ spl0_151 ),
inference(resolution,[],[f1318,f486]) ).
fof(f11242,plain,
( spl0_616
| ~ spl0_142
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1311,f1294,f1259,f11240]) ).
fof(f11240,plain,
( spl0_616
<=> ! [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_616])]) ).
fof(f1311,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_142
| ~ spl0_150 ),
inference(resolution,[],[f1295,f1260]) ).
fof(f11238,plain,
( spl0_615
| ~ spl0_142
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1306,f1290,f1259,f11236]) ).
fof(f11236,plain,
( spl0_615
<=> ! [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_615])]) ).
fof(f1306,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_142
| ~ spl0_149 ),
inference(resolution,[],[f1291,f1260]) ).
fof(f11194,plain,
( spl0_614
| ~ spl0_112
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1925,f1900,f881,f11192]) ).
fof(f11192,plain,
( spl0_614
<=> ! [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)))),x)
| ~ 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)
| x = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1925,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)))),x)
| ~ 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)
| x = X3 )
| ~ spl0_112
| ~ spl0_208 ),
inference(resolution,[],[f1901,f882]) ).
fof(f11190,plain,
( spl0_613
| ~ spl0_141
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1576,f1570,f1229,f11188]) ).
fof(f11188,plain,
( spl0_613
<=> ! [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)
| x = 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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1576,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)
| x = 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) = x )
| ~ spl0_141
| ~ spl0_175 ),
inference(superposition,[],[f1571,f1230]) ).
fof(f11147,plain,
( spl0_612
| ~ spl0_141
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1507,f1502,f1229,f11145]) ).
fof(f11145,plain,
( spl0_612
<=> ! [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(x,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| x = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f1507,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(x,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| x = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = x )
| ~ spl0_141
| ~ spl0_166 ),
inference(superposition,[],[f1503,f1230]) ).
fof(f11019,plain,
( spl0_610
| ~ spl0_611
| ~ spl0_80
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1687,f1644,f654,f11016,f11013]) ).
fof(f11013,plain,
( spl0_610
<=> ! [X0] :
( ~ member(X0,universal_class)
| domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f11016,plain,
( spl0_611
<=> subclass(domain_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f1687,plain,
( ! [X0] :
( ~ subclass(domain_relation,successor_relation)
| ~ member(X0,universal_class)
| domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
| ~ spl0_80
| ~ spl0_186 ),
inference(resolution,[],[f1645,f655]) ).
fof(f11011,plain,
( spl0_609
| ~ spl0_49
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1675,f1640,f434,f11009]) ).
fof(f11009,plain,
( spl0_609
<=> ! [X0] :
( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1675,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_49
| ~ spl0_185 ),
inference(superposition,[],[f1641,f436]) ).
fof(f11007,plain,
( spl0_608
| ~ spl0_48
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1674,f1640,f429,f11005]) ).
fof(f11005,plain,
( spl0_608
<=> ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1674,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_48
| ~ spl0_185 ),
inference(superposition,[],[f1641,f431]) ).
fof(f11003,plain,
( spl0_607
| ~ spl0_45
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1555,f1542,f417,f11001]) ).
fof(f1555,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_45
| ~ spl0_174 ),
inference(resolution,[],[f1543,f418]) ).
fof(f10999,plain,
( spl0_606
| ~ spl0_128
| ~ spl0_586 ),
inference(avatar_split_clause,[],[f10763,f10475,f993,f10996]) ).
fof(f993,plain,
( spl0_128
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f10763,plain,
( universal_class = complement(x)
| ~ spl0_128
| ~ spl0_586 ),
inference(resolution,[],[f10477,f994]) ).
fof(f994,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f10992,plain,
( ~ spl0_604
| spl0_605
| ~ spl0_135
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1498,f1456,f1116,f10990,f10986]) ).
fof(f10986,plain,
( spl0_604
<=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f10990,plain,
( spl0_605
<=> ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),subset_relation)
| member(unordered_pair(X0,X1),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1498,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_135
| ~ spl0_164 ),
inference(resolution,[],[f1457,f1117]) ).
fof(f10984,plain,
( ~ spl0_602
| spl0_603
| ~ spl0_135
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1476,f1452,f1116,f10982,f10978]) ).
fof(f10978,plain,
( spl0_602
<=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f10982,plain,
( spl0_603
<=> ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),element_relation)
| member(unordered_pair(X0,X1),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1476,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_135
| ~ spl0_163 ),
inference(resolution,[],[f1453,f1117]) ).
fof(f10951,plain,
( spl0_362
| ~ spl0_599
| spl0_600
| ~ spl0_601
| ~ spl0_27
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1488,f1456,f323,f10948,f10944,f10940,f4421]) ).
fof(f10940,plain,
( spl0_599
<=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f10944,plain,
( spl0_600
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f10948,plain,
( spl0_601
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1488,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)
| x = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_27
| ~ spl0_164 ),
inference(resolution,[],[f1457,f324]) ).
fof(f10937,plain,
( spl0_598
| ~ spl0_155
| ~ spl0_586 ),
inference(avatar_split_clause,[],[f10762,f10475,f1351,f10934]) ).
fof(f10934,plain,
( spl0_598
<=> member(x,complement(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1351,plain,
( spl0_155
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f10762,plain,
( member(x,complement(x))
| ~ spl0_155
| ~ spl0_586 ),
inference(resolution,[],[f10477,f1352]) ).
fof(f1352,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f10927,plain,
( spl0_359
| ~ spl0_595
| spl0_596
| ~ spl0_597
| ~ spl0_27
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1466,f1452,f323,f10924,f10920,f10916,f4405]) ).
fof(f10916,plain,
( spl0_595
<=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f10920,plain,
( spl0_596
<=> 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_596])]) ).
fof(f10924,plain,
( spl0_597
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1466,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
| complement(compose(element_relation,complement(identity_relation))) = x
| ~ spl0_27
| ~ spl0_163 ),
inference(resolution,[],[f1453,f324]) ).
fof(f10914,plain,
( spl0_594
| ~ spl0_54
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1199,f1178,f485,f10912]) ).
fof(f10912,plain,
( spl0_594
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
| x = intersection(X0,unordered_pair(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1199,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
| x = intersection(X0,unordered_pair(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 )
| ~ spl0_54
| ~ spl0_139 ),
inference(resolution,[],[f1179,f486]) ).
fof(f10910,plain,
( spl0_593
| ~ spl0_54
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1182,f1174,f485,f10908]) ).
fof(f10908,plain,
( spl0_593
<=> ! [X2,X0,X1] :
( ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
| x = intersection(unordered_pair(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1182,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
| x = intersection(unordered_pair(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 )
| ~ spl0_54
| ~ spl0_138 ),
inference(resolution,[],[f1175,f486]) ).
fof(f10779,plain,
( spl0_592
| ~ spl0_20
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2078,f2049,f294,f10777]) ).
fof(f10777,plain,
( spl0_592
<=> ! [X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))))))
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2078,plain,
( ! [X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x)))))))
| ~ member(X0,X1) )
| ~ spl0_20
| ~ spl0_213 ),
inference(resolution,[],[f2050,f295]) ).
fof(f10775,plain,
( spl0_591
| ~ spl0_45
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1588,f1579,f417,f10773]) ).
fof(f10773,plain,
( spl0_591
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| x = 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_591])]) ).
fof(f1588,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| x = 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_45
| ~ spl0_176 ),
inference(resolution,[],[f1580,f418]) ).
fof(f10584,plain,
( spl0_590
| ~ spl0_527
| ~ spl0_571
| ~ spl0_589 ),
inference(avatar_split_clause,[],[f10580,f10576,f9571,f8227,f10582]) ).
fof(f10582,plain,
( spl0_590
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| x = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f10576,plain,
( spl0_589
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f10580,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| x = 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_527
| ~ spl0_571
| ~ spl0_589 ),
inference(forward_demodulation,[],[f10579,f8228]) ).
fof(f10579,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(x,X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| x = 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_571
| ~ spl0_589 ),
inference(forward_demodulation,[],[f10577,f9573]) ).
fof(f9573,plain,
( x = cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class)
| ~ spl0_571 ),
inference(avatar_component_clause,[],[f9571]) ).
fof(f10577,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_589 ),
inference(avatar_component_clause,[],[f10576]) ).
fof(f10578,plain,
( spl0_589
| ~ spl0_89
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1505,f1502,f699,f10576]) ).
fof(f1505,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_89
| ~ spl0_166 ),
inference(resolution,[],[f1503,f700]) ).
fof(f10574,plain,
( spl0_588
| ~ spl0_112
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1206,f1178,f881,f10572]) ).
fof(f10572,plain,
( spl0_588
<=> ! [X0,X1] :
( ~ member(intersection(X0,regular(X1)),universal_class)
| x = intersection(X0,regular(X1))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),x)
| ~ member(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)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1206,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,regular(X1)),universal_class)
| x = intersection(X0,regular(X1))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),x)
| ~ member(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)
| x = X1 )
| ~ spl0_112
| ~ spl0_139 ),
inference(resolution,[],[f1179,f882]) ).
fof(f10570,plain,
( spl0_587
| ~ spl0_112
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1189,f1174,f881,f10568]) ).
fof(f10568,plain,
( spl0_587
<=> ! [X0,X1] :
( ~ member(intersection(regular(X0),X1),universal_class)
| x = intersection(regular(X0),X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),x)
| ~ 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)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1189,plain,
( ! [X0,X1] :
( ~ member(intersection(regular(X0),X1),universal_class)
| x = intersection(regular(X0),X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),x)
| ~ 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)
| x = X0 )
| ~ spl0_112
| ~ spl0_138 ),
inference(resolution,[],[f1175,f882]) ).
fof(f10478,plain,
( spl0_586
| ~ spl0_459
| ~ spl0_576 ),
inference(avatar_split_clause,[],[f9744,f9685,f6538,f10475]) ).
fof(f9744,plain,
( subclass(universal_class,complement(x))
| ~ spl0_459
| ~ spl0_576 ),
inference(resolution,[],[f9686,f6539]) ).
fof(f9723,plain,
( spl0_585
| ~ spl0_157
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1678,f1640,f1376,f9721]) ).
fof(f9721,plain,
( spl0_585
<=> ! [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_585])]) ).
fof(f1678,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_157
| ~ spl0_185 ),
inference(duplicate_literal_removal,[],[f1659]) ).
fof(f1659,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_157
| ~ spl0_185 ),
inference(resolution,[],[f1641,f1377]) ).
fof(f9719,plain,
( spl0_584
| ~ spl0_158
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1677,f1640,f1380,f9717]) ).
fof(f9717,plain,
( spl0_584
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f1677,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_158
| ~ spl0_185 ),
inference(duplicate_literal_removal,[],[f1660]) ).
fof(f1660,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_158
| ~ spl0_185 ),
inference(resolution,[],[f1641,f1381]) ).
fof(f9715,plain,
( spl0_583
| ~ spl0_38
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1559,f1542,f374,f9713]) ).
fof(f9713,plain,
( spl0_583
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1559,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_38
| ~ spl0_174 ),
inference(resolution,[],[f1543,f375]) ).
fof(f9711,plain,
( spl0_582
| ~ spl0_39
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1558,f1542,f378,f9709]) ).
fof(f9709,plain,
( spl0_582
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1558,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_39
| ~ spl0_174 ),
inference(resolution,[],[f1543,f379]) ).
fof(f9707,plain,
( spl0_581
| ~ spl0_49
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1553,f1538,f434,f9705]) ).
fof(f9705,plain,
( spl0_581
<=> ! [X0,X1] :
( ~ subclass(identity_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1553,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_49
| ~ spl0_173 ),
inference(superposition,[],[f1539,f436]) ).
fof(f9703,plain,
( spl0_580
| ~ spl0_48
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1552,f1538,f429,f9701]) ).
fof(f9701,plain,
( spl0_580
<=> ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,element_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1552,plain,
( ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,element_relation)
| member(X1,X0) )
| ~ spl0_48
| ~ spl0_173 ),
inference(superposition,[],[f1539,f431]) ).
fof(f9699,plain,
( spl0_579
| ~ spl0_38
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1425,f1380,f374,f9697]) ).
fof(f9697,plain,
( spl0_579
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1425,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
| ~ spl0_38
| ~ spl0_158 ),
inference(resolution,[],[f1381,f375]) ).
fof(f9695,plain,
( spl0_578
| ~ spl0_39
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1424,f1380,f378,f9693]) ).
fof(f9693,plain,
( spl0_578
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1424,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
| ~ spl0_39
| ~ spl0_158 ),
inference(resolution,[],[f1381,f379]) ).
fof(f9691,plain,
( spl0_577
| ~ spl0_38
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1404,f1376,f374,f9689]) ).
fof(f9689,plain,
( spl0_577
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1404,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
| ~ spl0_38
| ~ spl0_157 ),
inference(resolution,[],[f1377,f375]) ).
fof(f9687,plain,
( spl0_576
| ~ spl0_548
| ~ spl0_564 ),
inference(avatar_split_clause,[],[f9523,f9135,f8637,f9685]) ).
fof(f9523,plain,
( ! [X0] : ~ member(X0,x)
| ~ spl0_548
| ~ spl0_564 ),
inference(superposition,[],[f8638,f9137]) ).
fof(f9683,plain,
( spl0_575
| ~ spl0_39
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1403,f1376,f378,f9681]) ).
fof(f9681,plain,
( spl0_575
<=> ! [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_575])]) ).
fof(f1403,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
| ~ spl0_39
| ~ spl0_157 ),
inference(resolution,[],[f1377,f379]) ).
fof(f9679,plain,
( spl0_574
| ~ spl0_34
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1310,f1294,f358,f9677]) ).
fof(f9677,plain,
( spl0_574
<=> ! [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_574])]) ).
fof(f1310,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_34
| ~ spl0_150 ),
inference(resolution,[],[f1295,f359]) ).
fof(f9675,plain,
( spl0_573
| ~ spl0_34
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1305,f1290,f358,f9673]) ).
fof(f9673,plain,
( spl0_573
<=> ! [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_573])]) ).
fof(f1305,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_34
| ~ spl0_149 ),
inference(resolution,[],[f1291,f359]) ).
fof(f9577,plain,
( spl0_571
| spl0_572
| ~ spl0_6
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1591,f1579,f231,f9575,f9571]) ).
fof(f9575,plain,
( spl0_572
<=> ! [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(x,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = 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(x,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1591,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(x,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(X1,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| x = cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class)
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_176 ),
inference(superposition,[],[f1580,f232]) ).
fof(f9569,plain,
( spl0_570
| ~ spl0_56
| ~ spl0_176 ),
inference(avatar_split_clause,[],[f1590,f1579,f493,f9567]) ).
fof(f9567,plain,
( spl0_570
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),X1))
| ~ member(X2,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1590,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),X1))
| ~ member(X2,domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class) )
| ~ spl0_56
| ~ spl0_176 ),
inference(superposition,[],[f1580,f494]) ).
fof(f9562,plain,
( spl0_569
| ~ spl0_115
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1771,f1733,f905,f9560]) ).
fof(f9560,plain,
( spl0_569
<=> ! [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)
| x = 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_569])]) ).
fof(f9522,plain,
( spl0_567
| ~ spl0_568
| ~ spl0_6
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1373,f1366,f231,f9519,f9516]) ).
fof(f9516,plain,
( spl0_567
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),cross_product(universal_class,universal_class))
| x = 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(x,x))),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_567])]) ).
fof(f1366,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),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_156])]) ).
fof(f1373,plain,
( ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(x,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),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))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_6
| ~ spl0_156 ),
inference(superposition,[],[f1367,f232]) ).
fof(f1367,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(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X1,X2)) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1366]) ).
fof(f9470,plain,
( spl0_566
| ~ spl0_55
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1109,f1104,f489,f9468]) ).
fof(f9468,plain,
( spl0_566
<=> ! [X0,X1] :
( ~ member(complement(intersection(X0,X1)),universal_class)
| complement(intersection(X0,X1)) = x
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1109,plain,
( ! [X0,X1] :
( ~ member(complement(intersection(X0,X1)),universal_class)
| complement(intersection(X0,X1)) = x
| ~ 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_55
| ~ spl0_134 ),
inference(resolution,[],[f1105,f490]) ).
fof(f9465,plain,
( spl0_565
| ~ spl0_132
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1829,f1814,f1029,f9463]) ).
fof(f9463,plain,
( spl0_565
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f9138,plain,
( spl0_564
| ~ spl0_3
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f8836,f8637,f217,f9135]) ).
fof(f9128,plain,
( spl0_563
| ~ spl0_151
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1676,f1640,f1317,f9126]) ).
fof(f9126,plain,
( spl0_563
<=> ! [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_563])]) ).
fof(f1676,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) )
| ~ spl0_151
| ~ spl0_185 ),
inference(duplicate_literal_removal,[],[f1661]) ).
fof(f1661,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_151
| ~ spl0_185 ),
inference(resolution,[],[f1641,f1318]) ).
fof(f9124,plain,
( spl0_562
| ~ spl0_28
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1560,f1542,f327,f9122]) ).
fof(f9122,plain,
( spl0_562
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1560,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_28
| ~ spl0_174 ),
inference(resolution,[],[f1543,f328]) ).
fof(f9120,plain,
( spl0_561
| ~ spl0_30
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1547,f1538,f335,f9118]) ).
fof(f9118,plain,
( spl0_561
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1547,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(intersection(X1,X2)) )
| ~ spl0_30
| ~ spl0_173 ),
inference(resolution,[],[f1539,f336]) ).
fof(f9116,plain,
( spl0_560
| ~ spl0_50
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1463,f1452,f465,f9114]) ).
fof(f9114,plain,
( spl0_560
<=> ! [X0] :
( ~ member(X0,element_relation)
| member(X0,singleton_relation)
| member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1463,plain,
( ! [X0] :
( ~ member(X0,element_relation)
| member(X0,singleton_relation)
| member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,universal_class) )
| ~ spl0_50
| ~ spl0_163 ),
inference(resolution,[],[f1453,f466]) ).
fof(f9112,plain,
( spl0_559
| ~ spl0_45
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1421,f1380,f417,f9110]) ).
fof(f9110,plain,
( spl0_559
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1421,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) )
| ~ spl0_45
| ~ spl0_158 ),
inference(resolution,[],[f1381,f418]) ).
fof(f9108,plain,
( spl0_558
| ~ spl0_45
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1400,f1376,f417,f9106]) ).
fof(f9106,plain,
( spl0_558
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X0,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f1400,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X0,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) )
| ~ spl0_45
| ~ spl0_157 ),
inference(resolution,[],[f1377,f418]) ).
fof(f9104,plain,
( spl0_557
| ~ spl0_54
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1147,f1116,f485,f9102]) ).
fof(f9102,plain,
( spl0_557
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| unordered_pair(X2,X3) = X0
| unordered_pair(X2,X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f1147,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| unordered_pair(X2,X3) = X0
| unordered_pair(X2,X3) = X1 )
| ~ spl0_54
| ~ spl0_135 ),
inference(resolution,[],[f1117,f486]) ).
fof(f9097,plain,
( spl0_556
| ~ spl0_115
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1703,f1644,f905,f9095]) ).
fof(f9095,plain,
( spl0_556
<=> ! [X0] :
( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
| ~ member(X0,universal_class)
| x = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1703,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)
| x = 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_115
| ~ spl0_186 ),
inference(resolution,[],[f1645,f906]) ).
fof(f9092,plain,
( spl0_555
| ~ spl0_33
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f8830,f8637,f354,f9090]) ).
fof(f9090,plain,
( spl0_555
<=> ! [X0] : subclass(domain_of(x),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f8830,plain,
( ! [X0] : subclass(domain_of(x),X0)
| ~ spl0_33
| ~ spl0_548 ),
inference(resolution,[],[f8638,f355]) ).
fof(f9036,plain,
( spl0_554
| ~ spl0_45
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1506,f1502,f417,f9034]) ).
fof(f9034,plain,
( spl0_554
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X2,X2),universal_class)
| ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f1506,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = 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_45
| ~ spl0_166 ),
inference(resolution,[],[f1503,f418]) ).
fof(f9001,plain,
( spl0_553
| ~ spl0_11
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1983,f1954,f254,f8999]) ).
fof(f8999,plain,
( spl0_553
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| x = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f1983,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)
| x = 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_11
| ~ spl0_211 ),
inference(resolution,[],[f1955,f255]) ).
fof(f8997,plain,
( spl0_552
| ~ spl0_11
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1957,f1950,f254,f8995]) ).
fof(f8995,plain,
( spl0_552
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| x = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f1957,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)
| x = 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_11
| ~ spl0_210 ),
inference(resolution,[],[f1951,f255]) ).
fof(f8993,plain,
( spl0_551
| ~ spl0_115
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1748,f1729,f905,f8991]) ).
fof(f8991,plain,
( spl0_551
<=> ! [X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ member(X1,universal_class)
| x = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f8647,plain,
( spl0_550
| ~ spl0_39
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1628,f1625,f378,f8645]) ).
fof(f8645,plain,
( spl0_550
<=> ! [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_550])]) ).
fof(f1628,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
| ~ spl0_39
| ~ spl0_183 ),
inference(resolution,[],[f1626,f379]) ).
fof(f8643,plain,
( spl0_549
| ~ spl0_157
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1615,f1602,f1376,f8641]) ).
fof(f1602,plain,
( spl0_180
<=> ! [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_180])]) ).
fof(f1615,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_157
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f1610]) ).
fof(f1610,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1))
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_157
| ~ spl0_180 ),
inference(resolution,[],[f1603,f1377]) ).
fof(f1603,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_180 ),
inference(avatar_component_clause,[],[f1602]) ).
fof(f8639,plain,
( spl0_548
| ~ spl0_113
| ~ spl0_527 ),
inference(avatar_split_clause,[],[f8549,f8227,f885,f8637]) ).
fof(f885,plain,
( spl0_113
<=> ! [X0,X1] :
( x != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f8549,plain,
( ! [X0] : ~ member(X0,domain_of(x))
| ~ spl0_113
| ~ spl0_527 ),
inference(trivial_inequality_removal,[],[f8522]) ).
fof(f8522,plain,
( ! [X0] :
( x != x
| ~ member(X0,domain_of(x)) )
| ~ spl0_113
| ~ spl0_527 ),
inference(superposition,[],[f886,f8228]) ).
fof(f886,plain,
( ! [X0,X1] :
( x != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f8635,plain,
( spl0_547
| ~ spl0_158
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1614,f1602,f1380,f8633]) ).
fof(f1614,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_158
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f1611]) ).
fof(f1611,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1))
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_158
| ~ spl0_180 ),
inference(resolution,[],[f1603,f1381]) ).
fof(f8631,plain,
( spl0_546
| ~ spl0_30
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1461,f1448,f335,f8629]) ).
fof(f8629,plain,
( spl0_546
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f1448,plain,
( spl0_162
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(complement(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1461,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1)) )
| ~ spl0_30
| ~ spl0_162 ),
inference(resolution,[],[f1449,f336]) ).
fof(f1449,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X1),X2)
| ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,X2) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f8627,plain,
( spl0_545
| ~ spl0_28
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1426,f1380,f327,f8625]) ).
fof(f8625,plain,
( spl0_545
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f1426,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
| ~ spl0_28
| ~ spl0_158 ),
inference(resolution,[],[f1381,f328]) ).
