TSTP Solution File: SET473-6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET473-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:18:52 EDT 2024
% Result : Unsatisfiable 54.43s 8.11s
% Output : Refutation 54.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1430
% Syntax : Number of formulae : 4555 ( 137 unt; 0 def)
% Number of atoms : 17359 (2282 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 22524 (9720 ~;11479 |; 0 &)
% (1325 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 28 ( 4 avg)
% Number of predicates : 1337 (1335 usr;1326 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 14 con; 0-3 aty)
% Number of variables : 6188 (6188 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f54540,plain,
$false,
inference(avatar_sat_refutation,[],[f211,f215,f220,f226,f231,f236,f240,f244,f249,f253,f257,f263,f267,f271,f275,f280,f285,f290,f294,f299,f308,f312,f316,f320,f324,f328,f332,f336,f340,f344,f350,f355,f363,f367,f371,f375,f379,f383,f387,f391,f395,f399,f403,f407,f426,f430,f434,f439,f444,f474,f478,f482,f486,f494,f498,f502,f506,f510,f514,f518,f553,f557,f561,f571,f575,f579,f585,f594,f598,f607,f611,f615,f619,f627,f631,f635,f645,f649,f663,f667,f676,f681,f685,f690,f695,f699,f703,f708,f712,f717,f721,f727,f743,f748,f757,f761,f765,f769,f775,f780,f787,f791,f812,f816,f828,f833,f837,f854,f858,f890,f895,f899,f914,f921,f927,f955,f968,f976,f989,f994,f999,f1003,f1007,f1011,f1035,f1039,f1045,f1061,f1068,f1080,f1084,f1091,f1141,f1145,f1183,f1197,f1201,f1231,f1240,f1249,f1258,f1262,f1266,f1289,f1293,f1297,f1302,f1306,f1339,f1349,f1353,f1357,f1361,f1365,f1418,f1422,f1426,f1435,f1493,f1499,f1506,f1513,f1522,f1531,f1535,f1539,f1568,f1577,f1587,f1591,f1595,f1599,f1608,f1620,f1627,f1640,f1644,f1648,f1652,f1740,f1744,f1748,f1752,f1756,f1761,f1800,f1807,f1811,f1818,f1843,f1858,f1862,f1868,f1881,f1885,f1891,f1920,f1941,f1945,f2001,f2040,f2092,f2106,f2110,f2120,f2124,f2177,f2188,f2201,f2205,f2222,f2226,f2233,f2237,f2246,f2250,f2266,f2272,f2277,f2286,f2309,f2315,f2319,f2325,f2335,f2336,f2424,f2428,f2448,f2452,f2457,f2485,f2493,f2510,f2524,f2529,f2534,f2539,f2548,f2554,f2558,f2564,f2708,f2745,f2749,f2757,f2766,f2808,f2813,f2820,f2824,f2828,f2832,f2836,f2840,f2849,f2945,f2974,f2978,f2982,f2986,f2990,f2994,f2998,f3017,f3021,f3025,f3144,f3199,f3203,f3207,f3211,f3220,f3225,f3229,f3233,f3237,f3424,f3428,f3432,f3436,f3440,f3441,f3487,f3492,f3567,f3576,f3581,f3590,f3594,f3598,f3602,f3606,f3610,f3619,f3630,f3636,f3697,f3701,f3709,f3807,f3812,f3816,f3820,f3824,f3828,f3980,f4023,f4029,f4034,f4039,f4044,f4090,f4094,f4098,f4102,f4106,f4188,f4192,f4234,f4238,f4242,f4285,f4289,f4293,f4297,f4305,f4360,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4468,f4481,f4499,f4790,f4957,f4968,f4972,f4991,f5000,f5007,f5013,f5017,f5021,f5025,f5029,f5033,f5229,f5233,f5264,f5271,f5275,f5279,f5304,f5308,f5312,f5341,f5346,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5521,f5525,f5529,f5533,f5537,f5560,f5601,f5646,f5650,f5654,f5658,f5665,f5673,f5681,f5690,f5694,f5698,f5754,f5758,f5762,f5766,f5770,f5779,f5817,f5845,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5887,f6105,f6109,f6113,f6117,f6283,f6290,f6294,f6298,f6302,f6390,f6414,f6478,f6482,f6486,f6490,f6498,f6535,f6568,f6572,f6576,f6580,f6584,f6816,f6820,f6863,f6867,f6871,f6875,f6879,f6973,f6984,f7028,f7074,f7089,f7108,f7112,f7116,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7257,f7261,f7265,f7269,f7273,f7277,f7281,f7285,f7550,f7557,f7561,f7569,f7583,f7605,f7611,f7615,f7619,f7623,f7627,f7795,f7915,f7919,f7923,f7927,f7931,f7935,f7939,f8086,f8090,f8094,f8098,f8102,f8306,f8314,f8326,f8330,f8334,f8343,f8352,f8386,f8390,f8394,f8398,f8424,f8479,f8483,f8487,f8491,f8495,f8499,f8503,f8588,f8592,f8596,f8733,f8862,f8866,f8870,f8905,f8991,f9047,f9054,f9058,f9062,f9066,f9070,f9074,f9078,f9083,f9414,f9419,f9424,f9476,f9480,f9487,f9495,f9591,f9631,f9635,f9639,f9643,f9647,f9651,f9655,f9659,f9663,f9667,f9671,f9675,f10517,f10521,f10525