fof(f8623,plain,
( spl0_544
| ~ spl0_28
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1405,f1376,f327,f8621]) ).
fof(f8621,plain,
( spl0_544
<=> ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f1405,plain,
( ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
| ~ spl0_28
| ~ spl0_157 ),
inference(resolution,[],[f1377,f328]) ).
fof(f8619,plain,
( spl0_543
| ~ spl0_45
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1335,f1317,f417,f8617]) ).
fof(f8617,plain,
( spl0_543
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(X0,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f1335,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(X0,X2),X3) )
| ~ spl0_45
| ~ spl0_151 ),
inference(resolution,[],[f1318,f418]) ).
fof(f8615,plain,
( spl0_542
| ~ spl0_137
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1297,f1259,f1124,f8613]) ).
fof(f8613,plain,
( spl0_542
<=> ! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f1297,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_137
| ~ spl0_142 ),
inference(resolution,[],[f1260,f1125]) ).
fof(f8611,plain,
( spl0_541
| ~ spl0_72
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1167,f1124,f602,f8609]) ).
fof(f1167,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) )
| ~ spl0_72
| ~ spl0_137 ),
inference(resolution,[],[f1125,f603]) ).
fof(f8607,plain,
( spl0_540
| ~ spl0_73
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1166,f1124,f606,f8605]) ).
fof(f1166,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) )
| ~ spl0_73
| ~ spl0_137 ),
inference(resolution,[],[f1125,f607]) ).
fof(f8449,plain,
( spl0_539
| ~ spl0_108
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1998,f1954,f823,f8447]) ).
fof(f8447,plain,
( spl0_539
<=> ! [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)))))
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f1998,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)))))
| x = X1 )
| ~ spl0_108
| ~ spl0_211 ),
inference(resolution,[],[f1955,f824]) ).
fof(f8445,plain,
( spl0_538
| ~ spl0_108
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f1972,f1950,f823,f8443]) ).
fof(f8443,plain,
( spl0_538
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(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)))))
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f1972,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)))))
| x = X1 )
| ~ spl0_108
| ~ spl0_210 ),
inference(resolution,[],[f1951,f824]) ).
fof(f8441,plain,
( spl0_537
| ~ spl0_50
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1110,f1104,f465,f8439]) ).
fof(f8439,plain,
( spl0_537
<=> ! [X0] :
( ~ member(complement(complement(X0)),universal_class)
| x = complement(complement(X0))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f1110,plain,
( ! [X0] :
( ~ member(complement(complement(X0)),universal_class)
| x = complement(complement(X0))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) )
| ~ spl0_50
| ~ spl0_134 ),
inference(resolution,[],[f1105,f466]) ).
fof(f8437,plain,
( spl0_536
| ~ spl0_93
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f841,f823,f718,f8435]) ).
fof(f8435,plain,
( spl0_536
<=> ! [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)))))
| x = 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_536])]) ).
fof(f841,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)))))
| x = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_108 ),
inference(resolution,[],[f824,f719]) ).
fof(f8401,plain,
( spl0_535
| ~ spl0_6
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2005,f1954,f231,f8399]) ).
fof(f8399,plain,
( spl0_535
<=> ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2005,plain,
( ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_211 ),
inference(superposition,[],[f1955,f232]) ).
fof(f8392,plain,
( spl0_534
| ~ spl0_111
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1833,f1814,f849,f8390]) ).
fof(f8390,plain,
( spl0_534
<=> ! [X0] :
( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
| x = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f8388,plain,
( spl0_533
| ~ spl0_340
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f8041,f7604,f4123,f8386]) ).
fof(f7604,plain,
( spl0_500
<=> ! [X0] :
( x = X0
| ~ subclass(X0,x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f8041,plain,
( ! [X0] : x = intersection(X0,x)
| ~ spl0_340
| ~ spl0_500 ),
inference(resolution,[],[f7605,f4124]) ).
fof(f7605,plain,
( ! [X0] :
( ~ subclass(X0,x)
| x = X0 )
| ~ spl0_500 ),
inference(avatar_component_clause,[],[f7604]) ).
fof(f8379,plain,
( spl0_532
| ~ spl0_110
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1824,f1814,f845,f8377]) ).
fof(f8377,plain,
( spl0_532
<=> ! [X0] :
( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
| ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
| x = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f8375,plain,
( spl0_531
| ~ spl0_137
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1574,f1570,f1124,f8373]) ).
fof(f8373,plain,
( spl0_531
<=> ! [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)
| x = 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_531])]) ).
fof(f1574,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)
| x = 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_137
| ~ spl0_175 ),
inference(resolution,[],[f1571,f1125]) ).
fof(f8363,plain,
( spl0_529
| ~ spl0_530
| ~ spl0_106
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2047,f2010,f807,f8360,f8357]) ).
fof(f8357,plain,
( spl0_529
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| x = 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_529])]) ).
fof(f8360,plain,
( spl0_530
<=> subclass(composition_function,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f807,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ member(X1,x)
| member(X1,X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2047,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,x)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2)
| x = X2 )
| ~ spl0_106
| ~ spl0_212 ),
inference(resolution,[],[f2011,f808]) ).
fof(f808,plain,
( ! [X0,X1] :
( ~ member(X1,x)
| member(X1,X0)
| x = X0 )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f8355,plain,
( spl0_528
| ~ spl0_6
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1370,f1366,f231,f8353]) ).
fof(f8353,plain,
( spl0_528
<=> ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f1370,plain,
( ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_156 ),
inference(superposition,[],[f1367,f232]) ).
fof(f8229,plain,
( spl0_527
| ~ spl0_339
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f8040,f7604,f4119,f8227]) ).
fof(f8040,plain,
( ! [X0] : x = intersection(x,X0)
| ~ spl0_339
| ~ spl0_500 ),
inference(resolution,[],[f7605,f4120]) ).
fof(f8157,plain,
( spl0_526
| ~ spl0_141
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1657,f1636,f1229,f8155]) ).
fof(f8155,plain,
( spl0_526
<=> ! [X2,X0,X1] :
( subclass(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f1657,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) = x )
| ~ spl0_141
| ~ spl0_184 ),
inference(superposition,[],[f1637,f1230]) ).
fof(f8153,plain,
( spl0_525
| ~ spl0_91
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1243,f1229,f708,f8151]) ).
fof(f8151,plain,
( spl0_525
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f1243,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) = x )
| ~ spl0_91
| ~ spl0_141 ),
inference(superposition,[],[f709,f1230]) ).
fof(f8149,plain,
( spl0_524
| ~ spl0_27
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f895,f881,f323,f8147]) ).
fof(f8147,plain,
( spl0_524
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),x)
| ~ 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)
| x = X0
| ~ member(regular(X0),universal_class)
| regular(X0) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f895,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))))))),x)
| ~ 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)
| x = X0
| ~ member(regular(X0),universal_class)
| regular(X0) = x )
| ~ spl0_27
| ~ spl0_112 ),
inference(resolution,[],[f882,f324]) ).
fof(f8145,plain,
( spl0_523
| ~ spl0_81
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f868,f849,f658,f8143]) ).
fof(f868,plain,
( ! [X2,X0,X1] :
( x = 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_81
| ~ spl0_111 ),
inference(resolution,[],[f850,f659]) ).
fof(f8141,plain,
( spl0_522
| ~ spl0_81
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f854,f845,f658,f8139]) ).
fof(f854,plain,
( ! [X2,X0,X1] :
( x = 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_81
| ~ spl0_110 ),
inference(resolution,[],[f846,f659]) ).
fof(f8028,plain,
( spl0_521
| ~ spl0_75
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1689,f1644,f618,f8026]) ).
fof(f8026,plain,
( spl0_521
<=> ! [X0,X1] :
( ~ subclass(domain_relation,compose_class(X0))
| ~ member(X1,universal_class)
| compose(X0,X1) = domain_of(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f1689,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,compose_class(X0))
| ~ member(X1,universal_class)
| compose(X0,X1) = domain_of(X1) )
| ~ spl0_75
| ~ spl0_186 ),
inference(resolution,[],[f1645,f619]) ).
fof(f8024,plain,
( spl0_520
| ~ spl0_151
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1613,f1602,f1317,f8022]) ).
fof(f1613,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) )
| ~ spl0_151
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f1612]) ).
fof(f1612,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,complement(X1)) )
| ~ spl0_151
| ~ spl0_180 ),
inference(resolution,[],[f1603,f1318]) ).
fof(f8020,plain,
( spl0_519
| ~ spl0_38
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1339,f1317,f374,f8018]) ).
fof(f8018,plain,
( spl0_519
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f1339,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X1) )
| ~ spl0_38
| ~ spl0_151 ),
inference(resolution,[],[f1318,f375]) ).
fof(f8016,plain,
( spl0_518
| ~ spl0_39
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1338,f1317,f378,f8014]) ).
fof(f8014,plain,
( spl0_518
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f1338,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X2) )
| ~ spl0_39
| ~ spl0_151 ),
inference(resolution,[],[f1318,f379]) ).
fof(f8012,plain,
( spl0_517
| ~ spl0_45
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1309,f1294,f417,f8010]) ).
fof(f8010,plain,
( spl0_517
<=> ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f1309,plain,
( ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) )
| ~ spl0_45
| ~ spl0_150 ),
inference(resolution,[],[f1295,f418]) ).
fof(f8008,plain,
( spl0_516
| ~ spl0_45
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1304,f1290,f417,f8006]) ).
fof(f8006,plain,
( spl0_516
<=> ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f1304,plain,
( ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
| member(X0,X1) )
| ~ spl0_45
| ~ spl0_149 ),
inference(resolution,[],[f1291,f418]) ).
fof(f8004,plain,
( spl0_514
| ~ spl0_515
| ~ spl0_80
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1132,f1116,f654,f8001,f7998]) ).
fof(f7998,plain,
( spl0_514
<=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f8001,plain,
( spl0_515
<=> subclass(universal_class,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f1132,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,successor_relation)
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ spl0_80
| ~ spl0_135 ),
inference(resolution,[],[f1117,f655]) ).
fof(f7681,plain,
( spl0_513
| ~ spl0_15
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1512,f1509,f271,f7679]) ).
fof(f7679,plain,
( spl0_513
<=> ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f1509,plain,
( spl0_167
<=> ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| ~ member(unordered_pair(X0,X1),universal_class)
| unordered_pair(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1512,plain,
( ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_15
| ~ spl0_167 ),
inference(resolution,[],[f1510,f272]) ).
fof(f1510,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1509]) ).
fof(f7677,plain,
( spl0_512
| ~ spl0_132
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1495,f1456,f1029,f7675]) ).
fof(f7675,plain,
( spl0_512
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f1495,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| x = X0 )
| ~ spl0_132
| ~ spl0_164 ),
inference(resolution,[],[f1457,f1030]) ).
fof(f7673,plain,
( spl0_511
| ~ spl0_132
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1473,f1452,f1029,f7671]) ).
fof(f7671,plain,
( spl0_511
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f1473,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| x = X0 )
| ~ spl0_132
| ~ spl0_163 ),
inference(resolution,[],[f1453,f1030]) ).
fof(f7669,plain,
( spl0_510
| ~ spl0_117
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1255,f1229,f918,f7667]) ).
fof(f7667,plain,
( spl0_510
<=> ! [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)))
| x = regular(cross_product(X0,X1))
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f918,plain,
( spl0_117
<=> ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1255,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)))
| x = regular(cross_product(X0,X1))
| cross_product(X0,X1) = x )
| ~ spl0_117
| ~ spl0_141 ),
inference(superposition,[],[f919,f1230]) ).
fof(f919,plain,
( ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f7665,plain,
( spl0_509
| ~ spl0_112
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1093,f1029,f881,f7663]) ).
fof(f7663,plain,
( spl0_509
<=> ! [X0,X1] :
( ~ subclass(X0,regular(X1))
| ~ member(X0,universal_class)
| x = 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))))))),x)
| ~ 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)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f1093,plain,
( ! [X0,X1] :
( ~ subclass(X0,regular(X1))
| ~ member(X0,universal_class)
| x = 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))))))),x)
| ~ 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)
| x = X1 )
| ~ spl0_112
| ~ spl0_132 ),
inference(resolution,[],[f1030,f882]) ).
fof(f7661,plain,
( spl0_508
| ~ spl0_39
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f5760,f3421,f378,f7659]) ).
fof(f7659,plain,
( spl0_508
<=> ! [X0,X1] :
( ~ member(X1,x)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f3421,plain,
( spl0_303
<=> ! [X0] : x = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f5760,plain,
( ! [X0,X1] :
( ~ member(X1,x)
| member(X1,X0) )
| ~ spl0_39
| ~ spl0_303 ),
inference(superposition,[],[f379,f3422]) ).
fof(f3422,plain,
( ! [X0] : x = intersection(complement(X0),X0)
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f3421]) ).
fof(f7636,plain,
( spl0_505
| ~ spl0_506
| spl0_507
| ~ spl0_3
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1823,f1814,f217,f7633,f7629,f7625]) ).
fof(f7633,plain,
( spl0_507
<=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f1823,plain,
( member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
| ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
| x = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_3
| ~ spl0_198 ),
inference(resolution,[],[f1815,f218]) ).
fof(f7622,plain,
( ~ spl0_503
| spl0_504
| ~ spl0_135
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1575,f1570,f1116,f7620,f7616]) ).
fof(f7616,plain,
( spl0_503
<=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f7620,plain,
( spl0_504
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| x = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f1575,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)
| x = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ subclass(universal_class,cross_product(universal_class,universal_class)) )
| ~ spl0_135
| ~ spl0_175 ),
inference(resolution,[],[f1571,f1117]) ).
fof(f7614,plain,
( spl0_502
| ~ spl0_141
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1361,f1325,f1229,f7612]) ).
fof(f7612,plain,
( spl0_502
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f1361,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) = x )
| ~ spl0_141
| ~ spl0_153 ),
inference(superposition,[],[f1326,f1230]) ).
fof(f7610,plain,
( spl0_501
| ~ spl0_54
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1085,f1029,f485,f7608]) ).
fof(f7608,plain,
( spl0_501
<=> ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f1085,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 )
| ~ spl0_54
| ~ spl0_132 ),
inference(resolution,[],[f1030,f486]) ).
fof(f7606,plain,
( spl0_500
| ~ spl0_46
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f3894,f3008,f421,f7604]) ).
fof(f3008,plain,
( spl0_287
<=> ! [X0] :
( x = X0
| subclass(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f3894,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,x) )
| ~ spl0_46
| ~ spl0_287 ),
inference(duplicate_literal_removal,[],[f3883]) ).
fof(f3883,plain,
( ! [X0] :
( x = X0
| ~ subclass(X0,x)
| x = X0 )
| ~ spl0_46
| ~ spl0_287 ),
inference(resolution,[],[f3009,f422]) ).
fof(f3009,plain,
( ! [X0] :
( subclass(x,X0)
| x = X0 )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f3008]) ).
fof(f7432,plain,
( spl0_499
| ~ spl0_28
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2821,f2307,f327,f7430]) ).
fof(f7430,plain,
( spl0_499
<=> ! [X0] :
( ~ member(X0,x)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2821,plain,
( ! [X0] :
( ~ member(X0,x)
| ~ member(X0,universal_class) )
| ~ spl0_28
| ~ spl0_233 ),
inference(superposition,[],[f328,f2309]) ).
fof(f7368,plain,
( spl0_498
| ~ spl0_9
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1719,f1648,f244,f7366]) ).
fof(f7366,plain,
( spl0_498
<=> ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f1648,plain,
( spl0_187
<=> ! [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_187])]) ).
fof(f1719,plain,
( ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
| ~ spl0_9
| ~ spl0_187 ),
inference(resolution,[],[f1649,f245]) ).
fof(f1649,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_187 ),
inference(avatar_component_clause,[],[f1648]) ).
fof(f7364,plain,
( spl0_497
| ~ spl0_62
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1718,f1648,f548,f7362]) ).
fof(f7362,plain,
( spl0_497
<=> ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f548,plain,
( spl0_62
<=> ! [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_62])]) ).
fof(f1718,plain,
( ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) )
| ~ spl0_62
| ~ spl0_187 ),
inference(resolution,[],[f1649,f549]) ).
fof(f549,plain,
( ! [X8] :
( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| ~ operation(X8) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f7360,plain,
( spl0_496
| ~ spl0_72
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1682,f1644,f602,f7358]) ).
fof(f7358,plain,
( spl0_496
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f1682,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) )
| ~ spl0_72
| ~ spl0_186 ),
inference(resolution,[],[f1645,f603]) ).
fof(f7356,plain,
( spl0_495
| ~ spl0_33
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1679,f1640,f354,f7354]) ).
fof(f1679,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_33
| ~ spl0_185 ),
inference(duplicate_literal_removal,[],[f1658]) ).
fof(f1658,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_33
| ~ spl0_185 ),
inference(resolution,[],[f1641,f355]) ).
fof(f7352,plain,
( spl0_494
| ~ spl0_129
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1430,f1380,f997,f7350]) ).
fof(f7350,plain,
( spl0_494
<=> ! [X0,X1] :
( subclass(intersection(X0,singleton_relation),X1)
| member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1430,plain,
( ! [X0,X1] :
( subclass(intersection(X0,singleton_relation),X1)
| member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
| ~ spl0_129
| ~ spl0_158 ),
inference(resolution,[],[f1381,f998]) ).
fof(f7348,plain,
( spl0_493
| ~ spl0_130
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1428,f1380,f1001,f7346]) ).
fof(f7346,plain,
( spl0_493
<=> ! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f1428,plain,
( ! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
| ~ spl0_130
| ~ spl0_158 ),
inference(resolution,[],[f1381,f1002]) ).
fof(f7308,plain,
( spl0_492
| ~ spl0_49
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1416,f1376,f434,f7306]) ).
fof(f7306,plain,
( spl0_492
<=> ! [X0] :
( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f1416,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) )
| ~ spl0_49
| ~ spl0_157 ),
inference(superposition,[],[f1377,f436]) ).
fof(f7304,plain,
( spl0_491
| ~ spl0_48
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1415,f1376,f429,f7302]) ).
fof(f1415,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X0) )
| ~ spl0_48
| ~ spl0_157 ),
inference(superposition,[],[f1377,f431]) ).
fof(f7300,plain,
( spl0_490
| ~ spl0_129
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1409,f1376,f997,f7298]) ).
fof(f7298,plain,
( spl0_490
<=> ! [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_490])]) ).
fof(f1409,plain,
( ! [X0,X1] :
( subclass(intersection(singleton_relation,X0),X1)
| member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
| ~ spl0_129
| ~ spl0_157 ),
inference(resolution,[],[f1377,f998]) ).
fof(f7296,plain,
( spl0_489
| ~ spl0_130
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1407,f1376,f1001,f7294]) ).
fof(f7294,plain,
( spl0_489
<=> ! [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_489])]) ).
fof(f1407,plain,
( ! [X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
| ~ spl0_130
| ~ spl0_157 ),
inference(resolution,[],[f1377,f1002]) ).
fof(f7292,plain,
( spl0_488
| ~ spl0_30
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1360,f1325,f335,f7290]) ).
fof(f7290,plain,
( spl0_488
<=> ! [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_488])]) ).
fof(f1360,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) )
| ~ spl0_30
| ~ spl0_153 ),
inference(resolution,[],[f1326,f336]) ).
fof(f7288,plain,
( spl0_487
| ~ spl0_30
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1356,f1321,f335,f7286]) ).
fof(f7286,plain,
( spl0_487
<=> ! [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_487])]) ).
fof(f1356,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) )
| ~ spl0_30
| ~ spl0_152 ),
inference(resolution,[],[f1322,f336]) ).
fof(f7284,plain,
( spl0_486
| ~ spl0_28
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1340,f1317,f327,f7282]) ).
fof(f1340,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),X1) )
| ~ spl0_28
| ~ spl0_151 ),
inference(resolution,[],[f1318,f328]) ).
fof(f7280,plain,
( spl0_485
| ~ spl0_34
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1164,f1124,f358,f7278]) ).
fof(f7278,plain,
( spl0_485
<=> ! [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_485])]) ).
fof(f1164,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_34
| ~ spl0_137 ),
inference(resolution,[],[f1125,f359]) ).
fof(f7258,plain,
( spl0_484
| ~ spl0_233
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f7071,f3711,f2307,f7255]) ).
fof(f7255,plain,
( spl0_484
<=> x = intersection(universal_class,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f3711,plain,
( spl0_322
<=> ! [X0] : x = intersection(X0,complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f7071,plain,
( x = intersection(universal_class,x)
| ~ spl0_233
| ~ spl0_322 ),
inference(superposition,[],[f3712,f2309]) ).
fof(f3712,plain,
( ! [X0] : x = intersection(X0,complement(X0))
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f3711]) ).
fof(f7239,plain,
( spl0_483
| ~ spl0_56
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1372,f1366,f493,f7237]) ).
fof(f7237,plain,
( spl0_483
<=> ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f1372,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(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X2,X1)) )
| ~ spl0_56
| ~ spl0_156 ),
inference(superposition,[],[f1367,f494]) ).
fof(f7235,plain,
( spl0_482
| ~ spl0_56
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1369,f1366,f493,f7233]) ).
fof(f7233,plain,
( spl0_482
<=> ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f1369,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(x,x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X2,X1)) )
| ~ spl0_56
| ~ spl0_156 ),
inference(superposition,[],[f1367,f494]) ).
fof(f7231,plain,
( spl0_481
| ~ spl0_89
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1242,f1229,f699,f7229]) ).
fof(f7229,plain,
( spl0_481
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
| member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f1242,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) = x )
| ~ spl0_89
| ~ spl0_141 ),
inference(superposition,[],[f700,f1230]) ).
fof(f7211,plain,
( spl0_480
| ~ spl0_79
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1577,f1570,f640,f7209]) ).
fof(f7209,plain,
( spl0_480
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| x = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f1577,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)
| x = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X0,universal_class) )
| ~ spl0_79
| ~ spl0_175 ),
inference(duplicate_literal_removal,[],[f1573]) ).
fof(f1573,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| x = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_79
| ~ spl0_175 ),
inference(resolution,[],[f1571,f641]) ).
fof(f7196,plain,
( spl0_479
| ~ spl0_36
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1252,f1229,f366,f7194]) ).
fof(f7194,plain,
( spl0_479
<=> ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f1252,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) = x )
| ~ spl0_36
| ~ spl0_141 ),
inference(superposition,[],[f367,f1230]) ).
fof(f7150,plain,
( spl0_478
| ~ spl0_106
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1927,f1900,f807,f7148]) ).
fof(f7148,plain,
( spl0_478
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),x)
| ~ 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)
| x = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f1927,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),x)
| ~ 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)
| x = X3 )
| ~ spl0_106
| ~ spl0_208 ),
inference(resolution,[],[f1901,f808]) ).
fof(f7068,plain,
( spl0_319
| ~ spl0_476
| ~ spl0_477
| ~ spl0_134
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1313,f1294,f1104,f7065,f7061,f3549]) ).
fof(f7061,plain,
( spl0_476
<=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f7065,plain,
( spl0_477
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f1313,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| x = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_134
| ~ spl0_150 ),
inference(resolution,[],[f1295,f1105]) ).
fof(f7057,plain,
( spl0_316
| ~ spl0_474
| ~ spl0_475
| ~ spl0_134
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1307,f1290,f1104,f7054,f7050,f3533]) ).
fof(f7050,plain,
( spl0_474
<=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f7054,plain,
( spl0_475
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f1307,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
| x = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_134
| ~ spl0_149 ),
inference(resolution,[],[f1291,f1105]) ).
fof(f6963,plain,
( spl0_473
| ~ spl0_73
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1681,f1644,f606,f6961]) ).
fof(f6961,plain,
( spl0_473
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f1681,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(X2,X0) )
| ~ spl0_73
| ~ spl0_186 ),
inference(resolution,[],[f1645,f607]) ).
fof(f6959,plain,
( spl0_472
| ~ spl0_129
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1345,f1317,f997,f6957]) ).
fof(f6957,plain,
( spl0_472
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f1345,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),element_relation) )
| ~ spl0_129
| ~ spl0_151 ),
inference(resolution,[],[f1318,f998]) ).
fof(f6955,plain,
( spl0_471
| ~ spl0_130
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1343,f1317,f1001,f6953]) ).
fof(f6953,plain,
( spl0_471
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f1343,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) )
| ~ spl0_130
| ~ spl0_151 ),
inference(resolution,[],[f1318,f1002]) ).
fof(f6951,plain,
( spl0_470
| ~ spl0_45
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1163,f1124,f417,f6949]) ).
fof(f6949,plain,
( spl0_470
<=> ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f1163,plain,
( ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(X0,X1) )
| ~ spl0_45
| ~ spl0_137 ),
inference(resolution,[],[f1125,f418]) ).
fof(f6947,plain,
( spl0_469
| ~ spl0_45
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1146,f1116,f417,f6945]) ).
fof(f6945,plain,
( spl0_469
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f1146,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) )
| ~ spl0_45
| ~ spl0_135 ),
inference(resolution,[],[f1117,f418]) ).
fof(f6904,plain,
( spl0_468
| ~ spl0_54
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1253,f1229,f485,f6902]) ).
fof(f6902,plain,
( spl0_468
<=> ! [X2,X0,X1] :
( ~ member(X2,regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f1253,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) = x )
| ~ spl0_54
| ~ spl0_141 ),
inference(superposition,[],[f486,f1230]) ).
fof(f6900,plain,
( spl0_467
| ~ spl0_109
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1254,f1229,f828,f6898]) ).
fof(f6898,plain,
( spl0_467
<=> ! [X0,X1] :
( ~ inductive(regular(cross_product(X0,X1)))
| x = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
| x = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f828,plain,
( spl0_109
<=> ! [X0,X1] :
( x = X0
| x = X1
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1254,plain,
( ! [X0,X1] :
( ~ inductive(regular(cross_product(X0,X1)))
| x = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
| x = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = x )
| ~ spl0_109
| ~ spl0_141 ),
inference(superposition,[],[f829,f1230]) ).
fof(f829,plain,
( ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| x = X1
| x = X0 )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f6662,plain,
( spl0_466
| ~ spl0_11
| ~ spl0_56
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1680,f1640,f493,f254,f6660]) ).
fof(f6660,plain,
( spl0_466
<=> ! [X2,X0,X1] :
( x = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
| subclass(X0,intersection(X1,domain_of(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f1680,plain,
( ! [X2,X0,X1] :
( x = 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_11
| ~ spl0_56
| ~ spl0_185 ),
inference(forward_demodulation,[],[f1667,f494]) ).
fof(f1667,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)
| x = 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_11
| ~ spl0_185 ),
inference(resolution,[],[f1641,f255]) ).
fof(f6658,plain,
( spl0_465
| ~ spl0_38
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1202,f1178,f374,f6656]) ).
fof(f6656,plain,
( spl0_465
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| x = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f1202,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| x = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) )
| ~ spl0_38
| ~ spl0_139 ),
inference(resolution,[],[f1179,f375]) ).
fof(f6654,plain,
( spl0_464
| ~ spl0_39
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1201,f1178,f378,f6652]) ).
fof(f6652,plain,
( spl0_464
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| x = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f1201,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| x = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) )
| ~ spl0_39
| ~ spl0_139 ),
inference(resolution,[],[f1179,f379]) ).
fof(f6650,plain,
( spl0_463
| ~ spl0_38
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1185,f1174,f374,f6648]) ).
fof(f6648,plain,
( spl0_463
<=> ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| x = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f1185,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| x = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) )
| ~ spl0_38
| ~ spl0_138 ),
inference(resolution,[],[f1175,f375]) ).
fof(f6646,plain,
( spl0_462
| ~ spl0_39
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1184,f1174,f378,f6644]) ).
fof(f6644,plain,
( spl0_462
<=> ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| x = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f1184,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| x = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) )
| ~ spl0_39
| ~ spl0_138 ),
inference(resolution,[],[f1175,f379]) ).
fof(f6548,plain,
( spl0_460
| ~ spl0_461
| ~ spl0_64
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1685,f1644,f562,f6545,f6542]) ).
fof(f6542,plain,
( spl0_460
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(X0,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f6545,plain,
( spl0_461
<=> subclass(domain_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f1685,plain,
( ! [X0] :
( ~ subclass(domain_relation,element_relation)
| ~ member(X0,universal_class)
| member(X0,domain_of(X0)) )
| ~ spl0_64
| ~ spl0_186 ),
inference(resolution,[],[f1645,f563]) ).
fof(f6540,plain,
( spl0_459
| ~ spl0_33
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1616,f1602,f354,f6538]) ).
fof(f1616,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl0_33
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f1609]) ).
fof(f1609,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0))
| subclass(universal_class,complement(X0)) )
| ~ spl0_33
| ~ spl0_180 ),
inference(resolution,[],[f1603,f355]) ).
fof(f6536,plain,
( spl0_458
| ~ spl0_78
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1414,f1376,f635,f6534]) ).
fof(f6534,plain,
( spl0_458
<=> ! [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_458])]) ).
fof(f1414,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(subset_relation,X0) )
| ~ spl0_78
| ~ spl0_157 ),
inference(superposition,[],[f1377,f637]) ).
fof(f6532,plain,
( spl0_457
| ~ spl0_38
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1150,f1116,f374,f6530]) ).
fof(f6530,plain,
( spl0_457
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f1150,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) )
| ~ spl0_38
| ~ spl0_135 ),
inference(resolution,[],[f1117,f375]) ).
fof(f6528,plain,
( spl0_456
| ~ spl0_39
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1149,f1116,f378,f6526]) ).
fof(f6526,plain,
( spl0_456
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f1149,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) )
| ~ spl0_39
| ~ spl0_135 ),
inference(resolution,[],[f1117,f379]) ).
fof(f6524,plain,
( spl0_455
| ~ spl0_233
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f5755,f3421,f2307,f6521]) ).
fof(f6521,plain,
( spl0_455
<=> x = intersection(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f5755,plain,
( x = intersection(x,universal_class)
| ~ spl0_233
| ~ spl0_303 ),
inference(superposition,[],[f3422,f2309]) ).
fof(f6466,plain,
( spl0_454
| spl0_1
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1939,f1929,f208,f6463]) ).
fof(f1939,plain,
( not_subclass_element(cross_product(x,x),identity_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),first(not_subclass_element(cross_product(x,x),identity_relation))),unordered_pair(first(not_subclass_element(cross_product(x,x),identity_relation)),unordered_pair(second(not_subclass_element(cross_product(x,x),identity_relation)),second(not_subclass_element(cross_product(x,x),identity_relation)))))
| spl0_1
| ~ spl0_209 ),
inference(resolution,[],[f1930,f210]) ).
fof(f6459,plain,
( spl0_453
| ~ spl0_115
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1563,f1542,f905,f6457]) ).
fof(f6457,plain,
( spl0_453
<=> ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
| ~ member(X0,universal_class)
| x = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f1563,plain,
( ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
| ~ member(X0,universal_class)
| x = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class) )
| ~ spl0_115
| ~ spl0_174 ),
inference(resolution,[],[f1543,f906]) ).
fof(f6436,plain,
( spl0_452
| ~ spl0_112
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1774,f1733,f881,f6434]) ).
fof(f6434,plain,
( spl0_452
<=> ! [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))))),x)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f6348,plain,
( spl0_451
| ~ spl0_141
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1357,f1321,f1229,f6346]) ).
fof(f6346,plain,
( spl0_451
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f1357,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) = x )
| ~ spl0_141
| ~ spl0_152 ),
inference(superposition,[],[f1322,f1230]) ).
fof(f6344,plain,
( spl0_450
| ~ spl0_80
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1238,f1229,f654,f6342]) ).
fof(f6342,plain,
( spl0_450
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f1238,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) = x )
| ~ spl0_80
| ~ spl0_141 ),
inference(superposition,[],[f655,f1230]) ).
fof(f6340,plain,
( spl0_449
| ~ spl0_28
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1203,f1178,f327,f6338]) ).
fof(f6338,plain,
( spl0_449
<=> ! [X0,X1] :
( ~ member(intersection(X0,complement(X1)),universal_class)
| x = intersection(X0,complement(X1))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f1203,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,complement(X1)),universal_class)
| x = intersection(X0,complement(X1))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) )
| ~ spl0_28
| ~ spl0_139 ),
inference(resolution,[],[f1179,f328]) ).
fof(f6336,plain,
( spl0_448
| ~ spl0_28
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1186,f1174,f327,f6334]) ).
fof(f6334,plain,
( spl0_448
<=> ! [X0,X1] :
( ~ member(intersection(complement(X0),X1),universal_class)
| x = intersection(complement(X0),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f1186,plain,
( ! [X0,X1] :
( ~ member(intersection(complement(X0),X1),universal_class)
| x = intersection(complement(X0),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) )
| ~ spl0_28
| ~ spl0_138 ),
inference(resolution,[],[f1175,f328]) ).
fof(f6329,plain,
( spl0_275
| ~ spl0_446
| ~ spl0_447
| ~ spl0_134
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1170,f1124,f1104,f6326,f6322,f2813]) ).
fof(f6322,plain,
( spl0_446
<=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f6326,plain,
( spl0_447
<=> 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_447])]) ).
fof(f1170,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
| ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
| x = complement(cross_product(universal_class,universal_class))
| ~ spl0_134
| ~ spl0_137 ),
inference(resolution,[],[f1125,f1105]) ).
fof(f6169,plain,
( spl0_445
| ~ spl0_7
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1545,f1538,f235,f6167]) ).
fof(f1545,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) )
| ~ spl0_7
| ~ spl0_173 ),
inference(resolution,[],[f1539,f236]) ).
fof(f6165,plain,
( spl0_444
| ~ spl0_28
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1303,f1290,f327,f6163]) ).
fof(f1303,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) )
| ~ spl0_28
| ~ spl0_149 ),
inference(resolution,[],[f1291,f328]) ).
fof(f6161,plain,
( spl0_443
| ~ spl0_28
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1151,f1116,f327,f6159]) ).
fof(f1151,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) )
| ~ spl0_28
| ~ spl0_135 ),
inference(resolution,[],[f1117,f328]) ).
fof(f6157,plain,
( spl0_442
| ~ spl0_75
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1134,f1116,f618,f6155]) ).
fof(f6155,plain,
( spl0_442
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,compose_class(X0))
| compose(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f1134,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,compose_class(X0))
| compose(X0,X1) = X2 )
| ~ spl0_75
| ~ spl0_135 ),
inference(resolution,[],[f1117,f619]) ).
fof(f6033,plain,
( ~ spl0_440
| spl0_441
| ~ spl0_140
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f5902,f5839,f1216,f6030,f6026]) ).
fof(f5902,plain,
( function(x)
| ~ single_valued_class(x)
| ~ spl0_140
| ~ spl0_429 ),
inference(resolution,[],[f5840,f1217]) ).
fof(f5942,plain,
( spl0_439
| ~ spl0_141
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f1793,f1737,f1229,f5940]) ).
fof(f5940,plain,
( spl0_439
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f5938,plain,
( spl0_438
| ~ spl0_112
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1751,f1729,f881,f5936]) ).
fof(f5936,plain,
( spl0_438
<=> ! [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)))),x)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f5934,plain,
( spl0_437
| ~ spl0_112
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1706,f1644,f881,f5932]) ).
fof(f5932,plain,
( spl0_437
<=> ! [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)))),x)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f1706,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)))),x)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
| x = X0 )
| ~ spl0_112
| ~ spl0_186 ),
inference(resolution,[],[f1645,f882]) ).
fof(f5930,plain,
( spl0_436
| ~ spl0_106
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1208,f1178,f807,f5928]) ).
fof(f5928,plain,
( spl0_436
<=> ! [X0,X1] :
( ~ member(intersection(X0,x),universal_class)
| x = intersection(X0,x)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,x),intersection(X0,x)),universal_class)),universal_class))))))),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f1208,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,x),universal_class)
| x = intersection(X0,x)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,x),intersection(X0,x)),universal_class)),universal_class))))))),X1)
| x = X1 )
| ~ spl0_106
| ~ spl0_139 ),
inference(resolution,[],[f1179,f808]) ).
fof(f5926,plain,
( spl0_435
| ~ spl0_45
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1198,f1178,f417,f5924]) ).
fof(f5924,plain,
( spl0_435
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x
| ~ 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_435])]) ).
fof(f1198,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x
| ~ 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_45
| ~ spl0_139 ),
inference(resolution,[],[f1179,f418]) ).
fof(f5922,plain,
( spl0_434
| ~ spl0_106
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1191,f1174,f807,f5920]) ).
fof(f5920,plain,
( spl0_434
<=> ! [X0,X1] :
( ~ member(intersection(x,X0),universal_class)
| x = intersection(x,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(x,X0),intersection(x,X0)),universal_class)),universal_class))))))),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f1191,plain,
( ! [X0,X1] :
( ~ member(intersection(x,X0),universal_class)
| x = intersection(x,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(x,X0),intersection(x,X0)),universal_class)),universal_class))))))),X1)
| x = X1 )
| ~ spl0_106
| ~ spl0_138 ),
inference(resolution,[],[f1175,f808]) ).
fof(f5918,plain,
( spl0_433
| ~ spl0_45
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1181,f1174,f417,f5916]) ).
fof(f5916,plain,
( spl0_433
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x
| ~ 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_433])]) ).
fof(f1181,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x
| ~ 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_45
| ~ spl0_138 ),
inference(resolution,[],[f1175,f418]) ).
fof(f5897,plain,
( spl0_432
| ~ spl0_107
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1112,f1104,f819,f5895]) ).
fof(f5895,plain,
( spl0_432
<=> ! [X0] :
( ~ member(complement(regular(X0)),universal_class)
| x = complement(regular(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),x)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f819,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ member(X1,x)
| member(X1,regular(X0))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1112,plain,
( ! [X0] :
( ~ member(complement(regular(X0)),universal_class)
| x = complement(regular(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),x)
| x = X0 )
| ~ spl0_107
| ~ spl0_134 ),
inference(resolution,[],[f1105,f820]) ).
fof(f820,plain,
( ! [X0,X1] :
( member(X1,regular(X0))
| ~ member(X1,x)
| x = X0 )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f5892,plain,
( spl0_431
| ~ spl0_87
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1241,f1229,f690,f5890]) ).
fof(f5890,plain,
( spl0_431
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f690,plain,
( spl0_87
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1241,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) = x )
| ~ spl0_87
| ~ spl0_141 ),
inference(superposition,[],[f691,f1230]) ).
fof(f691,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function)
| compose(X0,X1) = X4 )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f5881,plain,
( spl0_430
| ~ spl0_35
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1251,f1229,f362,f5879]) ).
fof(f5879,plain,
( spl0_430
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f1251,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) = x )
| ~ spl0_35
| ~ spl0_141 ),
inference(superposition,[],[f363,f1230]) ).
fof(f5841,plain,
( spl0_429
| ~ spl0_303
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f5782,f4123,f3421,f5839]) ).
fof(f5782,plain,
( ! [X0] : subclass(x,X0)
| ~ spl0_303
| ~ spl0_340 ),
inference(superposition,[],[f4124,f3422]) ).
fof(f5837,plain,
( spl0_427
| ~ spl0_428
| ~ spl0_105
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1634,f1625,f803,f5834,f5830]) ).
fof(f5834,plain,
( spl0_428
<=> 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_428])]) ).
fof(f1634,plain,
( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| x = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_105
| ~ spl0_183 ),
inference(resolution,[],[f1626,f804]) ).
fof(f5828,plain,
( spl0_426
| ~ spl0_129
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1207,f1178,f997,f5826]) ).
fof(f5826,plain,
( spl0_426
<=> ! [X0] :
( ~ member(intersection(X0,singleton_relation),universal_class)
| x = intersection(X0,singleton_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f1207,plain,
( ! [X0] :
( ~ member(intersection(X0,singleton_relation),universal_class)
| x = intersection(X0,singleton_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_129
| ~ spl0_139 ),
inference(resolution,[],[f1179,f998]) ).
fof(f5824,plain,
( spl0_425
| ~ spl0_130
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1205,f1178,f1001,f5822]) ).
fof(f5822,plain,
( spl0_425
<=> ! [X0] :
( ~ member(intersection(X0,identity_relation),universal_class)
| x = intersection(X0,identity_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f1205,plain,
( ! [X0] :
( ~ member(intersection(X0,identity_relation),universal_class)
| x = intersection(X0,identity_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_130
| ~ spl0_139 ),
inference(resolution,[],[f1179,f1002]) ).
fof(f5820,plain,
( spl0_424
| ~ spl0_129
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1190,f1174,f997,f5818]) ).
fof(f5818,plain,
( spl0_424
<=> ! [X0] :
( ~ member(intersection(singleton_relation,X0),universal_class)
| x = intersection(singleton_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f1190,plain,
( ! [X0] :
( ~ member(intersection(singleton_relation,X0),universal_class)
| x = intersection(singleton_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_129
| ~ spl0_138 ),
inference(resolution,[],[f1175,f998]) ).
fof(f5816,plain,
( spl0_423
| ~ spl0_130
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1188,f1174,f1001,f5814]) ).
fof(f5814,plain,
( spl0_423
<=> ! [X0] :
( ~ member(intersection(identity_relation,X0),universal_class)
| x = intersection(identity_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f1188,plain,
( ! [X0] :
( ~ member(intersection(identity_relation,X0),universal_class)
| x = intersection(identity_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_130
| ~ spl0_138 ),
inference(resolution,[],[f1175,f1002]) ).
fof(f5737,plain,
( spl0_422
| ~ spl0_142
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1347,f1317,f1259,f5735]) ).
fof(f5735,plain,
( spl0_422
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f1347,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) )
| ~ spl0_142
| ~ spl0_151 ),
inference(duplicate_literal_removal,[],[f1334]) ).
fof(f1334,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1)
| subclass(complement(X0),X1) )
| ~ spl0_142
| ~ spl0_151 ),
inference(resolution,[],[f1318,f1260]) ).
fof(f5733,plain,
( spl0_421
| ~ spl0_29
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1225,f1216,f331,f5731]) ).
fof(f5731,plain,
( spl0_421
<=> ! [X0,X1] :
( function(compose(X0,X1))
| ~ single_valued_class(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f1225,plain,
( ! [X0,X1] :
( function(compose(X0,X1))
| ~ single_valued_class(compose(X0,X1)) )
| ~ spl0_29
| ~ spl0_140 ),
inference(resolution,[],[f1217,f332]) ).
fof(f5729,plain,
( ~ spl0_419
| spl0_420
| ~ spl0_9
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1220,f1216,f244,f5726,f5722]) ).
fof(f5722,plain,
( spl0_419
<=> single_valued_class(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f5726,plain,
( spl0_420
<=> function(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f1220,plain,
( function(cross_product(universal_class,universal_class))
| ~ single_valued_class(cross_product(universal_class,universal_class))
| ~ spl0_9
| ~ spl0_140 ),
inference(resolution,[],[f1217,f245]) ).
fof(f5720,plain,
( spl0_417
| ~ spl0_418
| ~ spl0_129
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1156,f1116,f997,f5717,f5714]) ).
fof(f5714,plain,
( spl0_417
<=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f5717,plain,
( spl0_418
<=> subclass(universal_class,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f1156,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,singleton_relation)
| member(unordered_pair(X0,X1),element_relation) )
| ~ spl0_129
| ~ spl0_135 ),
inference(resolution,[],[f1117,f998]) ).
fof(f5709,plain,
( spl0_415
| ~ spl0_416
| ~ spl0_87
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1138,f1116,f690,f5706,f5703]) ).
fof(f5703,plain,
( spl0_415
<=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f5706,plain,
( spl0_416
<=> subclass(universal_class,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f1138,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,composition_function)
| compose(X0,X1) = X2 )
| ~ spl0_87
| ~ spl0_135 ),
inference(resolution,[],[f1117,f691]) ).
fof(f5701,plain,
( spl0_414
| ~ spl0_72
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1128,f1116,f602,f5699]) ).
fof(f5699,plain,
( spl0_414
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f1128,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) )
| ~ spl0_72
| ~ spl0_135 ),
inference(resolution,[],[f1117,f603]) ).
fof(f5697,plain,
( spl0_413
| ~ spl0_73
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1127,f1116,f606,f5695]) ).
fof(f5695,plain,
( spl0_413
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f1127,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) )
| ~ spl0_73
| ~ spl0_135 ),
inference(resolution,[],[f1117,f607]) ).
fof(f5693,plain,
( spl0_412
| ~ spl0_33
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1016,f1001,f354,f5691]) ).
fof(f5691,plain,
( spl0_412
<=> ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f1016,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) )
| ~ spl0_33
| ~ spl0_130 ),
inference(resolution,[],[f1002,f355]) ).
fof(f5689,plain,
( spl0_411
| ~ spl0_33
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1010,f997,f354,f5687]) ).
fof(f1010,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_33
| ~ spl0_129 ),
inference(resolution,[],[f998,f355]) ).
fof(f5685,plain,
( spl0_410
| ~ spl0_44
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f916,f912,f398,f5683]) ).
fof(f5683,plain,
( spl0_410
<=> ! [X0] :
( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f912,plain,
( spl0_116
<=> ! [X0] :
( single_valued_class(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f916,plain,
( ! [X0] :
( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) )
| ~ spl0_44
| ~ spl0_116 ),
inference(resolution,[],[f913,f399]) ).
fof(f913,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f5640,plain,
( spl0_409
| ~ spl0_45
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1084,f1029,f417,f5638]) ).
fof(f5638,plain,
( spl0_409
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| x = X0
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f1084,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| x = X0
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
| ~ spl0_45
| ~ spl0_132 ),
inference(resolution,[],[f1030,f418]) ).
fof(f5635,plain,
( spl0_408
| ~ spl0_298
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4910,f4119,f3270,f5632]) ).
fof(f5632,plain,
( spl0_408
<=> subclass(x,complement(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f3270,plain,
( spl0_298
<=> x = intersection(complement(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f4910,plain,
( subclass(x,complement(element_relation))
| ~ spl0_298
| ~ spl0_339 ),
inference(superposition,[],[f4120,f3272]) ).
fof(f3272,plain,
( x = intersection(complement(element_relation),singleton_relation)
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f3270]) ).
fof(f5574,plain,
( spl0_407
| ~ spl0_86
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1240,f1229,f686,f5572]) ).
fof(f5572,plain,
( spl0_407
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f1240,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) = x )
| ~ spl0_86
| ~ spl0_141 ),
inference(superposition,[],[f687,f1230]) ).
fof(f5570,plain,
( spl0_406
| ~ spl0_84
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1239,f1229,f676,f5568]) ).
fof(f5568,plain,
( spl0_406
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f1239,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) = x )
| ~ spl0_84
| ~ spl0_141 ),
inference(superposition,[],[f677,f1230]) ).
fof(f5566,plain,
( spl0_405
| ~ spl0_38
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1088,f1029,f374,f5564]) ).
fof(f5564,plain,
( spl0_405
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f1088,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
| ~ spl0_38
| ~ spl0_132 ),
inference(resolution,[],[f1030,f375]) ).
fof(f5562,plain,
( spl0_404
| ~ spl0_39
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1087,f1029,f378,f5560]) ).
fof(f5560,plain,
( spl0_404
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f1087,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
| ~ spl0_39
| ~ spl0_132 ),
inference(resolution,[],[f1030,f379]) ).
fof(f5558,plain,
( spl0_403
| ~ spl0_81
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f837,f823,f658,f5556]) ).
fof(f5556,plain,
( spl0_403
<=> ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| x = 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_403])]) ).
fof(f837,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| x = 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_81
| ~ spl0_108 ),
inference(resolution,[],[f824,f659]) ).
fof(f5415,plain,
( spl0_402
| ~ spl0_111
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1494,f1456,f849,f5413]) ).
fof(f5413,plain,
( spl0_402
<=> ! [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)
| x = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f1494,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)
| x = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_111
| ~ spl0_164 ),
inference(resolution,[],[f1457,f850]) ).
fof(f5411,plain,
( spl0_401
| ~ spl0_110
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1491,f1456,f845,f5409]) ).
fof(f5409,plain,
( spl0_401
<=> ! [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)
| x = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f1491,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)
| x = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
| ~ spl0_110
| ~ spl0_164 ),
inference(resolution,[],[f1457,f846]) ).
fof(f5407,plain,
( spl0_400
| ~ spl0_111
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1472,f1452,f849,f5405]) ).
fof(f5405,plain,
( spl0_400
<=> ! [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)
| x = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f1472,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)
| x = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_111
| ~ spl0_163 ),
inference(resolution,[],[f1453,f850]) ).
fof(f5403,plain,
( spl0_399
| ~ spl0_110
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1469,f1452,f845,f5401]) ).
fof(f5401,plain,
( spl0_399
<=> ! [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)
| x = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f1469,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)
| x = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
| ~ spl0_110
| ~ spl0_163 ),
inference(resolution,[],[f1453,f846]) ).
fof(f5399,plain,
( spl0_398
| ~ spl0_11
| ~ spl0_56
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1302,f1259,f493,f254,f5397]) ).
fof(f5397,plain,
( spl0_398
<=> ! [X0,X1] :
( x = 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_398])]) ).
fof(f1302,plain,
( ! [X0,X1] :
( x = 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_11
| ~ spl0_56
| ~ spl0_142 ),
inference(forward_demodulation,[],[f1300,f494]) ).
fof(f1300,plain,
( ! [X0,X1] :
( subclass(complement(domain_of(X0)),X1)
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
| x = 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_11
| ~ spl0_142 ),
inference(resolution,[],[f1260,f255]) ).
fof(f5395,plain,
( spl0_397
| ~ spl0_298
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4911,f4123,f3270,f5392]) ).
fof(f5392,plain,
( spl0_397
<=> subclass(x,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f4911,plain,
( subclass(x,singleton_relation)
| ~ spl0_298
| ~ spl0_340 ),
inference(superposition,[],[f4124,f3272]) ).
fof(f5390,plain,
( spl0_396
| ~ spl0_28
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1089,f1029,f327,f5388]) ).
fof(f5388,plain,
( spl0_396
<=> ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| ~ member(X0,universal_class)
| x = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f1089,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| ~ member(X0,universal_class)
| x = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
| ~ spl0_28
| ~ spl0_132 ),
inference(resolution,[],[f1030,f328]) ).
fof(f5386,plain,
( spl0_394
| ~ spl0_395
| ~ spl0_86
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1137,f1116,f686,f5383,f5380]) ).
fof(f5380,plain,
( spl0_394
<=> ! [X0,X1] : member(X0,domain_of(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f5383,plain,
( spl0_395
<=> subclass(universal_class,application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f1137,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,application_function)
| member(X0,domain_of(X1)) )
| ~ spl0_86
| ~ spl0_135 ),
inference(resolution,[],[f1117,f687]) ).
fof(f5378,plain,
( spl0_392
| ~ spl0_393
| ~ spl0_67
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1135,f1116,f576,f5375,f5372]) ).
fof(f5372,plain,
( spl0_392
<=> ! [X0,X1] : domain_of(X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f5375,plain,
( spl0_393
<=> subclass(universal_class,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f1135,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,domain_relation)
| domain_of(X0) = X1 )
| ~ spl0_67
| ~ spl0_135 ),
inference(resolution,[],[f1117,f577]) ).
fof(f5369,plain,
( ~ spl0_390
| spl0_391
| ~ spl0_30
| ~ spl0_126 ),
inference(avatar_split_clause,[],[f1006,f985,f335,f5366,f5362]) ).
fof(f5362,plain,
( spl0_390
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f985,plain,
( spl0_126
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1006,plain,
( member(omega,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl0_30
| ~ spl0_126 ),
inference(resolution,[],[f986,f336]) ).
fof(f986,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f5339,plain,
( spl0_389
| ~ spl0_108
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1832,f1814,f823,f5337]) ).
fof(f5337,plain,
( spl0_389
<=> ! [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)))))))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f5335,plain,
( spl0_388
| ~ spl0_129
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1094,f1029,f997,f5333]) ).
fof(f5333,plain,
( spl0_388
<=> ! [X0] :
( ~ subclass(X0,singleton_relation)
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f1094,plain,
( ! [X0] :
( ~ subclass(X0,singleton_relation)
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_129
| ~ spl0_132 ),
inference(resolution,[],[f1030,f998]) ).
fof(f5331,plain,
( spl0_387
| ~ spl0_130
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1092,f1029,f1001,f5329]) ).
fof(f5329,plain,
( spl0_387
<=> ! [X0] :
( ~ subclass(X0,identity_relation)
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f1092,plain,
( ! [X0] :
( ~ subclass(X0,identity_relation)
| ~ member(X0,universal_class)
| x = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_130
| ~ spl0_132 ),
inference(resolution,[],[f1030,f1002]) ).
fof(f5306,plain,
( spl0_386
| ~ spl0_134
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1554,f1542,f1104,f5304]) ).
fof(f5304,plain,
( spl0_386
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class)
| ~ member(complement(X0),universal_class)
| complement(X0) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f1554,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class)
| ~ member(complement(X0),universal_class)
| complement(X0) = x )
| ~ spl0_134
| ~ spl0_174 ),
inference(resolution,[],[f1543,f1105]) ).
fof(f5302,plain,
( spl0_385
| ~ spl0_115
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1342,f1317,f905,f5300]) ).
fof(f5300,plain,
( spl0_385
<=> ! [X0,X1] :
( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
| subclass(X0,X1)
| x = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f1342,plain,
( ! [X0,X1] :
( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
| subclass(X0,X1)
| x = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class) )
| ~ spl0_115
| ~ spl0_151 ),
inference(resolution,[],[f1318,f906]) ).
fof(f5298,plain,
( spl0_384
| ~ spl0_79
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1237,f1229,f640,f5296]) ).
fof(f5296,plain,
( spl0_384
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f1237,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) = x )
| ~ spl0_79
| ~ spl0_141 ),
inference(superposition,[],[f641,f1230]) ).
fof(f5291,plain,
( spl0_237
| ~ spl0_239
| spl0_383
| ~ spl0_78
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1195,f1174,f635,f5288,f2358,f2334]) ).
fof(f5288,plain,
( spl0_383
<=> 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_383])]) ).
fof(f1195,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ member(subset_relation,universal_class)
| subset_relation = x
| ~ spl0_78
| ~ spl0_138 ),
inference(superposition,[],[f1175,f637]) ).
fof(f5260,plain,
( spl0_382
| ~ spl0_112
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f1566,f1542,f881,f5258]) ).
fof(f5258,plain,
( spl0_382
<=> ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),x)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f1566,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),x)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
| x = X0 )
| ~ spl0_112
| ~ spl0_174 ),
inference(resolution,[],[f1543,f882]) ).
fof(f5256,plain,
( spl0_381
| ~ spl0_11
| ~ spl0_56
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f813,f803,f493,f254,f5254]) ).
fof(f5254,plain,
( spl0_381
<=> ! [X0] :
( x = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
| x = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f813,plain,
( ! [X0] :
( x = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
| x = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class) )
| ~ spl0_11
| ~ spl0_56
| ~ spl0_105 ),
inference(forward_demodulation,[],[f812,f494]) ).
fof(f812,plain,
( ! [X0] :
( x = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class)
| x = intersection(cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class),X0) )
| ~ spl0_11
| ~ spl0_105 ),
inference(resolution,[],[f804,f255]) ).
fof(f5128,plain,
( spl0_380
| ~ spl0_188
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f4977,f4974,f1710,f5126]) ).
fof(f5126,plain,
( spl0_380
<=> ! [X2,X0,X1] :
( cross_product(X0,X1) = singleton_relation
| ~ member(regular(cross_product(X0,X1)),compose_class(X2))
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f4974,plain,
( spl0_373
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f4977,plain,
( ! [X2,X0,X1] :
( cross_product(X0,X1) = singleton_relation
| ~ member(regular(cross_product(X0,X1)),compose_class(X2))
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1)))) )
| ~ spl0_188
| ~ spl0_373 ),
inference(forward_demodulation,[],[f4975,f1712]) ).
fof(f4975,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) = x )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f4974]) ).
fof(f5008,plain,
( spl0_379
| ~ spl0_107
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1669,f1640,f819,f5006]) ).
fof(f5006,plain,
( spl0_379
<=> ! [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))),x)
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f1669,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))),x)
| x = X2 )
| ~ spl0_107
| ~ spl0_185 ),
inference(resolution,[],[f1641,f820]) ).
fof(f5003,plain,
( spl0_378
| ~ spl0_131
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1438,f1380,f1023,f5001]) ).
fof(f1023,plain,
( spl0_131
<=> ! [X0,X1] :
( x = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
| subclass(X0,domain_of(X1))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1438,plain,
( ! [X0,X1] :
( subclass(intersection(X0,universal_class),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) )
| ~ spl0_131
| ~ spl0_158 ),
inference(duplicate_literal_removal,[],[f1420]) ).
fof(f1420,plain,
( ! [X0,X1] :
( subclass(intersection(X0,universal_class),domain_of(X1))
| subclass(intersection(X0,universal_class),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) )
| ~ spl0_131
| ~ spl0_158 ),
inference(resolution,[],[f1381,f1024]) ).
fof(f1024,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| subclass(X0,domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f4997,plain,
( spl0_377
| ~ spl0_112
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1429,f1380,f881,f4995]) ).
fof(f1429,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,regular(X1)),X2)
| member(not_subclass_element(intersection(X0,regular(X1)),X2),x)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| x = X1 )
| ~ spl0_112
| ~ spl0_158 ),
inference(resolution,[],[f1381,f882]) ).
fof(f4992,plain,
( spl0_376
| ~ spl0_131
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1417,f1376,f1023,f4990]) ).
fof(f1417,plain,
( ! [X0,X1] :
( subclass(intersection(universal_class,X0),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) )
| ~ spl0_131
| ~ spl0_157 ),
inference(duplicate_literal_removal,[],[f1399]) ).
fof(f1399,plain,
( ! [X0,X1] :
( subclass(intersection(universal_class,X0),domain_of(X1))
| subclass(intersection(universal_class,X0),domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) )
| ~ spl0_131
| ~ spl0_157 ),
inference(resolution,[],[f1377,f1024]) ).
fof(f4986,plain,
( spl0_375
| ~ spl0_112
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1408,f1376,f881,f4984]) ).
fof(f1408,plain,
( ! [X2,X0,X1] :
( subclass(intersection(regular(X0),X1),X2)
| member(not_subclass_element(intersection(regular(X0),X1),X2),x)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| x = X0 )
| ~ spl0_112
| ~ spl0_157 ),
inference(resolution,[],[f1377,f882]) ).
fof(f4982,plain,
( ~ spl0_374
| spl0_69
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1785,f1710,f584,f4979]) ).
fof(f4979,plain,
( spl0_374
<=> member(singleton_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f1785,plain,
( ~ member(singleton_relation,element_relation)
| spl0_69
| ~ spl0_188 ),
inference(superposition,[],[f585,f1712]) ).
fof(f585,plain,
( ~ member(x,element_relation)
| spl0_69 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f4976,plain,
( spl0_373
| ~ spl0_75
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1236,f1229,f618,f4974]) ).
fof(f1236,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) = x )
| ~ spl0_75
| ~ spl0_141 ),
inference(superposition,[],[f619,f1230]) ).
fof(f4970,plain,
( spl0_222
| ~ spl0_371
| spl0_372
| ~ spl0_27
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1017,f1001,f323,f4967,f4963,f2213]) ).
fof(f4967,plain,
( spl0_372
<=> 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_372])]) ).
fof(f1017,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
| ~ member(identity_relation,universal_class)
| identity_relation = x
| ~ spl0_27
| ~ spl0_130 ),
inference(resolution,[],[f1002,f324]) ).
fof(f4924,plain,
( spl0_188
| ~ spl0_200
| spl0_370
| ~ spl0_27
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1011,f997,f323,f4921,f1851,f1710]) ).
fof(f4921,plain,
( spl0_370
<=> 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_370])]) ).
fof(f1011,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation)
| ~ member(singleton_relation,universal_class)
| singleton_relation = x
| ~ spl0_27
| ~ spl0_129 ),
inference(resolution,[],[f998,f324]) ).
fof(f4919,plain,
( spl0_369
| ~ spl0_66
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f950,f946,f570,f4917]) ).
fof(f4917,plain,
( spl0_369
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| x = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f946,plain,
( spl0_118
<=> ! [X2,X0,X1] :
( ~ subclass(domain_of(X0),X1)
| member(X2,X1)
| ~ member(X2,universal_class)
| x = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f950,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| x = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
| ~ inductive(X1) )
| ~ spl0_66
| ~ spl0_118 ),
inference(resolution,[],[f947,f571]) ).
fof(f947,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_of(X0),X1)
| member(X2,X1)
| ~ member(X2,universal_class)
| x = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f946]) ).
fof(f4915,plain,
( spl0_368
| ~ spl0_25
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1226,f1216,f315,f4913]) ).
fof(f4913,plain,
( spl0_368
<=> ! [X0] :
( function(compose_class(X0))
| ~ single_valued_class(compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f1226,plain,
( ! [X0] :
( function(compose_class(X0))
| ~ single_valued_class(compose_class(X0)) )
| ~ spl0_25
| ~ spl0_140 ),
inference(resolution,[],[f1217,f316]) ).
fof(f4885,plain,
( spl0_366
| ~ spl0_367
| ~ spl0_64
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1130,f1116,f562,f4882,f4879]) ).
fof(f4879,plain,
( spl0_366
<=> ! [X0,X1] : member(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f4882,plain,
( spl0_367
<=> subclass(universal_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f1130,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,element_relation)
| member(X0,X1) )
| ~ spl0_64
| ~ spl0_135 ),
inference(resolution,[],[f1117,f563]) ).
fof(f4874,plain,
( spl0_365
| ~ spl0_115
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1153,f1116,f905,f4872]) ).
fof(f4872,plain,
( spl0_365
<=> ! [X0,X1] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class))))
| x = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f1153,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class))))
| x = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class) )
| ~ spl0_115
| ~ spl0_135 ),
inference(resolution,[],[f1117,f906]) ).
fof(f4432,plain,
( spl0_362
| spl0_363
| ~ spl0_364
| ~ spl0_3
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1490,f1456,f217,f4429,f4425,f4421]) ).
fof(f1490,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)
| x = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_3
| ~ spl0_164 ),
inference(resolution,[],[f1457,f218]) ).
fof(f4416,plain,
( spl0_359
| spl0_360
| ~ spl0_361
| ~ spl0_3
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1468,f1452,f217,f4413,f4409,f4405]) ).
fof(f1468,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
| member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| complement(compose(element_relation,complement(identity_relation))) = x
| ~ spl0_3
| ~ spl0_163 ),
inference(resolution,[],[f1453,f218]) ).
fof(f4403,plain,
( spl0_358
| ~ spl0_67
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1233,f1229,f576,f4401]) ).
fof(f4401,plain,
( spl0_358
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f1233,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) = x )
| ~ spl0_67
| ~ spl0_141 ),
inference(superposition,[],[f577,f1230]) ).
fof(f4399,plain,
( spl0_357
| ~ spl0_290
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f4144,f4119,f3178,f4396]) ).
fof(f4396,plain,
( spl0_357
<=> subclass(x,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f3178,plain,
( spl0_290
<=> x = intersection(complement(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f4144,plain,
( subclass(x,complement(subset_relation))
| ~ spl0_290
| ~ spl0_339 ),
inference(superposition,[],[f4120,f3180]) ).
fof(f3180,plain,
( x = intersection(complement(subset_relation),identity_relation)
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3178]) ).
fof(f4394,plain,
( spl0_356
| ~ spl0_62
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f949,f946,f548,f4392]) ).
fof(f4392,plain,
( spl0_356
<=> ! [X0,X1] :
( member(X0,domain_of(domain_of(X1)))
| ~ member(X0,universal_class)
| x = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
| ~ operation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f949,plain,
( ! [X0,X1] :
( member(X0,domain_of(domain_of(X1)))
| ~ member(X0,universal_class)
| x = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
| ~ operation(X1) )
| ~ spl0_62
| ~ spl0_118 ),
inference(resolution,[],[f947,f549]) ).
fof(f4390,plain,
( spl0_355
| ~ spl0_108
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f910,f905,f823,f4388]) ).
fof(f4388,plain,
( spl0_355
<=> ! [X0] :
( x = 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))))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f910,plain,
( ! [X0] :
( x = 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))))
| x = X0 )
| ~ spl0_108
| ~ spl0_115 ),
inference(resolution,[],[f906,f824]) ).
fof(f4386,plain,
( spl0_354
| ~ spl0_111
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f900,f881,f849,f4384]) ).
fof(f900,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,regular(X1))),x)
| ~ member(regular(intersection(X0,regular(X1))),X1)
| x = X1
| x = intersection(X0,regular(X1)) )
| ~ spl0_111
| ~ spl0_112 ),
inference(resolution,[],[f882,f850]) ).
fof(f4382,plain,
( spl0_353
| ~ spl0_110
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f897,f881,f845,f4380]) ).
fof(f897,plain,
( ! [X0,X1] :
( member(regular(intersection(regular(X0),X1)),x)
| ~ member(regular(intersection(regular(X0),X1)),X0)
| x = X0
| x = intersection(regular(X0),X1) )
| ~ spl0_110
| ~ spl0_112 ),
inference(resolution,[],[f882,f846]) ).
fof(f4378,plain,
( spl0_352
| ~ spl0_54
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f867,f849,f485,f4376]) ).
fof(f4376,plain,
( spl0_352
<=> ! [X2,X0,X1] :
( x = 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_352])]) ).
fof(f867,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,unordered_pair(X1,X2))
| regular(intersection(X0,unordered_pair(X1,X2))) = X1
| regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
| ~ spl0_54
| ~ spl0_111 ),
inference(resolution,[],[f850,f486]) ).
fof(f4374,plain,
( spl0_351
| ~ spl0_54
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f853,f845,f485,f4372]) ).
fof(f4372,plain,
( spl0_351
<=> ! [X2,X0,X1] :
( x = 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_351])]) ).
fof(f853,plain,
( ! [X2,X0,X1] :
( x = intersection(unordered_pair(X0,X1),X2)
| regular(intersection(unordered_pair(X0,X1),X2)) = X0
| regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
| ~ spl0_54
| ~ spl0_110 ),
inference(resolution,[],[f846,f486]) ).
fof(f4245,plain,
( ~ spl0_350
| ~ spl0_123
| spl0_97
| ~ spl0_2
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1825,f1814,f213,f747,f971,f4242]) ).
fof(f4242,plain,
( spl0_350
<=> 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_350])]) ).
fof(f1825,plain,
( member(x,subset_relation)
| ~ member(x,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_2
| ~ spl0_198 ),
inference(resolution,[],[f1815,f214]) ).
fof(f4240,plain,
( spl0_348
| ~ spl0_349
| ~ spl0_106
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1708,f1644,f807,f4237,f4234]) ).
fof(f4234,plain,
( spl0_348
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| x = 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_348])]) ).
fof(f4237,plain,
( spl0_349
<=> subclass(domain_relation,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f1708,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,x)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
| x = X1 )
| ~ spl0_106
| ~ spl0_186 ),
inference(resolution,[],[f1645,f808]) ).
fof(f4232,plain,
( spl0_347
| ~ spl0_131
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1348,f1317,f1023,f4230]) ).
fof(f4230,plain,
( spl0_347
<=> ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f1348,plain,
( ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
| ~ spl0_131
| ~ spl0_151 ),
inference(duplicate_literal_removal,[],[f1333]) ).
fof(f1333,plain,
( ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,domain_of(X1))
| subclass(X0,domain_of(X1))
| x = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
| ~ spl0_131
| ~ spl0_151 ),
inference(resolution,[],[f1318,f1024]) ).
fof(f4228,plain,
( spl0_346
| ~ spl0_64
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1232,f1229,f562,f4226]) ).
fof(f4226,plain,
( spl0_346
<=> ! [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) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f1232,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) = x )
| ~ spl0_64
| ~ spl0_141 ),
inference(superposition,[],[f563,f1230]) ).
fof(f4224,plain,
( spl0_345
| ~ spl0_112
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f944,f918,f881,f4222]) ).
fof(f4222,plain,
( spl0_345
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,x)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f944,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,x)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_112
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f923]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,x)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_112
| ~ spl0_117 ),
inference(superposition,[],[f882,f919]) ).
fof(f4220,plain,
( spl0_344
| ~ spl0_112
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f939,f918,f881,f4218]) ).
fof(f4218,plain,
( spl0_344
<=> ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,x)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f939,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,x)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_112
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f928]) ).
fof(f928,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,x)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x )
| ~ spl0_112
| ~ spl0_117 ),
inference(superposition,[],[f882,f919]) ).
fof(f4178,plain,
( spl0_343
| ~ spl0_290
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4164,f4123,f3178,f4175]) ).
fof(f4164,plain,
( subclass(x,identity_relation)
| ~ spl0_290
| ~ spl0_340 ),
inference(superposition,[],[f4124,f3180]) ).
fof(f4173,plain,
( spl0_342
| ~ spl0_104
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1653,f1636,f782,f4171]) ).
fof(f4171,plain,
( spl0_342
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(x,X2)
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f1653,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(x,X2)
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_104
| ~ spl0_184 ),
inference(resolution,[],[f1637,f783]) ).
fof(f4169,plain,
( spl0_341
| ~ spl0_11
| ~ spl0_56
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1500,f1456,f493,f254,f4167]) ).
fof(f4167,plain,
( spl0_341
<=> ! [X0] :
( x = 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_341])]) ).
fof(f1500,plain,
( ! [X0] :
( x = 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_11
| ~ spl0_56
| ~ spl0_164 ),
inference(forward_demodulation,[],[f1484,f494]) ).
fof(f1484,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class)
| x = intersection(cross_product(unordered_pair(X0,X0),universal_class),flip(cross_product(subset_relation,universal_class))) )
| ~ spl0_11
| ~ spl0_164 ),
inference(resolution,[],[f1457,f255]) ).
fof(f4125,plain,
( spl0_340
| ~ spl0_34
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1439,f1380,f358,f4123]) ).
fof(f1439,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_34
| ~ spl0_158 ),
inference(duplicate_literal_removal,[],[f1419]) ).
fof(f1419,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) )
| ~ spl0_34
| ~ spl0_158 ),
inference(resolution,[],[f1381,f359]) ).
fof(f4121,plain,
( spl0_339
| ~ spl0_34
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1418,f1376,f358,f4119]) ).
fof(f1418,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl0_34
| ~ spl0_157 ),
inference(duplicate_literal_removal,[],[f1398]) ).
fof(f1398,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) )
| ~ spl0_34
| ~ spl0_157 ),
inference(resolution,[],[f1377,f359]) ).
fof(f4023,plain,
( spl0_338
| ~ spl0_112
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1344,f1317,f881,f4021]) ).
fof(f1344,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,regular(X1))
| subclass(X0,X2)
| member(not_subclass_element(X0,X2),x)
| ~ member(not_subclass_element(X0,X2),X1)
| x = X1 )
| ~ spl0_112
| ~ spl0_151 ),
inference(resolution,[],[f1318,f882]) ).
fof(f4019,plain,
( spl0_337
| ~ spl0_73
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1235,f1229,f606,f4017]) ).
fof(f1235,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) = x )
| ~ spl0_73
| ~ spl0_141 ),
inference(superposition,[],[f607,f1230]) ).
fof(f4015,plain,
( spl0_336
| ~ spl0_72
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1234,f1229,f602,f4013]) ).
fof(f1234,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) = x )
| ~ spl0_72
| ~ spl0_141 ),
inference(superposition,[],[f603,f1230]) ).
fof(f4011,plain,
( spl0_335
| ~ spl0_30
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f953,f946,f335,f4009]) ).
fof(f4009,plain,
( spl0_335
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| x = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ function(domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f953,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| x = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ function(domain_of(X1)) )
| ~ spl0_30
| ~ spl0_118 ),
inference(resolution,[],[f947,f336]) ).
fof(f4007,plain,
( spl0_334
| ~ spl0_55
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f810,f803,f489,f4005]) ).
fof(f4005,plain,
( spl0_334
<=> ! [X0,X1] :
( complement(intersection(X0,X1)) = x
| ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f810,plain,
( ! [X0,X1] :
( complement(intersection(X0,X1)) = x
| ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0) )
| ~ spl0_55
| ~ spl0_105 ),
inference(resolution,[],[f804,f490]) ).
fof(f3959,plain,
( spl0_333
| ~ spl0_237
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f3940,f3936,f2334,f3957]) ).
fof(f3957,plain,
( spl0_333
<=> ! [X0,X1] :
( subset_relation = X0
| member(not_subclass_element(regular(X0),X1),subset_relation)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| subclass(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f3936,plain,
( spl0_329
<=> ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),x)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| x = X0
| subclass(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f3940,plain,
( ! [X0,X1] :
( subset_relation = X0
| member(not_subclass_element(regular(X0),X1),subset_relation)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| subclass(regular(X0),X1) )
| ~ spl0_237
| ~ spl0_329 ),
inference(forward_demodulation,[],[f3939,f2336]) ).
fof(f3939,plain,
( ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),subset_relation)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| x = X0
| subclass(regular(X0),X1) )
| ~ spl0_237
| ~ spl0_329 ),
inference(forward_demodulation,[],[f3937,f2336]) ).
fof(f3937,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(regular(X0),X1),X0)
| member(not_subclass_element(regular(X0),X1),x)
| x = X0
| subclass(regular(X0),X1) )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f3936]) ).
fof(f3954,plain,
( spl0_332
| ~ spl0_33
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1027,f1023,f354,f3952]) ).
fof(f3952,plain,
( spl0_332
<=> ! [X0] :
( subclass(universal_class,domain_of(X0))
| x = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f1027,plain,
( ! [X0] :
( subclass(universal_class,domain_of(X0))
| x = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class)) )
| ~ spl0_33
| ~ spl0_131 ),
inference(duplicate_literal_removal,[],[f1026]) ).
fof(f1026,plain,
( ! [X0] :
( subclass(universal_class,domain_of(X0))
| x = 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_33
| ~ spl0_131 ),
inference(resolution,[],[f1024,f355]) ).
fof(f3949,plain,
( spl0_331
| ~ spl0_108
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f943,f918,f823,f3947]) ).
fof(f943,plain,
( ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_108
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f924]) ).
fof(f924,plain,
( ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_108
| ~ spl0_117 ),
inference(superposition,[],[f824,f919]) ).
fof(f3944,plain,
( spl0_330
| ~ spl0_108
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f938,f918,f823,f3942]) ).
fof(f938,plain,
( ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_108
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f929]) ).
fof(f929,plain,
( ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x )
| ~ spl0_108
| ~ spl0_117 ),
inference(superposition,[],[f824,f919]) ).
fof(f3938,plain,
( spl0_329
| ~ spl0_33
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f894,f881,f354,f3936]) ).
fof(f894,plain,
( ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),x)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| x = X0
| subclass(regular(X0),X1) )
| ~ spl0_33
| ~ spl0_112 ),
inference(resolution,[],[f882,f355]) ).
fof(f3899,plain,
( spl0_237
| spl0_328
| ~ spl0_78
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f877,f849,f635,f3896,f2334]) ).
fof(f877,plain,
( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subset_relation = x
| ~ spl0_78
| ~ spl0_111 ),
inference(superposition,[],[f850,f637]) ).
fof(f3733,plain,
( spl0_327
| ~ spl0_108
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f1493,f1456,f823,f3731]) ).
fof(f3731,plain,
( spl0_327
<=> ! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f1493,plain,
( ! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| x = X0 )
| ~ spl0_108
| ~ spl0_164 ),
inference(resolution,[],[f1457,f824]) ).
fof(f3729,plain,
( spl0_326
| ~ spl0_108
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f1471,f1452,f823,f3727]) ).
fof(f1471,plain,
( ! [X0] :
( ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| x = X0 )
| ~ spl0_108
| ~ spl0_163 ),
inference(resolution,[],[f1453,f824]) ).
fof(f3725,plain,
( spl0_325
| ~ spl0_6
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f941,f918,f231,f3723]) ).
fof(f3723,plain,
( spl0_325
<=> ! [X0,X1] :
( x = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f941,plain,
( ! [X0,X1] :
( x = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_6
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f926]) ).
fof(f926,plain,
( ! [X0,X1] :
( x = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_6
| ~ spl0_117 ),
inference(superposition,[],[f232,f919]) ).
fof(f3721,plain,
( spl0_324
| ~ spl0_6
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f936,f918,f231,f3719]) ).
fof(f3719,plain,
( spl0_324
<=> ! [X0,X1] :
( x = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f936,plain,
( ! [X0,X1] :
( x = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_6
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f931]) ).
fof(f931,plain,
( ! [X0,X1] :
( x = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x )
| ~ spl0_6
| ~ spl0_117 ),
inference(superposition,[],[f232,f919]) ).
fof(f3717,plain,
( spl0_323
| ~ spl0_108
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f899,f881,f823,f3715]) ).
fof(f899,plain,
( ! [X0,X1] :
( member(regular(X0),x)
| ~ member(regular(X0),X1)
| x = X1
| ~ subclass(X0,regular(X1))
| x = X0 )
| ~ spl0_108
| ~ spl0_112 ),
inference(resolution,[],[f882,f824]) ).
fof(f3713,plain,
( spl0_322
| ~ spl0_110
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2953,f2809,f845,f3711]) ).
fof(f2953,plain,
( ! [X0] : x = intersection(X0,complement(X0))
| ~ spl0_110
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2930]) ).
fof(f2930,plain,
( ! [X0] :
( x = intersection(X0,complement(X0))
| x = intersection(X0,complement(X0)) )
| ~ spl0_110
| ~ spl0_274 ),
inference(resolution,[],[f2810,f846]) ).
fof(f3562,plain,
( spl0_321
| ~ spl0_6
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1670,f1640,f231,f3560]) ).
fof(f1670,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X1,x),regular(X0))
| ~ member(not_subclass_element(X1,x),X0)
| subclass(X1,x)
| x = X0 )
| ~ spl0_6
| ~ spl0_185 ),
inference(superposition,[],[f1641,f232]) ).
fof(f3556,plain,
( spl0_319
| ~ spl0_320
| ~ spl0_105
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1314,f1294,f803,f3553,f3549]) ).
fof(f1314,plain,
( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| x = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_105
| ~ spl0_150 ),
inference(resolution,[],[f1295,f804]) ).
fof(f3547,plain,
( spl0_318
| ~ spl0_251
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2950,f2809,f2491,f3544]) ).
fof(f2950,plain,
( x = intersection(singleton_relation,complement(element_relation))
| ~ spl0_251
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2934]) ).
fof(f2934,plain,
( x = intersection(singleton_relation,complement(element_relation))
| x = intersection(singleton_relation,complement(element_relation))
| ~ spl0_251
| ~ spl0_274 ),
inference(resolution,[],[f2810,f2492]) ).
fof(f3540,plain,
( spl0_316
| ~ spl0_317
| ~ spl0_105
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1308,f1290,f803,f3537,f3533]) ).
fof(f1308,plain,
( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| x = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_105
| ~ spl0_149 ),
inference(resolution,[],[f1291,f804]) ).
fof(f3531,plain,
( spl0_315
| ~ spl0_112
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1155,f1116,f881,f3529]) ).
fof(f1155,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,regular(X0))
| member(unordered_pair(X1,X2),x)
| ~ member(unordered_pair(X1,X2),X0)
| x = X0 )
| ~ spl0_112
| ~ spl0_135 ),
inference(resolution,[],[f1117,f882]) ).
fof(f3527,plain,
( spl0_314
| ~ spl0_107
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f942,f918,f819,f3525]) ).
fof(f3525,plain,
( spl0_314
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,x)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f942,plain,
( ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,x)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_107
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f925]) ).
fof(f925,plain,
( ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,x)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_107
| ~ spl0_117 ),
inference(superposition,[],[f820,f919]) ).
fof(f3523,plain,
( spl0_313
| ~ spl0_107
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f937,f918,f819,f3521]) ).
fof(f3521,plain,
( spl0_313
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,x)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f937,plain,
( ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,x)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_107
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f930]) ).
fof(f930,plain,
( ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,x)
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x )
| ~ spl0_107
| ~ spl0_117 ),
inference(superposition,[],[f820,f919]) ).
fof(f3519,plain,
( spl0_312
| ~ spl0_3
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f896,f881,f217,f3517]) ).
fof(f896,plain,
( ! [X0] :
( member(regular(regular(X0)),x)
| ~ member(regular(regular(X0)),X0)
| x = X0
| regular(X0) = x )
| ~ spl0_3
| ~ spl0_112 ),
inference(resolution,[],[f882,f218]) ).
fof(f3515,plain,
( spl0_311
| ~ spl0_50
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f811,f803,f465,f3513]) ).
fof(f811,plain,
( ! [X0] :
( x = complement(complement(X0))
| member(regular(complement(complement(X0))),X0)
| ~ member(regular(complement(complement(X0))),universal_class) )
| ~ spl0_50
| ~ spl0_105 ),
inference(resolution,[],[f804,f466]) ).
fof(f3511,plain,
( spl0_310
| ~ spl0_253
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2948,f2809,f2501,f3508]) ).
fof(f3508,plain,
( spl0_310
<=> x = intersection(identity_relation,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2948,plain,
( x = intersection(identity_relation,complement(subset_relation))
| ~ spl0_253
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2943]) ).
fof(f2943,plain,
( x = intersection(identity_relation,complement(subset_relation))
| x = intersection(identity_relation,complement(subset_relation))
| ~ spl0_253
| ~ spl0_274 ),
inference(resolution,[],[f2810,f2502]) ).
fof(f3506,plain,
( ~ spl0_308
| spl0_309
| ~ spl0_19
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1227,f1216,f289,f3503,f3499]) ).
fof(f3499,plain,
( spl0_308
<=> single_valued_class(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f3503,plain,
( spl0_309
<=> function(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f1227,plain,
( function(domain_relation)
| ~ single_valued_class(domain_relation)
| ~ spl0_19
| ~ spl0_140 ),
inference(resolution,[],[f1217,f291]) ).
fof(f3497,plain,
( ~ spl0_306
| spl0_307
| ~ spl0_17
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1223,f1216,f280,f3494,f3490]) ).
fof(f3490,plain,
( spl0_306
<=> single_valued_class(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f3494,plain,
( spl0_307
<=> function(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f1223,plain,
( function(successor_relation)
| ~ single_valued_class(successor_relation)
| ~ spl0_17
| ~ spl0_140 ),
inference(resolution,[],[f1217,f282]) ).
fof(f3488,plain,
( ~ spl0_304
| spl0_305
| ~ spl0_16
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1221,f1216,f275,f3485,f3481]) ).
fof(f3481,plain,
( spl0_304
<=> single_valued_class(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f3485,plain,
( spl0_305
<=> function(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f1221,plain,
( function(element_relation)
| ~ single_valued_class(element_relation)
| ~ spl0_16
| ~ spl0_140 ),
inference(resolution,[],[f1217,f277]) ).
fof(f3423,plain,
( spl0_303
| ~ spl0_111
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2928,f2805,f849,f3421]) ).
fof(f2928,plain,
( ! [X0] : x = intersection(complement(X0),X0)
| ~ spl0_111
| ~ spl0_273 ),
inference(duplicate_literal_removal,[],[f2903]) ).
fof(f2903,plain,
( ! [X0] :
( x = intersection(complement(X0),X0)
| x = intersection(complement(X0),X0) )
| ~ spl0_111
| ~ spl0_273 ),
inference(resolution,[],[f2806,f850]) ).
fof(f3413,plain,
( spl0_302
| ~ spl0_6
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1548,f1538,f231,f3411]) ).
fof(f3411,plain,
( spl0_302
<=> ! [X2,X0,X1] :
( ~ subclass(x,X1)
| ~ member(X2,X0)
| ~ member(X2,regular(X0))
| member(X2,X1)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f1548,plain,
( ! [X2,X0,X1] :
( ~ subclass(x,X1)
| ~ member(X2,X0)
| ~ member(X2,regular(X0))
| member(X2,X1)
| x = X0 )
| ~ spl0_6
| ~ spl0_173 ),
inference(superposition,[],[f1539,f232]) ).
fof(f3409,plain,
( spl0_301
| ~ spl0_3
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f940,f918,f217,f3407]) ).
fof(f3407,plain,
( spl0_301
<=> ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f940,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_3
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f927]) ).
fof(f927,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_3
| ~ spl0_117 ),
inference(superposition,[],[f218,f919]) ).
fof(f3405,plain,
( spl0_300
| ~ spl0_3
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f935,f918,f217,f3403]) ).
fof(f3403,plain,
( spl0_300
<=> ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f935,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_3
| ~ spl0_117 ),
inference(duplicate_literal_removal,[],[f932]) ).
fof(f932,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = x
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x )
| ~ spl0_3
| ~ spl0_117 ),
inference(superposition,[],[f218,f919]) ).
fof(f3401,plain,
( spl0_299
| ~ spl0_54
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f836,f823,f485,f3399]) ).
fof(f836,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| x = X0
| regular(X0) = X1
| regular(X0) = X2 )
| ~ spl0_54
| ~ spl0_108 ),
inference(resolution,[],[f824,f486]) ).
fof(f3273,plain,
( spl0_298
| ~ spl0_252
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2925,f2805,f2496,f3270]) ).
fof(f2925,plain,
( x = intersection(complement(element_relation),singleton_relation)
| ~ spl0_252
| ~ spl0_273 ),
inference(duplicate_literal_removal,[],[f2907]) ).
fof(f2907,plain,
( x = intersection(complement(element_relation),singleton_relation)
| x = intersection(complement(element_relation),singleton_relation)
| ~ spl0_252
| ~ spl0_273 ),
inference(resolution,[],[f2806,f2497]) ).
fof(f3210,plain,
( spl0_297
| ~ spl0_106
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1431,f1380,f807,f3208]) ).
fof(f1431,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,x),X1)
| member(not_subclass_element(intersection(X0,x),X1),X2)
| x = X2 )
| ~ spl0_106
| ~ spl0_158 ),
inference(resolution,[],[f1381,f808]) ).
fof(f3206,plain,
( spl0_296
| ~ spl0_106
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1410,f1376,f807,f3204]) ).
fof(f1410,plain,
( ! [X2,X0,X1] :
( subclass(intersection(x,X0),X1)
| member(not_subclass_element(intersection(x,X0),X1),X2)
| x = X2 )
| ~ spl0_106
| ~ spl0_157 ),
inference(resolution,[],[f1377,f808]) ).
fof(f3202,plain,
( spl0_295
| ~ spl0_107
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1301,f1259,f819,f3200]) ).
fof(f3200,plain,
( spl0_295
<=> ! [X0,X1] :
( subclass(complement(regular(X0)),X1)
| ~ member(not_subclass_element(complement(regular(X0)),X1),x)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f1301,plain,
( ! [X0,X1] :
( subclass(complement(regular(X0)),X1)
| ~ member(not_subclass_element(complement(regular(X0)),X1),x)
| x = X0 )
| ~ spl0_107
| ~ spl0_142 ),
inference(resolution,[],[f1260,f820]) ).
fof(f3198,plain,
( ~ spl0_293
| spl0_294
| ~ spl0_2
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f909,f905,f213,f3195,f3191]) ).
fof(f909,plain,
( x = cross_product(unordered_pair(x,x),universal_class)
| ~ inductive(domain_of(regular(cross_product(unordered_pair(x,x),universal_class))))
| ~ spl0_2
| ~ spl0_115 ),
inference(resolution,[],[f906,f214]) ).
fof(f3189,plain,
( spl0_292
| ~ spl0_38
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f870,f849,f374,f3187]) ).
fof(f870,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X1) )
| ~ spl0_38
| ~ spl0_111 ),
inference(resolution,[],[f850,f375]) ).
fof(f3185,plain,
( spl0_291
| ~ spl0_39
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f869,f849,f378,f3183]) ).
fof(f869,plain,
( ! [X2,X0,X1] :
( x = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X2) )
| ~ spl0_39
| ~ spl0_111 ),
inference(resolution,[],[f850,f379]) ).
fof(f3181,plain,
( spl0_290
| ~ spl0_254
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2923,f2805,f2506,f3178]) ).
fof(f2923,plain,
( x = intersection(complement(subset_relation),identity_relation)
| ~ spl0_254
| ~ spl0_273 ),
inference(duplicate_literal_removal,[],[f2916]) ).
fof(f2916,plain,
( x = intersection(complement(subset_relation),identity_relation)
| x = intersection(complement(subset_relation),identity_relation)
| ~ spl0_254
| ~ spl0_273 ),
inference(resolution,[],[f2806,f2507]) ).
fof(f3176,plain,
( spl0_289
| ~ spl0_38
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f856,f845,f374,f3174]) ).
fof(f856,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X0) )
| ~ spl0_38
| ~ spl0_110 ),
inference(resolution,[],[f846,f375]) ).
fof(f3172,plain,
( spl0_288
| ~ spl0_39
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f855,f845,f378,f3170]) ).
fof(f855,plain,
( ! [X2,X0,X1] :
( x = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X1) )
| ~ spl0_39
| ~ spl0_110 ),
inference(resolution,[],[f846,f379]) ).
fof(f3010,plain,
( spl0_287
| ~ spl0_34
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2560,f2406,f358,f3008]) ).
fof(f2406,plain,
( spl0_245
<=> ! [X0,X1] :
( member(not_subclass_element(x,X0),X1)
| x = X1
| subclass(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2560,plain,
( ! [X0] :
( x = X0
| subclass(x,X0) )
| ~ spl0_34
| ~ spl0_245 ),
inference(duplicate_literal_removal,[],[f2534]) ).
fof(f2534,plain,
( ! [X0] :
( x = X0
| subclass(x,X0)
| subclass(x,X0) )
| ~ spl0_34
| ~ spl0_245 ),
inference(resolution,[],[f2407,f359]) ).
fof(f2407,plain,
( ! [X0,X1] :
( member(not_subclass_element(x,X0),X1)
| x = X1
| subclass(x,X0) )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2406]) ).
fof(f2998,plain,
( spl0_286
| ~ spl0_106
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1346,f1317,f807,f2996]) ).
fof(f2996,plain,
( spl0_286
<=> ! [X2,X0,X1] :
( ~ subclass(X0,x)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f1346,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,x)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| x = X2 )
| ~ spl0_106
| ~ spl0_151 ),
inference(resolution,[],[f1318,f808]) ).
fof(f2994,plain,
( spl0_285
| ~ spl0_135
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1257,f1229,f1116,f2992]) ).
fof(f1257,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = x )
| ~ spl0_135
| ~ spl0_141 ),
inference(superposition,[],[f1117,f1230]) ).
fof(f2990,plain,
( spl0_284
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f934,f918,f2988]) ).
fof(f2988,plain,
( spl0_284
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f934,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x )
| ~ spl0_117 ),
inference(equality_factoring,[],[f919]) ).
fof(f2986,plain,
( spl0_283
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f933,f918,f2984]) ).
fof(f933,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = x )
| ~ spl0_117 ),
inference(equality_factoring,[],[f919]) ).
fof(f2982,plain,
( spl0_282
| ~ spl0_106
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f873,f849,f807,f2980]) ).
fof(f2980,plain,
( spl0_282
<=> ! [X0,X1] :
( x = intersection(X0,x)
| member(regular(intersection(X0,x)),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f873,plain,
( ! [X0,X1] :
( x = intersection(X0,x)
| member(regular(intersection(X0,x)),X1)
| x = X1 )
| ~ spl0_106
| ~ spl0_111 ),
inference(resolution,[],[f850,f808]) ).
fof(f2978,plain,
( spl0_281
| ~ spl0_45
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f866,f849,f417,f2976]) ).
fof(f866,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_45
| ~ spl0_111 ),
inference(resolution,[],[f850,f418]) ).
fof(f2974,plain,
( spl0_280
| ~ spl0_106
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f859,f845,f807,f2972]) ).
fof(f2972,plain,
( spl0_280
<=> ! [X0,X1] :
( x = intersection(x,X0)
| member(regular(intersection(x,X0)),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f859,plain,
( ! [X0,X1] :
( x = intersection(x,X0)
| member(regular(intersection(x,X0)),X1)
| x = X1 )
| ~ spl0_106
| ~ spl0_110 ),
inference(resolution,[],[f846,f808]) ).
fof(f2967,plain,
( spl0_123
| ~ spl0_9
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2316,f2290,f244,f971]) ).
fof(f2316,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ spl0_9
| ~ spl0_230 ),
inference(resolution,[],[f2291,f245]) ).
fof(f2291,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(x,X0) )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2290]) ).
fof(f2966,plain,
( spl0_279
| ~ spl0_45
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f852,f845,f417,f2964]) ).
fof(f852,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = x
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_45
| ~ spl0_110 ),
inference(resolution,[],[f846,f418]) ).
fof(f2962,plain,
( spl0_278
| ~ spl0_105
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f833,f819,f803,f2960]) ).
fof(f2960,plain,
( spl0_278
<=> ! [X0] :
( ~ member(regular(complement(regular(X0))),x)
| x = X0
| x = complement(regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f833,plain,
( ! [X0] :
( ~ member(regular(complement(regular(X0))),x)
| x = X0
| x = complement(regular(X0)) )
| ~ spl0_105
| ~ spl0_107 ),
inference(resolution,[],[f820,f804]) ).
fof(f2958,plain,
( spl0_277
| ~ spl0_62
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f789,f782,f548,f2956]) ).
fof(f2956,plain,
( spl0_277
<=> ! [X0] :
( member(x,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_277])]) ).
fof(f789,plain,
( ! [X0] :
( member(x,domain_of(domain_of(X0)))
| ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| ~ operation(X0) )
| ~ spl0_62
| ~ spl0_104 ),
inference(resolution,[],[f783,f549]) ).
fof(f2820,plain,
( spl0_275
| ~ spl0_276
| ~ spl0_105
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1171,f1124,f803,f2817,f2813]) ).
fof(f1171,plain,
( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
| x = complement(cross_product(universal_class,universal_class))
| ~ spl0_105
| ~ spl0_137 ),
inference(resolution,[],[f1125,f804]) ).
fof(f2811,plain,
( spl0_274
| ~ spl0_28
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f871,f849,f327,f2809]) ).
fof(f871,plain,
( ! [X0,X1] :
( x = intersection(X0,complement(X1))
| ~ member(regular(intersection(X0,complement(X1))),X1) )
| ~ spl0_28
| ~ spl0_111 ),
inference(resolution,[],[f850,f328]) ).
fof(f2807,plain,
( spl0_273
| ~ spl0_28
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f857,f845,f327,f2805]) ).
fof(f857,plain,
( ! [X0,X1] :
( x = intersection(complement(X0),X1)
| ~ member(regular(intersection(complement(X0),X1)),X0) )
| ~ spl0_28
| ~ spl0_110 ),
inference(resolution,[],[f846,f328]) ).
fof(f2803,plain,
( spl0_272
| ~ spl0_106
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f842,f823,f807,f2801]) ).
fof(f2801,plain,
( spl0_272
<=> ! [X0,X1] :
( ~ subclass(X0,x)
| x = X0
| member(regular(X0),X1)
| x = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f842,plain,
( ! [X0,X1] :
( ~ subclass(X0,x)
| x = X0
| member(regular(X0),X1)
| x = X1 )
| ~ spl0_106
| ~ spl0_108 ),
inference(resolution,[],[f824,f808]) ).
fof(f2799,plain,
( spl0_271
| ~ spl0_45
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f835,f823,f417,f2797]) ).
fof(f835,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| x = X0
| ~ subclass(X1,X2)
| member(regular(X0),X2) )
| ~ spl0_45
| ~ spl0_108 ),
inference(resolution,[],[f824,f418]) ).
fof(f2795,plain,
( spl0_270
| ~ spl0_34
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f832,f819,f358,f2793]) ).
fof(f832,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),x)
| x = X1
| subclass(X0,regular(X1)) )
| ~ spl0_34
| ~ spl0_107 ),
inference(resolution,[],[f820,f359]) ).
fof(f2791,plain,
( spl0_269
| ~ spl0_45
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f831,f819,f417,f2789]) ).
fof(f2789,plain,
( spl0_269
<=> ! [X2,X0,X1] :
( ~ member(X0,x)
| x = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f831,plain,
( ! [X2,X0,X1] :
( ~ member(X0,x)
| x = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) )
| ~ spl0_45
| ~ spl0_107 ),
inference(resolution,[],[f820,f418]) ).
fof(f2786,plain,
( spl0_97
| ~ spl0_130
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f2783,f2774,f1001,f747]) ).
fof(f2783,plain,
( member(x,subset_relation)
| ~ spl0_130
| ~ spl0_267 ),
inference(resolution,[],[f2776,f1002]) ).
fof(f2776,plain,
( member(x,identity_relation)
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f2774]) ).
fof(f2782,plain,
( spl0_268
| spl0_267
| ~ spl0_57
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f797,f782,f497,f2774,f2780]) ).
fof(f2780,plain,
( spl0_268
<=> ! [X0] :
( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f497,plain,
( spl0_57
<=> ! [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_57])]) ).
fof(f797,plain,
( ! [X0] :
( member(x,identity_relation)
| ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ single_valued_class(X0) )
| ~ spl0_57
| ~ spl0_104 ),
inference(resolution,[],[f783,f498]) ).
fof(f498,plain,
( ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ single_valued_class(X0) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f2777,plain,
( spl0_266
| spl0_267
| ~ spl0_58
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f796,f782,f501,f2774,f2771]) ).
fof(f2771,plain,
( spl0_266
<=> ! [X0] :
( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f501,plain,
( spl0_58
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f796,plain,
( ! [X0] :
( member(x,identity_relation)
| ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) )
| ~ spl0_58
| ~ spl0_104 ),
inference(resolution,[],[f783,f502]) ).
fof(f502,plain,
( ! [X8] :
( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
| ~ function(X8) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f2735,plain,
( spl0_265
| ~ spl0_6
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f1432,f1380,f231,f2733]) ).
fof(f2733,plain,
( spl0_265
<=> ! [X0,X1] :
( member(not_subclass_element(x,X1),regular(X0))
| subclass(x,X1)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1432,plain,
( ! [X0,X1] :
( member(not_subclass_element(x,X1),regular(X0))
| subclass(x,X1)
| x = X0 )
| ~ spl0_6
| ~ spl0_158 ),
inference(superposition,[],[f1381,f232]) ).
fof(f2724,plain,
( spl0_263
| spl0_264
| ~ spl0_2
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f898,f881,f213,f2721,f2718]) ).
fof(f2718,plain,
( spl0_263
<=> ! [X0] :
( ~ member(x,X0)
| ~ inductive(regular(X0))
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2721,plain,
( spl0_264
<=> member(x,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f898,plain,
( ! [X0] :
( member(x,x)
| ~ member(x,X0)
| x = X0
| ~ inductive(regular(X0)) )
| ~ spl0_2
| ~ spl0_112 ),
inference(resolution,[],[f882,f214]) ).
fof(f2716,plain,
( spl0_262
| ~ spl0_38
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f839,f823,f374,f2714]) ).
fof(f839,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = X0
| member(regular(X0),X1) )
| ~ spl0_38
| ~ spl0_108 ),
inference(resolution,[],[f824,f375]) ).
fof(f2712,plain,
( spl0_261
| ~ spl0_39
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f838,f823,f378,f2710]) ).
fof(f838,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| x = X0
| member(regular(X0),X2) )
| ~ spl0_39
| ~ spl0_108 ),
inference(resolution,[],[f824,f379]) ).
fof(f2677,plain,
( spl0_260
| ~ spl0_222
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2494,f2491,f2213,f2675]) ).
fof(f2494,plain,
( ! [X0] :
( identity_relation = intersection(singleton_relation,X0)
| member(regular(intersection(singleton_relation,X0)),element_relation) )
| ~ spl0_222
| ~ spl0_251 ),
inference(forward_demodulation,[],[f2492,f2215]) ).
fof(f2532,plain,
( spl0_259
| ~ spl0_15
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1250,f1229,f271,f2530]) ).
fof(f2530,plain,
( spl0_259
<=> ! [X0,X1] :
( member(regular(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1250,plain,
( ! [X0,X1] :
( member(regular(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = x )
| ~ spl0_15
| ~ spl0_141 ),
inference(superposition,[],[f272,f1230]) ).
fof(f2528,plain,
( ~ spl0_258
| ~ spl0_222
| spl0_257 ),
inference(avatar_split_clause,[],[f2523,f2519,f2213,f2525]) ).
fof(f2525,plain,
( spl0_258
<=> subclass(universal_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2519,plain,
( spl0_257
<=> subclass(universal_class,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2523,plain,
( ~ subclass(universal_class,identity_relation)
| ~ spl0_222
| spl0_257 ),
inference(forward_demodulation,[],[f2521,f2215]) ).
fof(f2521,plain,
( ~ subclass(universal_class,x)
| spl0_257 ),
inference(avatar_component_clause,[],[f2519]) ).
fof(f2522,plain,
( spl0_256
| ~ spl0_257
| ~ spl0_106
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1157,f1116,f807,f2519,f2516]) ).
fof(f2516,plain,
( spl0_256
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| x = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1157,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,x)
| member(unordered_pair(X0,X1),X2)
| x = X2 )
| ~ spl0_106
| ~ spl0_135 ),
inference(resolution,[],[f1117,f808]) ).
fof(f2514,plain,
( ~ spl0_255
| ~ spl0_5
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2488,f2303,f226,f2511]) ).
fof(f2511,plain,
( spl0_255
<=> inductive(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f226,plain,
( spl0_5
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f2488,plain,
( ~ inductive(choice)
| ~ spl0_5
| ~ spl0_232 ),
inference(resolution,[],[f2304,f228]) ).
fof(f228,plain,
( function(choice)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f2508,plain,
( spl0_254
| ~ spl0_111
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1021,f1001,f849,f2506]) ).
fof(f1021,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),subset_relation)
| x = intersection(X0,identity_relation) )
| ~ spl0_111
| ~ spl0_130 ),
inference(resolution,[],[f1002,f850]) ).
fof(f2503,plain,
( spl0_253
| ~ spl0_110
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1019,f1001,f845,f2501]) ).
fof(f1019,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| x = intersection(identity_relation,X0) )
| ~ spl0_110
| ~ spl0_130 ),
inference(resolution,[],[f1002,f846]) ).
fof(f2498,plain,
( spl0_252
| ~ spl0_111
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1015,f997,f849,f2496]) ).
fof(f1015,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),element_relation)
| x = intersection(X0,singleton_relation) )
| ~ spl0_111
| ~ spl0_129 ),
inference(resolution,[],[f998,f850]) ).
fof(f2493,plain,
( spl0_251
| ~ spl0_110
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1013,f997,f845,f2491]) ).
fof(f1013,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| x = intersection(singleton_relation,X0) )
| ~ spl0_110
| ~ spl0_129 ),
inference(resolution,[],[f998,f846]) ).
fof(f2480,plain,
( spl0_250
| ~ spl0_45
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2443,f2270,f417,f2478]) ).
fof(f2443,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(identity_relation,X0) )
| ~ spl0_45
| ~ spl0_227 ),
inference(resolution,[],[f2272,f418]) ).
fof(f2451,plain,
( spl0_249
| ~ spl0_188
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2440,f2213,f1710,f2448]) ).
fof(f2448,plain,
( spl0_249
<=> identity_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2440,plain,
( identity_relation = singleton_relation
| ~ spl0_188
| ~ spl0_222 ),
inference(forward_demodulation,[],[f2215,f1712]) ).
fof(f2439,plain,
( spl0_222
| spl0_248
| ~ spl0_49
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f865,f845,f434,f2436,f2213]) ).
fof(f865,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| identity_relation = x
| ~ spl0_49
| ~ spl0_110 ),
inference(superposition,[],[f846,f436]) ).
fof(f2417,plain,
( spl0_188
| spl0_247
| ~ spl0_48
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f864,f845,f429,f2414,f1710]) ).
fof(f864,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| singleton_relation = x
| ~ spl0_48
| ~ spl0_110 ),
inference(superposition,[],[f846,f431]) ).
fof(f2412,plain,
( spl0_246
| ~ spl0_28
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f840,f823,f327,f2410]) ).
fof(f840,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| x = X0
| ~ member(regular(X0),X1) )
| ~ spl0_28
| ~ spl0_108 ),
inference(resolution,[],[f824,f328]) ).
fof(f2408,plain,
( spl0_245
| ~ spl0_33
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f814,f807,f354,f2406]) ).
fof(f814,plain,
( ! [X0,X1] :
( member(not_subclass_element(x,X0),X1)
| x = X1
| subclass(x,X0) )
| ~ spl0_33
| ~ spl0_106 ),
inference(resolution,[],[f808,f355]) ).
fof(f2388,plain,
( spl0_244
| ~ spl0_108
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1020,f1001,f823,f2386]) ).
fof(f1020,plain,
( ! [X0] :
( member(regular(X0),subset_relation)
| ~ subclass(X0,identity_relation)
| x = X0 )
| ~ spl0_108
| ~ spl0_130 ),
inference(resolution,[],[f1002,f824]) ).
fof(f2384,plain,
( spl0_243
| ~ spl0_108
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1014,f997,f823,f2382]) ).
fof(f1014,plain,
( ! [X0] :
( member(regular(X0),element_relation)
| ~ subclass(X0,singleton_relation)
| x = X0 )
| ~ spl0_108
| ~ spl0_129 ),
inference(resolution,[],[f998,f824]) ).
fof(f2377,plain,
( spl0_242
| spl0_241
| ~ spl0_41
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f792,f782,f386,f2369,f2375]) ).
fof(f2375,plain,
( spl0_242
<=> ! [X0] : ~ inductive(flip(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f792,plain,
( ! [X0] :
( member(x,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X0)) )
| ~ spl0_41
| ~ spl0_104 ),
inference(resolution,[],[f783,f387]) ).
fof(f2372,plain,
( spl0_240
| spl0_241
| ~ spl0_40
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f791,f782,f382,f2369,f2366]) ).
fof(f2366,plain,
( spl0_240
<=> ! [X0] : ~ inductive(rotate(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f791,plain,
( ! [X0] :
( member(x,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X0)) )
| ~ spl0_40
| ~ spl0_104 ),
inference(resolution,[],[f783,f383]) ).
fof(f2361,plain,
( spl0_239
| ~ spl0_20
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2344,f2334,f294,f2358]) ).
fof(f2344,plain,
( member(subset_relation,universal_class)
| ~ spl0_20
| ~ spl0_237 ),
inference(superposition,[],[f295,f2336]) ).
fof(f2341,plain,
( spl0_237
| spl0_238
| ~ spl0_78
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f863,f845,f635,f2338,f2334]) ).
fof(f863,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| subset_relation = x
| ~ spl0_78
| ~ spl0_110 ),
inference(superposition,[],[f846,f637]) ).
fof(f2332,plain,
( ~ spl0_236
| spl0_235
| ~ spl0_32
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f801,f782,f345,f2323,f2329]) ).
fof(f2329,plain,
( spl0_236
<=> inductive(application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f801,plain,
( member(x,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(application_function)
| ~ spl0_32
| ~ spl0_104 ),
inference(resolution,[],[f783,f347]) ).
fof(f2326,plain,
( ~ spl0_234
| spl0_235
| ~ spl0_31
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f799,f782,f339,f2323,f2319]) ).
fof(f2319,plain,
( spl0_234
<=> inductive(composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f799,plain,
( member(x,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(composition_function)
| ~ spl0_31
| ~ spl0_104 ),
inference(resolution,[],[f783,f341]) ).
fof(f2310,plain,
( spl0_233
| ~ spl0_7
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2295,f2286,f235,f2307]) ).
fof(f2295,plain,
( x = complement(universal_class)
| ~ spl0_7
| ~ spl0_229 ),
inference(resolution,[],[f2287,f236]) ).
fof(f2305,plain,
( spl0_232
| spl0_123
| ~ spl0_30
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f787,f782,f335,f971,f2303]) ).
fof(f787,plain,
( ! [X0] :
( member(x,cross_product(universal_class,universal_class))
| ~ inductive(X0)
| ~ function(X0) )
| ~ spl0_30
| ~ spl0_104 ),
inference(resolution,[],[f783,f336]) ).
fof(f2301,plain,
( spl0_231
| ~ spl0_5
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f915,f912,f226,f2298]) ).
fof(f2298,plain,
( spl0_231
<=> single_valued_class(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f915,plain,
( single_valued_class(choice)
| ~ spl0_5
| ~ spl0_116 ),
inference(resolution,[],[f913,f228]) ).
fof(f2292,plain,
( spl0_230
| ~ spl0_45
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f2276,f971,f417,f2290]) ).
fof(f2288,plain,
( spl0_229
| ~ spl0_105
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f843,f823,f803,f2286]) ).
fof(f843,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = x )
| ~ spl0_105
| ~ spl0_108 ),
inference(duplicate_literal_removal,[],[f834]) ).
fof(f834,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = x
| complement(X0) = x )
| ~ spl0_105
| ~ spl0_108 ),
inference(resolution,[],[f824,f804]) ).
fof(f2282,plain,
( ~ spl0_228
| ~ spl0_137
| spl0_227 ),
inference(avatar_split_clause,[],[f2277,f2270,f1124,f2279]) ).
fof(f2279,plain,
( spl0_228
<=> member(identity_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2277,plain,
( ~ member(identity_relation,subset_relation)
| ~ spl0_137
| spl0_227 ),
inference(resolution,[],[f2271,f1125]) ).
fof(f2273,plain,
( spl0_227
| ~ spl0_123
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2268,f2213,f971,f2270]) ).
fof(f2268,plain,
( member(identity_relation,cross_product(universal_class,universal_class))
| ~ spl0_123
| ~ spl0_222 ),
inference(forward_demodulation,[],[f972,f2215]) ).
fof(f2265,plain,
( spl0_226
| spl0_123
| ~ spl0_25
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f798,f782,f315,f971,f2263]) ).
fof(f2263,plain,
( spl0_226
<=> ! [X0] : ~ inductive(compose_class(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f798,plain,
( ! [X0] :
( member(x,cross_product(universal_class,universal_class))
| ~ inductive(compose_class(X0)) )
| ~ spl0_25
| ~ spl0_104 ),
inference(resolution,[],[f783,f316]) ).
fof(f2260,plain,
( spl0_224
| ~ spl0_225
| ~ spl0_6
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f518,f425,f231,f2257,f2254]) ).
fof(f2254,plain,
( spl0_224
<=> ! [X0] :
( member(x,X0)
| x = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2257,plain,
( spl0_225
<=> inductive(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f425,plain,
( spl0_47
<=> ! [X0,X1] :
( member(x,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f518,plain,
( ! [X0] :
( ~ inductive(x)
| member(x,X0)
| x = X0 )
| ~ spl0_6
| ~ spl0_47 ),
inference(superposition,[],[f426,f232]) ).
fof(f426,plain,
( ! [X0,X1] :
( ~ inductive(intersection(X0,X1))
| member(x,X0) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f425]) ).
fof(f2220,plain,
( spl0_222
| spl0_223
| ~ spl0_49
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f879,f849,f434,f2217,f2213]) ).
fof(f879,plain,
( member(regular(identity_relation),subset_relation)
| identity_relation = x
| ~ spl0_49
| ~ spl0_111 ),
inference(superposition,[],[f850,f436]) ).
fof(f2211,plain,
( spl0_221
| ~ spl0_90
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f722,f718,f703,f2209]) ).
fof(f722,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_90
| ~ spl0_93 ),
inference(resolution,[],[f719,f704]) ).
fof(f2207,plain,
( spl0_220
| ~ spl0_56
| ~ spl0_90
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f776,f771,f703,f493,f2205]) ).
fof(f2205,plain,
( spl0_220
<=> ! [X2,X4,X0,X3,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
| ~ homomorphism(X0,X1,X2)
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f776,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_56
| ~ spl0_90
| ~ spl0_102 ),
inference(forward_demodulation,[],[f774,f494]) ).
fof(f774,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) )
| ~ spl0_90
| ~ spl0_102 ),
inference(resolution,[],[f772,f704]) ).
fof(f2194,plain,
( spl0_219
| ~ spl0_33
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f723,f718,f354,f2192]) ).
fof(f723,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_33
| ~ spl0_93 ),
inference(resolution,[],[f719,f355]) ).
fof(f2183,plain,
( spl0_218
| ~ spl0_79
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f769,f766,f640,f2181]) ).
fof(f769,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(X1))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class) )
| ~ spl0_79
| ~ spl0_101 ),
inference(resolution,[],[f767,f641]) ).
fof(f2130,plain,
( spl0_217
| ~ spl0_79
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f764,f760,f640,f2128]) ).
fof(f764,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_79
| ~ spl0_100 ),
inference(resolution,[],[f761,f641]) ).
fof(f2124,plain,
( spl0_216
| ~ spl0_79
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f763,f756,f640,f2122]) ).
fof(f763,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_79
| ~ spl0_99 ),
inference(resolution,[],[f757,f641]) ).
fof(f2114,plain,
( spl0_215
| ~ spl0_11
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f775,f771,f254,f2112]) ).
fof(f775,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)
| x = 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_11
| ~ spl0_102 ),
inference(resolution,[],[f772,f255]) ).
fof(f2101,plain,
( spl0_214
| ~ spl0_27
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f724,f718,f323,f2099]) ).
fof(f724,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)
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_27
| ~ spl0_93 ),
inference(resolution,[],[f719,f324]) ).
fof(f2051,plain,
( spl0_213
| ~ spl0_79
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f661,f658,f640,f2049]) ).
fof(f661,plain,
( ! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X1,X2)
| ~ member(X0,X3) )
| ~ spl0_79
| ~ spl0_81 ),
inference(resolution,[],[f659,f641]) ).
fof(f2012,plain,
( spl0_212
| ~ spl0_45
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f716,f712,f417,f2010]) ).
fof(f716,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_45
| ~ spl0_92 ),
inference(resolution,[],[f713,f418]) ).
fof(f1956,plain,
( spl0_211
| ~ spl0_56
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f730,f718,f493,f1954]) ).
fof(f730,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_56
| ~ spl0_93 ),
inference(superposition,[],[f719,f494]) ).
fof(f1952,plain,
( spl0_210
| ~ spl0_56
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f727,f718,f493,f1950]) ).
fof(f727,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_56
| ~ spl0_93 ),
inference(superposition,[],[f719,f494]) ).
fof(f1931,plain,
( spl0_209
| ~ spl0_33
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f662,f658,f354,f1929]) ).
fof(f662,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_33
| ~ spl0_81 ),
inference(resolution,[],[f659,f355]) ).
fof(f1902,plain,
( spl0_208
| ~ spl0_45
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f706,f703,f417,f1900]) ).
fof(f706,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_45
| ~ spl0_90 ),
inference(resolution,[],[f704,f418]) ).
fof(f1896,plain,
( spl0_207
| ~ spl0_79
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f737,f734,f640,f1894]) ).
fof(f737,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_79
| ~ spl0_94 ),
inference(resolution,[],[f735,f641]) ).
fof(f1892,plain,
( spl0_206
| ~ spl0_27
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f663,f658,f323,f1890]) ).
fof(f1890,plain,
( spl0_206
<=> ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))))))
| ~ member(cross_product(X0,X1),universal_class)
| cross_product(X0,X1) = x ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f663,plain,
( ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))))))
| ~ member(cross_product(X0,X1),universal_class)
| cross_product(X0,X1) = x )
| ~ spl0_27
| ~ spl0_81 ),
inference(resolution,[],[f659,f324]) ).
fof(f1879,plain,
( spl0_205
| ~ spl0_3
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f725,f718,f217,f1877]) ).
fof(f725,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))
| x = domain_of(domain_of(flip(cross_product(intersection(cross_product(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_3
| ~ spl0_93 ),
inference(resolution,[],[f719,f218]) ).
fof(f1873,plain,
( spl0_204
| ~ spl0_46
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f574,f570,f421,f1871]) ).
fof(f574,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_46
| ~ spl0_66 ),
inference(resolution,[],[f571,f422]) ).
fof(f1869,plain,
( ~ spl0_201
| ~ spl0_202
| spl0_203
| ~ spl0_76
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f643,f635,f622,f1866,f1862,f1858]) ).
fof(f1858,plain,
( spl0_201
<=> 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_201])]) ).
fof(f1862,plain,
( spl0_202
<=> member(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1866,plain,
( spl0_203
<=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f622,plain,
( spl0_76
<=> ! [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_76])]) ).
fof(f643,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_76
| ~ spl0_78 ),
inference(superposition,[],[f623,f637]) ).
fof(f623,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_76 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f1854,plain,
( spl0_200
| ~ spl0_20
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1784,f1710,f294,f1851]) ).
fof(f1784,plain,
( member(singleton_relation,universal_class)
| ~ spl0_20
| ~ spl0_188 ),
inference(superposition,[],[f295,f1712]) ).
fof(f1849,plain,
( spl0_199
| ~ spl0_79
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f697,f694,f640,f1847]) ).
fof(f697,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_79
| ~ spl0_88 ),
inference(resolution,[],[f695,f641]) ).
fof(f1816,plain,
( spl0_198
| ~ spl0_55
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f645,f635,f489,f1814]) ).
fof(f645,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_55
| ~ spl0_78 ),
inference(superposition,[],[f490,f637]) ).
fof(f1809,plain,
( spl0_197
| ~ spl0_45
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f651,f640,f417,f1807]) ).
fof(f651,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_45
| ~ spl0_79 ),
inference(resolution,[],[f641,f418]) ).
fof(f1805,plain,
( spl0_196
| ~ spl0_46
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f560,f548,f421,f1803]) ).
fof(f1803,plain,
( spl0_196
<=> ! [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_196])]) ).
fof(f560,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_46
| ~ spl0_62 ),
inference(resolution,[],[f549,f422]) ).
fof(f1798,plain,
( spl0_195
| ~ spl0_66
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f593,f580,f570,f1796]) ).
fof(f1796,plain,
( spl0_195
<=> ! [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_195])]) ).
fof(f580,plain,
( spl0_68
<=> ! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f593,plain,
( ! [X0] :
( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
| maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
| ~ inductive(X0) )
| ~ spl0_66
| ~ spl0_68 ),
inference(resolution,[],[f581,f571]) ).
fof(f581,plain,
( ! [X1,X8] :
( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| ~ function(X8)
| maps(X8,domain_of(X8),X1) )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f1739,plain,
( spl0_194
| ~ spl0_79
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f679,f676,f640,f1737]) ).
fof(f679,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_79
| ~ spl0_84 ),
inference(resolution,[],[f677,f641]) ).
fof(f1735,plain,
( spl0_193
| ~ spl0_45
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f633,f626,f417,f1733]) ).
fof(f626,plain,
( spl0_77
<=> ! [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_77])]) ).
fof(f633,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_45
| ~ spl0_77 ),
inference(resolution,[],[f627,f418]) ).
fof(f627,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_77 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f1731,plain,
( spl0_192
| ~ spl0_45
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f629,f622,f417,f1729]) ).
fof(f629,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_45
| ~ spl0_76 ),
inference(resolution,[],[f623,f418]) ).
fof(f1727,plain,
( spl0_191
| ~ spl0_46
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f539,f501,f421,f1725]) ).
fof(f1725,plain,
( spl0_191
<=> ! [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_191])]) ).
fof(f539,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_46
| ~ spl0_58 ),
inference(resolution,[],[f502,f422]) ).
fof(f1723,plain,
( spl0_190
| ~ spl0_46
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f538,f497,f421,f1721]) ).
fof(f1721,plain,
( spl0_190
<=> ! [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_190])]) ).
fof(f538,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_46
| ~ spl0_57 ),
inference(resolution,[],[f498,f422]) ).
fof(f1717,plain,
( spl0_188
| spl0_189
| ~ spl0_48
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f878,f849,f429,f1714,f1710]) ).
fof(f878,plain,
( member(regular(singleton_relation),element_relation)
| singleton_relation = x
| ~ spl0_48
| ~ spl0_111 ),
inference(superposition,[],[f850,f431]) ).
fof(f1650,plain,
( spl0_187
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f670,f667,f1648]) ).
fof(f667,plain,
( spl0_82
<=> ! [X9,X11,X10] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f670,plain,
( ! [X0,X1] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
| ~ spl0_82 ),
inference(equality_resolution,[],[f668]) ).
fof(f668,plain,
( ! [X10,X11,X9] :
( domain_of(domain_of(X10)) != domain_of(X9)
| compatible(X9,X10,X11)
| ~ function(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f1646,plain,
( spl0_186
| ~ spl0_45
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f614,f598,f417,f1644]) ).
fof(f614,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_45
| ~ spl0_71 ),
inference(resolution,[],[f599,f418]) ).
fof(f1642,plain,
( spl0_185
| ~ spl0_34
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f524,f489,f358,f1640]) ).
fof(f524,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_34
| ~ spl0_55 ),
inference(resolution,[],[f490,f359]) ).
fof(f1638,plain,
( spl0_184
| ~ spl0_33
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f514,f485,f354,f1636]) ).
fof(f514,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_33
| ~ spl0_54 ),
inference(resolution,[],[f486,f355]) ).
fof(f1627,plain,
( spl0_183
| ~ spl0_39
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f647,f635,f378,f1625]) ).
fof(f647,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_39
| ~ spl0_78 ),
inference(superposition,[],[f379,f637]) ).
fof(f1620,plain,
( spl0_182
| ~ spl0_56
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f630,f622,f493,f1618]) ).
fof(f630,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_56
| ~ spl0_76 ),
inference(superposition,[],[f623,f494]) ).
fof(f1608,plain,
( spl0_181
| ~ spl0_30
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f596,f580,f335,f1606]) ).
fof(f1606,plain,
( spl0_181
<=> ! [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_181])]) ).
fof(f596,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_30
| ~ spl0_68 ),
inference(resolution,[],[f581,f336]) ).
fof(f1604,plain,
( spl0_180
| ~ spl0_34
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f478,f465,f358,f1602]) ).
fof(f478,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_34
| ~ spl0_50 ),
inference(resolution,[],[f466,f359]) ).
fof(f1600,plain,
( spl0_179
| ~ spl0_41
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f452,f421,f386,f1598]) ).
fof(f452,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_41
| ~ spl0_46 ),
inference(resolution,[],[f422,f387]) ).
fof(f1596,plain,
( spl0_178
| ~ spl0_40
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f451,f421,f382,f1594]) ).
fof(f451,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_40
| ~ spl0_46 ),
inference(resolution,[],[f422,f383]) ).
fof(f1586,plain,
( ~ spl0_177
| spl0_123
| ~ spl0_19
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f800,f782,f289,f971,f1583]) ).
fof(f1583,plain,
( spl0_177
<=> inductive(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f800,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ inductive(domain_relation)
| ~ spl0_19
| ~ spl0_104 ),
inference(resolution,[],[f783,f291]) ).
fof(f1581,plain,
( spl0_176
| ~ spl0_6
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f731,f718,f231,f1579]) ).
fof(f731,plain,
( ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_6
| ~ spl0_93 ),
inference(superposition,[],[f719,f232]) ).
fof(f1572,plain,
( spl0_175
| ~ spl0_11
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f721,f718,f254,f1570]) ).
fof(f721,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)
| x = 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_11
| ~ spl0_93 ),
inference(resolution,[],[f719,f255]) ).
fof(f1544,plain,
( spl0_174
| ~ spl0_45
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f542,f509,f417,f1542]) ).
fof(f509,plain,
( spl0_60
<=> ! [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_60])]) ).
fof(f542,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
| ~ spl0_45
| ~ spl0_60 ),
inference(resolution,[],[f510,f418]) ).
fof(f510,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f1540,plain,
( spl0_173
| ~ spl0_45
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f523,f489,f417,f1538]) ).
fof(f523,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(intersection(X2,X1),X3)
| member(X0,X3) )
| ~ spl0_45
| ~ spl0_55 ),
inference(resolution,[],[f490,f418]) ).
fof(f1536,plain,
( spl0_171
| ~ spl0_172
| ~ spl0_32
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f459,f421,f345,f1533,f1529]) ).
fof(f459,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_32
| ~ spl0_46 ),
inference(resolution,[],[f422,f347]) ).
fof(f1527,plain,
( spl0_169
| ~ spl0_170
| ~ spl0_31
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f457,f421,f339,f1524,f1520]) ).
fof(f457,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_31
| ~ spl0_46 ),
inference(resolution,[],[f422,f341]) ).
fof(f1518,plain,
( spl0_168
| ~ spl0_29
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f455,f421,f331,f1516]) ).
fof(f455,plain,
( ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_29
| ~ spl0_46 ),
inference(resolution,[],[f422,f332]) ).
fof(f1511,plain,
( spl0_167
| ~ spl0_27
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f515,f485,f323,f1509]) ).
fof(f515,plain,
( ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| ~ member(unordered_pair(X0,X1),universal_class)
| unordered_pair(X0,X1) = x )
| ~ spl0_27
| ~ spl0_54 ),
inference(resolution,[],[f486,f324]) ).
fof(f1504,plain,
( spl0_166
| ~ spl0_6
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f728,f718,f231,f1502]) ).
fof(f728,plain,
( ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(x,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))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_93 ),
inference(superposition,[],[f719,f232]) ).
fof(f1482,plain,
( ~ spl0_165
| spl0_123
| ~ spl0_17
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f793,f782,f280,f971,f1479]) ).
fof(f1479,plain,
( spl0_165
<=> inductive(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f793,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation)
| ~ spl0_17
| ~ spl0_104 ),
inference(resolution,[],[f783,f282]) ).
fof(f1458,plain,
( spl0_164
| ~ spl0_49
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f527,f489,f434,f1456]) ).
fof(f527,plain,
( ! [X0] :
( member(X0,identity_relation)
| ~ member(X0,subset_relation)
| ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_49
| ~ spl0_55 ),
inference(superposition,[],[f490,f436]) ).
fof(f1454,plain,
( spl0_163
| ~ spl0_48
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f526,f489,f429,f1452]) ).
fof(f526,plain,
( ! [X0] :
( member(X0,singleton_relation)
| ~ member(X0,element_relation)
| ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_48
| ~ spl0_55 ),
inference(superposition,[],[f490,f431]) ).
fof(f1450,plain,
( spl0_162
| ~ spl0_45
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f477,f465,f417,f1448]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(complement(X1),X2)
| member(X0,X2) )
| ~ spl0_45
| ~ spl0_50 ),
inference(resolution,[],[f466,f418]) ).
fof(f1394,plain,
( spl0_161
| ~ spl0_9
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f595,f580,f244,f1392]) ).
fof(f1392,plain,
( spl0_161
<=> ! [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_161])]) ).
fof(f595,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
| ~ spl0_9
| ~ spl0_68 ),
inference(resolution,[],[f581,f245]) ).
fof(f1390,plain,
( spl0_160
| ~ spl0_25
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f456,f421,f315,f1388]) ).
fof(f456,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_25
| ~ spl0_46 ),
inference(resolution,[],[f422,f316]) ).
fof(f1386,plain,
( spl0_159
| ~ spl0_30
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f449,f421,f335,f1384]) ).
fof(f449,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_30
| ~ spl0_46 ),
inference(resolution,[],[f422,f336]) ).
fof(f1382,plain,
( spl0_158
| ~ spl0_33
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f411,f378,f354,f1380]) ).
fof(f411,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_33
| ~ spl0_39 ),
inference(resolution,[],[f379,f355]) ).
fof(f1378,plain,
( spl0_157
| ~ spl0_33
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f406,f374,f354,f1376]) ).
fof(f406,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_33
| ~ spl0_38 ),
inference(resolution,[],[f375,f355]) ).
fof(f1368,plain,
( spl0_156
| ~ spl0_2
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f726,f718,f213,f1366]) ).
fof(f726,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,x))),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_2
| ~ spl0_93 ),
inference(resolution,[],[f719,f214]) ).
fof(f1353,plain,
( spl0_155
| ~ spl0_20
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f1054,f417,f294,f1351]) ).
fof(f1054,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl0_20
| ~ spl0_45 ),
inference(resolution,[],[f295,f418]) ).
fof(f1331,plain,
( spl0_154
| ~ spl0_62
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f592,f580,f548,f1329]) ).
fof(f1329,plain,
( spl0_154
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(X0)))
| ~ operation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f592,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(X0)))
| ~ operation(X0) )
| ~ spl0_62
| ~ spl0_68 ),
inference(resolution,[],[f581,f549]) ).
fof(f1327,plain,
( spl0_153
| ~ spl0_36
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f445,f417,f366,f1325]) ).
fof(f445,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_36
| ~ spl0_45 ),
inference(resolution,[],[f418,f367]) ).
fof(f1323,plain,
( spl0_152
| ~ spl0_35
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f444,f417,f362,f1321]) ).
fof(f444,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_35
| ~ spl0_45 ),
inference(resolution,[],[f418,f363]) ).
fof(f1319,plain,
( spl0_151
| ~ spl0_33
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f438,f417,f354,f1317]) ).
fof(f438,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) )
| ~ spl0_33
| ~ spl0_45 ),
inference(resolution,[],[f418,f355]) ).
fof(f1296,plain,
( spl0_150
| ~ spl0_38
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f463,f434,f374,f1294]) ).
fof(f463,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_38
| ~ spl0_49 ),
inference(superposition,[],[f375,f436]) ).
fof(f1292,plain,
( spl0_149
| ~ spl0_38
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f461,f429,f374,f1290]) ).
fof(f461,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_38
| ~ spl0_48 ),
inference(superposition,[],[f375,f431]) ).
fof(f1288,plain,
( spl0_147
| ~ spl0_148
| ~ spl0_19
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f458,f421,f289,f1285,f1281]) ).
fof(f458,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| cross_product(universal_class,universal_class) = domain_relation
| ~ spl0_19
| ~ spl0_46 ),
inference(resolution,[],[f422,f291]) ).
fof(f1279,plain,
( spl0_145
| ~ spl0_146
| ~ spl0_17
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f453,f421,f280,f1276,f1272]) ).
fof(f453,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| cross_product(universal_class,universal_class) = successor_relation
| ~ spl0_17
| ~ spl0_46 ),
inference(resolution,[],[f422,f282]) ).
fof(f1270,plain,
( spl0_143
| ~ spl0_144
| ~ spl0_16
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f450,f421,f275,f1267,f1263]) ).
fof(f450,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| element_relation = cross_product(universal_class,universal_class)
| ~ spl0_16
| ~ spl0_46 ),
inference(resolution,[],[f422,f277]) ).
fof(f1261,plain,
( spl0_142
| ~ spl0_28
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f401,f354,f327,f1259]) ).
fof(f401,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) )
| ~ spl0_28
| ~ spl0_33 ),
inference(resolution,[],[f355,f328]) ).
fof(f1231,plain,
( spl0_141
| ~ spl0_3
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f664,f658,f217,f1229]) ).
fof(f664,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) = x )
| ~ spl0_3
| ~ spl0_81 ),
inference(resolution,[],[f659,f218]) ).
fof(f1218,plain,
( spl0_140
| ~ spl0_57
| ~ spl0_74 ),
inference(avatar_split_clause,[],[f616,f610,f497,f1216]) ).
fof(f610,plain,
( spl0_74
<=> ! [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_74])]) ).
fof(f616,plain,
( ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) )
| ~ spl0_57
| ~ spl0_74 ),
inference(resolution,[],[f611,f498]) ).
fof(f611,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_74 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f1180,plain,
( spl0_139
| ~ spl0_27
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f412,f378,f323,f1178]) ).
fof(f412,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x )
| ~ spl0_27
| ~ spl0_39 ),
inference(resolution,[],[f379,f324]) ).
fof(f1176,plain,
( spl0_138
| ~ spl0_27
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f407,f374,f323,f1174]) ).
fof(f407,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = x )
| ~ spl0_27
| ~ spl0_38 ),
inference(resolution,[],[f375,f324]) ).
fof(f1126,plain,
( spl0_137
| ~ spl0_38
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f648,f635,f374,f1124]) ).
fof(f648,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_38
| ~ spl0_78 ),
inference(superposition,[],[f375,f637]) ).
fof(f1122,plain,
( spl0_136
| ~ spl0_18
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f454,f421,f285,f1120]) ).
fof(f454,plain,
( ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) )
| ~ spl0_18
| ~ spl0_46 ),
inference(resolution,[],[f422,f286]) ).
fof(f1118,plain,
( spl0_135
| ~ spl0_15
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f443,f417,f271,f1116]) ).
fof(f443,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X0) )
| ~ spl0_15
| ~ spl0_45 ),
inference(resolution,[],[f418,f272]) ).
fof(f1106,plain,
( spl0_134
| ~ spl0_27
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f351,f327,f323,f1104]) ).
fof(f351,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = x )
| ~ spl0_27
| ~ spl0_28 ),
inference(resolution,[],[f328,f324]) ).
fof(f1099,plain,
( spl0_133
| ~ spl0_7
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f594,f580,f235,f1097]) ).
fof(f1097,plain,
( spl0_133
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f594,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),universal_class) )
| ~ spl0_7
| ~ spl0_68 ),
inference(resolution,[],[f581,f236]) ).
fof(f1033,plain,
( ~ spl0_4
| ~ spl0_127 ),
inference(avatar_contradiction_clause,[],[f1032]) ).
fof(f1032,plain,
( $false
| ~ spl0_4
| ~ spl0_127 ),
inference(resolution,[],[f990,f223]) ).
fof(f223,plain,
( inductive(omega)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f990,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f989]) ).
fof(f989,plain,
( spl0_127
<=> ! [X0] : ~ inductive(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1031,plain,
( spl0_132
| ~ spl0_27
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f439,f417,f323,f1029]) ).
fof(f439,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| ~ member(X0,universal_class)
| x = X0 )
| ~ spl0_27
| ~ spl0_45 ),
inference(resolution,[],[f418,f324]) ).
fof(f1025,plain,
( spl0_131
| ~ spl0_11
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f405,f358,f254,f1023]) ).
fof(f405,plain,
( ! [X0,X1] :
( x = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
| subclass(X0,domain_of(X1))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) )
| ~ spl0_11
| ~ spl0_34 ),
inference(forward_demodulation,[],[f403,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(f403,plain,
( ! [X0,X1] :
( subclass(X0,domain_of(X1))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| x = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1) )
| ~ spl0_11
| ~ spl0_34 ),
inference(resolution,[],[f359,f255]) ).
fof(f1003,plain,
( spl0_130
| ~ spl0_39
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f462,f434,f378,f1001]) ).
fof(f462,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_39
| ~ spl0_49 ),
inference(superposition,[],[f379,f436]) ).
fof(f999,plain,
( spl0_129
| ~ spl0_39
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f460,f429,f378,f997]) ).
fof(f460,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_39
| ~ spl0_48 ),
inference(superposition,[],[f379,f431]) ).
fof(f995,plain,
( spl0_128
| ~ spl0_7
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f447,f421,f235,f993]) ).
fof(f447,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_7
| ~ spl0_46 ),
inference(resolution,[],[f422,f236]) ).
fof(f991,plain,
( spl0_127
| spl0_20
| ~ spl0_7
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f785,f782,f235,f294,f989]) ).
fof(f785,plain,
( ! [X0] :
( member(x,universal_class)
| ~ inductive(X0) )
| ~ spl0_7
| ~ spl0_104 ),
inference(resolution,[],[f783,f236]) ).
fof(f987,plain,
( spl0_126
| ~ spl0_8
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f442,f417,f239,f985]) ).
fof(f442,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_8
| ~ spl0_45 ),
inference(resolution,[],[f418,f241]) ).
fof(f982,plain,
( ~ spl0_123
| spl0_124
| ~ spl0_125
| ~ spl0_14
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f352,f335,f266,f979,f975,f971]) ).
fof(f975,plain,
( spl0_124
<=> inductive(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f266,plain,
( spl0_14
<=> ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f352,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
| inductive(cross_product(universal_class,universal_class))
| ~ member(x,cross_product(universal_class,universal_class))
| ~ spl0_14
| ~ spl0_30 ),
inference(resolution,[],[f336,f267]) ).
fof(f267,plain,
( ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(x,X0) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f969,plain,
( spl0_121
| spl0_122
| ~ spl0_6
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f631,f622,f231,f966,f963]) ).
fof(f963,plain,
( spl0_121
<=> ! [X0] :
( ~ member(X0,universal_class)
| x = cross_product(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f631,plain,
( ! [X0] :
( member(domain_of(domain_of(flip(cross_product(x,universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class)))
| x = cross_product(X0,universal_class) )
| ~ spl0_6
| ~ spl0_76 ),
inference(superposition,[],[f623,f232]) ).
fof(f961,plain,
( spl0_119
| spl0_120
| ~ spl0_2
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f665,f658,f213,f958,f955]) ).
fof(f955,plain,
( spl0_119
<=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f665,plain,
( ! [X0,X1] :
( x = unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x))))
| ~ inductive(cross_product(X0,X1)) )
| ~ spl0_2
| ~ spl0_81 ),
inference(resolution,[],[f659,f214]) ).
fof(f948,plain,
( spl0_118
| ~ spl0_11
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f446,f417,f254,f946]) ).
fof(f446,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_of(X0),X1)
| member(X2,X1)
| ~ member(X2,universal_class)
| x = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) )
| ~ spl0_11
| ~ spl0_45 ),
inference(resolution,[],[f418,f255]) ).
fof(f920,plain,
( spl0_117
| ~ spl0_3
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f516,f485,f217,f918]) ).
fof(f516,plain,
( ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = x )
| ~ spl0_3
| ~ spl0_54 ),
inference(resolution,[],[f486,f218]) ).
fof(f914,plain,
( spl0_116
| ~ spl0_58
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f540,f505,f501,f912]) ).
fof(f505,plain,
( spl0_59
<=> ! [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_59])]) ).
fof(f540,plain,
( ! [X0] :
( single_valued_class(X0)
| ~ function(X0) )
| ~ spl0_58
| ~ spl0_59 ),
inference(resolution,[],[f506,f502]) ).
fof(f506,plain,
( ! [X0] :
( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| single_valued_class(X0) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f907,plain,
( spl0_115
| ~ spl0_6
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f252,f248,f231,f905]) ).
fof(f248,plain,
( spl0_10
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| x != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f252,plain,
( ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f251]) ).
fof(f251,plain,
( ! [X0] :
( x != x
| ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| x = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_6
| ~ spl0_10 ),
inference(superposition,[],[f249,f232]) ).
fof(f249,plain,
( ! [X0,X4] :
( x != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
| ~ member(X4,domain_of(X0)) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f892,plain,
( ~ spl0_114
| ~ spl0_2
| spl0_97 ),
inference(avatar_split_clause,[],[f826,f747,f213,f889]) ).
fof(f889,plain,
( spl0_114
<=> inductive(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f826,plain,
( ~ inductive(subset_relation)
| ~ spl0_2
| spl0_97 ),
inference(resolution,[],[f748,f214]) ).
fof(f887,plain,
( spl0_113
| ~ spl0_10
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f533,f493,f248,f885]) ).
fof(f533,plain,
( ! [X0,X1] :
( x != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) )
| ~ spl0_10
| ~ spl0_56 ),
inference(superposition,[],[f249,f494]) ).
fof(f883,plain,
( spl0_112
| ~ spl0_6
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f525,f489,f231,f881]) ).
fof(f525,plain,
( ! [X0,X1] :
( member(X1,x)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| x = X0 )
| ~ spl0_6
| ~ spl0_55 ),
inference(superposition,[],[f490,f232]) ).
fof(f851,plain,
( spl0_111
| ~ spl0_3
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f413,f378,f217,f849]) ).
fof(f413,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = x )
| ~ spl0_3
| ~ spl0_39 ),
inference(resolution,[],[f379,f218]) ).
fof(f847,plain,
( spl0_110
| ~ spl0_3
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f408,f374,f217,f845]) ).
fof(f408,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = x )
| ~ spl0_3
| ~ spl0_38 ),
inference(resolution,[],[f375,f218]) ).
fof(f830,plain,
( spl0_109
| ~ spl0_2
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f517,f485,f213,f828]) ).
fof(f517,plain,
( ! [X0,X1] :
( x = X0
| x = X1
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_2
| ~ spl0_54 ),
inference(resolution,[],[f486,f214]) ).
fof(f825,plain,
( spl0_108
| ~ spl0_3
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f440,f417,f217,f823]) ).
fof(f440,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| x = X0 )
| ~ spl0_3
| ~ spl0_45 ),
inference(resolution,[],[f418,f218]) ).
fof(f821,plain,
( spl0_107
| ~ spl0_6
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f415,f378,f231,f819]) ).
fof(f415,plain,
( ! [X0,X1] :
( ~ member(X1,x)
| member(X1,regular(X0))
| x = X0 )
| ~ spl0_6
| ~ spl0_39 ),
inference(superposition,[],[f379,f232]) ).
fof(f809,plain,
( spl0_106
| ~ spl0_6
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f410,f374,f231,f807]) ).
fof(f410,plain,
( ! [X0,X1] :
( ~ member(X1,x)
| member(X1,X0)
| x = X0 )
| ~ spl0_6
| ~ spl0_38 ),
inference(superposition,[],[f375,f232]) ).
fof(f805,plain,
( spl0_105
| ~ spl0_3
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f350,f327,f217,f803]) ).
fof(f350,plain,
( ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = x )
| ~ spl0_3
| ~ spl0_28 ),
inference(resolution,[],[f328,f218]) ).
fof(f784,plain,
( spl0_104
| ~ spl0_2
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f441,f417,f213,f782]) ).
fof(f441,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(x,X1)
| ~ inductive(X0) )
| ~ spl0_2
| ~ spl0_45 ),
inference(resolution,[],[f418,f214]) ).
fof(f780,plain,
spl0_103,
inference(avatar_split_clause,[],[f206,f778]) ).
fof(f778,plain,
( spl0_103
<=> ! [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_103])]) ).
fof(f206,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f205,f129]) ).
fof(f205,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(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,[],[f204,f129]) ).
fof(f204,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f203,f129]) ).
fof(f203,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(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,[],[f202,f129]) ).
fof(f202,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(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,[],[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(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,[],[f200,f129]) ).
fof(f200,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(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,[],[f199,f129]) ).
fof(f199,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(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,[],[f198,f129]) ).
fof(f198,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(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,[],[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(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,[],[f179,f129]) ).
fof(f179,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f91,f118,f119,f118,f118,f118,f118,f119]) ).
fof(f119,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f118,plain,
! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
inference(definition_unfolding,[],[f68,f115,f117,f12]) ).
fof(f117,plain,
! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
inference(definition_unfolding,[],[f42,f116,f29]) ).
fof(f116,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f115,plain,
! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
inference(definition_unfolding,[],[f53,f29]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
fof(f91,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).
fof(f773,plain,
spl0_102,
inference(avatar_split_clause,[],[f196,f771]) ).
fof(f196,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(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,[],[f195,f129]) ).
fof(f195,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(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,[],[f194,f129]) ).
fof(f194,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(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,[],[f193,f129]) ).
fof(f193,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(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,[],[f192,f129]) ).
fof(f192,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,[],[f171,f129]) ).
fof(f171,plain,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f89,f119,f118,f119,f118,f118,f118,f118,f119]) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).
fof(f768,plain,
spl0_101,
inference(avatar_split_clause,[],[f191,f766]) ).
fof(f191,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,[],[f170,f129]) ).
fof(f170,plain,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(definition_unfolding,[],[f108,f119,f119,f118,f119,f119]) ).
fof(f108,axiom,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).
fof(f762,plain,
spl0_100,
inference(avatar_split_clause,[],[f175,f760]) ).
fof(f175,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f37,f119,f119,f119,f119,f119,f119]) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).
fof(f758,plain,
spl0_99,
inference(avatar_split_clause,[],[f174,f756]) ).
fof(f174,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f34,f119,f119,f119,f119,f119,f119]) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).
fof(f754,plain,
( spl0_97
| ~ spl0_98
| ~ spl0_49
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f559,f480,f434,f751,f747]) ).
fof(f751,plain,
( spl0_98
<=> inductive(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f480,plain,
( spl0_53
<=> ! [X0,X1] :
( member(x,X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f559,plain,
( ~ inductive(identity_relation)
| member(x,subset_relation)
| ~ spl0_49
| ~ spl0_53 ),
inference(superposition,[],[f481,f436]) ).
fof(f481,plain,
( ! [X0,X1] :
( ~ inductive(intersection(X1,X0))
| member(x,X0) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f745,plain,
spl0_96,
inference(avatar_split_clause,[],[f159,f743]) ).
fof(f159,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
inference(definition_unfolding,[],[f36,f119,f119,f119,f119]) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).
fof(f741,plain,
spl0_95,
inference(avatar_split_clause,[],[f158,f739]) ).
fof(f158,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
inference(definition_unfolding,[],[f33,f119,f119,f119,f119]) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).
fof(f736,plain,
spl0_94,
inference(avatar_split_clause,[],[f182,f734]) ).
fof(f182,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,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f46,f125,f119,f119]) ).
fof(f125,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f43,f26,f12]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).
fof(f720,plain,
spl0_93,
inference(avatar_split_clause,[],[f173,f718]) ).
fof(f173,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f59,f119,f119,f117,f117,f12]) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).
fof(f714,plain,
spl0_92,
inference(avatar_split_clause,[],[f156,f712]) ).
fof(f156,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
inference(definition_unfolding,[],[f97,f119,f119,f119]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).
fof(f710,plain,
spl0_91,
inference(avatar_split_clause,[],[f187,f708]) ).
fof(f187,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,[],[f153,f129]) ).
fof(f153,plain,
! [X0,X1,X4] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(definition_unfolding,[],[f107,f118,f119,f119]) ).
fof(f107,axiom,
! [X0,X1,X4] :
( apply(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).
fof(f705,plain,
spl0_90,
inference(avatar_split_clause,[],[f178,f703]) ).
fof(f178,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
inference(definition_unfolding,[],[f90,f119]) ).
fof(f90,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).
fof(f701,plain,
spl0_89,
inference(avatar_split_clause,[],[f157,f699]) ).
fof(f157,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f58,f119,f117,f117,f12]) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
fof(f696,plain,
spl0_88,
inference(avatar_split_clause,[],[f183,f694]) ).
fof(f183,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,[],[f172]) ).
fof(f172,plain,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f94,f119,f119]) ).
fof(f94,axiom,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).
fof(f692,plain,
spl0_87,
inference(avatar_split_clause,[],[f155,f690]) ).
fof(f155,plain,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
inference(definition_unfolding,[],[f96,f119,f119]) ).
fof(f96,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).
fof(f688,plain,
spl0_86,
inference(avatar_split_clause,[],[f151,f686]) ).
fof(f151,plain,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(definition_unfolding,[],[f106,f119,f119]) ).
fof(f106,axiom,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).
fof(f684,plain,
( ~ spl0_85
| ~ spl0_2
| spl0_69 ),
inference(avatar_split_clause,[],[f652,f584,f213,f681]) ).
fof(f681,plain,
( spl0_85
<=> inductive(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f652,plain,
( ~ inductive(element_relation)
| ~ spl0_2
| spl0_69 ),
inference(resolution,[],[f585,f214]) ).
fof(f678,plain,
spl0_84,
inference(avatar_split_clause,[],[f166,f676]) ).
fof(f166,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f20,f119,f119]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
fof(f674,plain,
spl0_83,
inference(avatar_split_clause,[],[f176,f672]) ).
fof(f672,plain,
( spl0_83
<=> ! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f176,plain,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f81,f116]) ).
fof(f81,axiom,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).
fof(f669,plain,
spl0_82,
inference(avatar_split_clause,[],[f177,f667]) ).
fof(f177,plain,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f85,f116]) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).
fof(f660,plain,
spl0_81,
inference(avatar_split_clause,[],[f152,f658]) ).
fof(f152,plain,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
inference(definition_unfolding,[],[f17,f119]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f656,plain,
spl0_80,
inference(avatar_split_clause,[],[f149,f654]) ).
fof(f149,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f45,f125,f119]) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).
fof(f642,plain,
spl0_79,
inference(avatar_split_clause,[],[f165,f640]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f16,f119]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f638,plain,
spl0_78,
inference(avatar_split_clause,[],[f130,f635]) ).
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(f628,plain,
spl0_77,
inference(avatar_split_clause,[],[f185,f626]) ).
fof(f185,plain,
! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ),
inference(forward_demodulation,[],[f138,f129]) ).
fof(f138,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
inference(definition_unfolding,[],[f56,f126]) ).
fof(f126,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
inference(definition_unfolding,[],[f55,f117]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).
fof(f624,plain,
spl0_76,
inference(avatar_split_clause,[],[f161,f622]) ).
fof(f161,plain,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
inference(definition_unfolding,[],[f65,f117]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
fof(f620,plain,
spl0_75,
inference(avatar_split_clause,[],[f154,f618]) ).
fof(f154,plain,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
inference(definition_unfolding,[],[f93,f119]) ).
fof(f93,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).
fof(f612,plain,
spl0_74,
inference(avatar_split_clause,[],[f164,f610]) ).
fof(f164,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(f608,plain,
spl0_73,
inference(avatar_split_clause,[],[f145,f606]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f14,f119]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f604,plain,
spl0_72,
inference(avatar_split_clause,[],[f144,f602]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f15,f119]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f600,plain,
spl0_71,
inference(avatar_split_clause,[],[f140,f598]) ).
fof(f140,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
inference(definition_unfolding,[],[f100,f119]) ).
fof(f100,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
fof(f591,plain,
( spl0_69
| ~ spl0_70
| ~ spl0_48
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f558,f480,f429,f588,f584]) ).
fof(f588,plain,
( spl0_70
<=> inductive(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f558,plain,
( ~ inductive(singleton_relation)
| member(x,element_relation)
| ~ spl0_48
| ~ spl0_53 ),
inference(superposition,[],[f481,f431]) ).
fof(f582,plain,
spl0_68,
inference(avatar_split_clause,[],[f162,f580]) ).
fof(f162,plain,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ),
inference(definition_unfolding,[],[f112,f116]) ).
fof(f112,axiom,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).
fof(f578,plain,
spl0_67,
inference(avatar_split_clause,[],[f150,f576]) ).
fof(f150,plain,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
inference(definition_unfolding,[],[f99,f119]) ).
fof(f99,axiom,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
fof(f572,plain,
spl0_66,
inference(avatar_split_clause,[],[f184,f570]) ).
fof(f184,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(forward_demodulation,[],[f134,f129]) ).
fof(f134,plain,
! [X0] :
( ~ inductive(X0)
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f48,f117]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
fof(f568,plain,
spl0_65,
inference(avatar_split_clause,[],[f148,f566]) ).
fof(f566,plain,
( spl0_65
<=> ! [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_65])]) ).
fof(f148,plain,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f84,f116]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).
fof(f564,plain,
spl0_64,
inference(avatar_split_clause,[],[f143,f562]) ).
fof(f143,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f19,f119]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
fof(f554,plain,
spl0_63,
inference(avatar_split_clause,[],[f147,f552]) ).
fof(f552,plain,
( spl0_63
<=> ! [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_63])]) ).
fof(f147,plain,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
inference(definition_unfolding,[],[f111,f116]) ).
fof(f111,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).
fof(f550,plain,
spl0_62,
inference(avatar_split_clause,[],[f135,f548]) ).
fof(f135,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f116]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).
fof(f546,plain,
spl0_61,
inference(avatar_split_clause,[],[f79,f544]) ).
fof(f544,plain,
( spl0_61
<=> ! [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_61])]) ).
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(f511,plain,
spl0_60,
inference(avatar_split_clause,[],[f186,f509]) ).
fof(f186,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f139,f129]) ).
fof(f139,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f115]) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
fof(f507,plain,
spl0_59,
inference(avatar_split_clause,[],[f137,f505]) ).
fof(f137,plain,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f61,f38]) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f503,plain,
spl0_58,
inference(avatar_split_clause,[],[f136,f501]) ).
fof(f136,plain,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f63,f38]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
fof(f499,plain,
spl0_57,
inference(avatar_split_clause,[],[f131,f497]) ).
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(f495,plain,
spl0_56,
inference(avatar_split_clause,[],[f129,f493]) ).
fof(f491,plain,
spl0_55,
inference(avatar_split_clause,[],[f23,f489]) ).
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(f487,plain,
spl0_54,
inference(avatar_split_clause,[],[f8,f485]) ).
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(f482,plain,
( spl0_53
| ~ spl0_2
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f414,f378,f213,f480]) ).
fof(f414,plain,
( ! [X0,X1] :
( member(x,X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl0_2
| ~ spl0_39 ),
inference(resolution,[],[f379,f214]) ).
fof(f475,plain,
spl0_52,
inference(avatar_split_clause,[],[f160,f473]) ).
fof(f473,plain,
( spl0_52
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f160,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(f471,plain,
spl0_51,
inference(avatar_split_clause,[],[f83,f469]) ).
fof(f469,plain,
( spl0_51
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
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(f467,plain,
spl0_50,
inference(avatar_split_clause,[],[f25,f465]) ).
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(f437,plain,
spl0_49,
inference(avatar_split_clause,[],[f128,f434]) ).
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(f432,plain,
spl0_48,
inference(avatar_split_clause,[],[f104,f429]) ).
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(f427,plain,
( spl0_47
| ~ spl0_2
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f409,f374,f213,f425]) ).
fof(f409,plain,
( ! [X0,X1] :
( member(x,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl0_2
| ~ spl0_38 ),
inference(resolution,[],[f375,f214]) ).
fof(f423,plain,
spl0_46,
inference(avatar_split_clause,[],[f7,f421]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f419,plain,
spl0_45,
inference(avatar_split_clause,[],[f1,f417]) ).
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(f400,plain,
spl0_44,
inference(avatar_split_clause,[],[f132,f398]) ).
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(f396,plain,
spl0_43,
inference(avatar_split_clause,[],[f110,f394]) ).
fof(f394,plain,
( spl0_43
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f110,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).
fof(f392,plain,
spl0_42,
inference(avatar_split_clause,[],[f88,f390]) ).
fof(f390,plain,
( spl0_42
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
fof(f388,plain,
spl0_41,
inference(avatar_split_clause,[],[f35,f386]) ).
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(f384,plain,
spl0_40,
inference(avatar_split_clause,[],[f32,f382]) ).
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(f380,plain,
spl0_39,
inference(avatar_split_clause,[],[f22,f378]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f376,plain,
spl0_38,
inference(avatar_split_clause,[],[f21,f374]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f372,plain,
( spl0_37
| ~ spl0_2
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f349,f327,f213,f370]) ).
fof(f370,plain,
( spl0_37
<=> ! [X0] :
( ~ member(x,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f349,plain,
( ! [X0] :
( ~ member(x,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_2
| ~ spl0_28 ),
inference(resolution,[],[f328,f214]) ).
fof(f368,plain,
spl0_36,
inference(avatar_split_clause,[],[f10,f366]) ).
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(f364,plain,
spl0_35,
inference(avatar_split_clause,[],[f9,f362]) ).
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(f360,plain,
spl0_34,
inference(avatar_split_clause,[],[f3,f358]) ).
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(f356,plain,
spl0_33,
inference(avatar_split_clause,[],[f2,f354]) ).
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(f348,plain,
spl0_32,
inference(avatar_split_clause,[],[f105,f345]) ).
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(f342,plain,
spl0_31,
inference(avatar_split_clause,[],[f95,f339]) ).
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(f337,plain,
spl0_30,
inference(avatar_split_clause,[],[f62,f335]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
fof(f333,plain,
spl0_29,
inference(avatar_split_clause,[],[f57,f331]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f329,plain,
spl0_28,
inference(avatar_split_clause,[],[f24,f327]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f325,plain,
spl0_27,
inference(avatar_split_clause,[],[f190,f323]) ).
fof(f190,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)
| x = X1 ),
inference(forward_demodulation,[],[f189,f129]) ).
fof(f189,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)
| x = X1 ),
inference(forward_demodulation,[],[f167,f129]) ).
fof(f167,plain,
! [X1] :
( ~ member(X1,universal_class)
| x = X1
| member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
inference(definition_unfolding,[],[f70,f113,f118]) ).
fof(f113,axiom,
null_class = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sets_with_one_member2_1) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
fof(f321,plain,
spl0_26,
inference(avatar_split_clause,[],[f109,f319]) ).
fof(f319,plain,
( spl0_26
<=> ! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).
fof(f317,plain,
spl0_25,
inference(avatar_split_clause,[],[f92,f315]) ).
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(f313,plain,
spl0_24,
inference(avatar_split_clause,[],[f87,f311]) ).
fof(f311,plain,
( spl0_24
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f309,plain,
spl0_23,
inference(avatar_split_clause,[],[f86,f307]) ).
fof(f307,plain,
( spl0_23
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f305,plain,
spl0_22,
inference(avatar_split_clause,[],[f82,f303]) ).
fof(f303,plain,
( spl0_22
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
fof(f301,plain,
( ~ spl0_20
| spl0_21
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f269,f266,f235,f298,f294]) ).
fof(f269,plain,
( inductive(universal_class)
| ~ member(x,universal_class)
| ~ spl0_7
| ~ spl0_14 ),
inference(resolution,[],[f267,f236]) ).
fof(f292,plain,
spl0_19,
inference(avatar_split_clause,[],[f98,f289]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
fof(f287,plain,
spl0_18,
inference(avatar_split_clause,[],[f51,f285]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f283,plain,
spl0_17,
inference(avatar_split_clause,[],[f44,f280]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
fof(f278,plain,
spl0_16,
inference(avatar_split_clause,[],[f18,f275]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
fof(f273,plain,
spl0_15,
inference(avatar_split_clause,[],[f11,f271]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f268,plain,
spl0_14,
inference(avatar_split_clause,[],[f188,f266]) ).
fof(f188,plain,
! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(x,X0) ),
inference(forward_demodulation,[],[f163,f129]) ).
fof(f163,plain,
! [X0] :
( inductive(X0)
| ~ member(x,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f49,f113,f117]) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).
fof(f264,plain,
spl0_13,
inference(avatar_split_clause,[],[f78,f262]) ).
fof(f262,plain,
( spl0_13
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
fof(f260,plain,
spl0_12,
inference(avatar_split_clause,[],[f71,f258]) ).
fof(f258,plain,
( spl0_12
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
fof(f256,plain,
spl0_11,
inference(avatar_split_clause,[],[f168,f254]) ).
fof(f168,plain,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| x = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f31,f29,f12,f113]) ).
fof(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f250,plain,
spl0_10,
inference(avatar_split_clause,[],[f146,f248]) ).
fof(f146,plain,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| x != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f30,f29,f12,f113]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f246,plain,
spl0_9,
inference(avatar_split_clause,[],[f180,f244]) ).
fof(f180,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).
fof(f242,plain,
spl0_8,
inference(avatar_split_clause,[],[f52,f239]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f237,plain,
spl0_7,
inference(avatar_split_clause,[],[f4,f235]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f233,plain,
spl0_6,
inference(avatar_split_clause,[],[f142,f231]) ).
fof(f142,plain,
! [X0] :
( x = X0
| intersection(X0,regular(X0)) = x ),
inference(definition_unfolding,[],[f67,f113,f113]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f229,plain,
spl0_5,
inference(avatar_split_clause,[],[f69,f226]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f224,plain,
spl0_4,
inference(avatar_split_clause,[],[f50,f221]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f219,plain,
spl0_3,
inference(avatar_split_clause,[],[f141,f217]) ).
fof(f141,plain,
! [X0] :
( x = X0
| member(regular(X0),X0) ),
inference(definition_unfolding,[],[f66,f113]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f215,plain,
spl0_2,
inference(avatar_split_clause,[],[f133,f213]) ).
fof(f133,plain,
! [X0] :
( ~ inductive(X0)
| member(x,X0) ),
inference(definition_unfolding,[],[f47,f113]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f211,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f114,f208]) ).
fof(f114,axiom,
~ subclass(cross_product(x,x),identity_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sets_with_one_member2_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SET468-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n019.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Apr 30 01:28:59 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % (21536)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34 % (21539)WARNING: value z3 for option sas not known
% 0.10/0.34 % (21539)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)
% 0.10/0.34 % (21538)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34 % (21541)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)
% 0.10/0.34 % (21537)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34 % (21542)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)
% 0.10/0.34 % (21540)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.34 % (21543)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)
% 0.10/0.37 TRYING [1]
% 0.10/0.38 TRYING [2]
% 0.15/0.43 TRYING [3]
% 0.15/0.52 TRYING [1]
% 0.15/0.53 TRYING [2]
% 0.15/0.57 TRYING [4]
% 2.24/0.66 TRYING [3]
% 4.78/1.04 TRYING [5]
% 7.95/1.46 TRYING [1]
% 7.95/1.46 TRYING [2]
% 7.95/1.48 TRYING [3]
% 8.38/1.55 TRYING [4]
% 9.50/1.69 TRYING [4]
% 10.19/1.79 TRYING [5]
% 15.48/2.55 TRYING [6]
% 17.58/2.90 TRYING [6]
% 30.52/4.71 TRYING [7]
% 62.88/9.33 TRYING [8]
% 65.85/9.83 % (21541)First to succeed.
% 67.06/9.98 % (21541)Refutation found. Thanks to Tanya!
% 67.06/9.98 % SZS status Unsatisfiable for theBenchmark
% 67.06/9.98 % SZS output start Proof for theBenchmark
% See solution above
% 67.53/10.03 % (21541)------------------------------
% 67.53/10.03 % (21541)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 67.53/10.03 % (21541)Termination reason: Refutation
% 67.53/10.03
% 67.53/10.03 % (21541)Memory used [KB]: 38827
% 67.53/10.03 % (21541)Time elapsed: 9.629 s
% 67.53/10.03 % (21541)Instructions burned: 19121 (million)
% 67.53/10.03 % (21541)------------------------------
% 67.53/10.03 % (21541)------------------------------
% 67.53/10.03 % (21536)Success in time 9.698 s
%------------------------------------------------------------------------------