,f10531,f10599,f10715,f10719,f10848,f10852,f10865,f10894,f10925,f10930,f10939,f10945,f10949,f10953,f10961,f11090,f11094,f11104,f11108,f11152,f11156,f11160,f11218,f11232,f11236,f11244,f11252,f11377,f11507,f11516,f11523,f11540,f11545,f11550,f11554,f11558,f11656,f11661,f11752,f11829,f12139,f12593,f12621,f12625,f12629,f12633,f12637,f12641,f12649,f12672,f12911,f12915,f13048,f13053,f13057,f13061,f13065,f13069,f13073,f13143,f13178,f13199,f13277,f13281,f13285,f13289,f13290,f13296,f13300,f13487,f13530,f13534,f13538,f13558,f13562,f13566,f13570,f13574,f13802,f13806,f13810,f13814,f13863,f13867,f13871,f13875,f13879,f13883,f13887,f13891,f13965,f14098,f14152,f14331,f14691,f14695,f14707,f14729,f14833,f14888,f14892,f14896,f14965,f14969,f15084,f15092,f15096,f15211,f15216,f15220,f15302,f15309,f15326,f15375,f15379,f15383,f15387,f15433,f15437,f15441,f15492,f15496,f15500,f15660,f15665,f15690,f15694,f15698,f15702,f15706,f15710,f15715,f15719,f15727,f15926,f15930,f15938,f16003,f16038,f16070,f16077,f16167,f16186,f16190,f16226,f16230,f16234,f16238,f16242,f16391,f16395,f16443,f16447,f16451,f16455,f16605,f16609,f16617,f16625,f16630,f16660,f16713,f16717,f16767,f16775,f16782,f16786,f17001,f17005,f17026,f17226,f17231,f17329,f17359,f17736,f17743,f18377,f18515,f18715,f18721,f18726,f18743,f18943,f18948,f18953,f19234,f19238,f19242,f19246,f19352,f19434,f19439,f19443,f19465,f19483,f19525,f19529,f19545,f19549,f19593,f19600,f19622,f19626,f19632,f19713,f19717,f19721,f19748,f19782,f19790,f19794,f19799,f19884,f19889,f19895,f19899,f19903,f19907,f20288,f20292,f20296,f20300,f20386,f20391,f20417,f20421,f20425,f20466,f20520,f20535,f20539,f20543,f20547,f20724,f20754,f20787,f20791,f20795,f20985,f20989,f20993,f20997,f21001,f21091,f21115,f21119,f21123,f21327,f21331,f21335,f21448,f21510,f21532,f21536,f21540,f21544,f21548,f21591,f21623,f21627,f21663,f21696,f21700,f21733,f21737,f21741,f21745,f21760,f21764,f21889,f21904,f21908,f21924,f21954,f21958,f22011,f22015,f22019,f22027,f22035,f22040,f22122,f22126,f22130,f22134,f22236,f22247,f22251,f22255,f22259,f22287,f22333,f22377,f22381,f22385,f22410,f22414,f22472,f22480,f22488,f22492,f22499,f22539,f22540,f22541,f24016,f24326,f25005,f25485,f25843,f26653,f27612,f27719,f27758,f27864,f27868,f27873,f27877,f27881,f27950,f27954,f28018,f28128,f28133,f28137,f28141,f28145,f28307,f28311,f28911,f29107,f29306,f29526,f29788,f29836,f29840,f29877,f29887,f29908,f29930,f29934,f29938,f29943,f29947,f30195,f30199,f30266,f30271,f30275,f30647,f30651,f30814,f30862,f30866,f30929,f30933,f30937,f30941,f30945,f30949,f31216,f31220,f31224,f31249,f31307,f31331,f31368,f31432,f31469,f31533,f31537,f31541,f31566,f31607,f31611,f31779,f31783,f31820,f31824,f31846,f31883,f31920,f31966,f31970,f32007,f32047,f32091,f32095,f32161,f32166,f32171,f32242,f32247,f32251,f32263,f32268,f32273,f32278,f32283,f32290,f32295,f32300,f32345,f32346,f32347,f32359,f32364,f32369,f32374,f32379,f32384,f32389,f32397,f32421,f32450,f32475,f32480,f32484,f32488,f32490,f32494,f32498,f33132,f33137,f33142,f33146,f33152,f33158,f33163,f33168,f33178,f33182,f33268,f33273,f33278,f33283,f33288,f33293,f33299,f33303,f33318,f33322,f33326,f33330,f33334,f33338,f33530,f33534,f33538,f33543,f33549,f33554,f33558,f33562,f33567,f33572,f33577,f33582,f33606,f33630,f33635,f33641,f33651,f33655,f33664,f33668,f33672,f33676,f33681,f33883,f33889,f33894,f33898,f33903,f33908,f33913,f33918,f33923,f33928,f33933,f33938,f33944,f33948,f33961,f33967,f33972,f33976,f33981,f33986,f33991,f33997,f34001,f34005,f34009,f34013,f34017,f34032,f34036,f34177,f34613,f34623,f34628,f34633,f34722,f34727,f34732,f34737,f34744,f34748,f34752,f34756,f34760,f34764,f35066,f35071,f35076,f35081,f35086,f35091,f35096,f35101,f35106,f35111,f35116,f35121,f35126,f35131,f35137,f35141,f35146,f35151,f35156,f35161,f35171,f35175,f35180,f35186,f35250,f35255,f35260,f35264,f35269,f35274,f35280,f35284,f35288,f35295,f35306,f35310,f35314,f35318,f35322,f35326,f35330,f35334,f35338,f35342,f35346,f35350,f35354,f35358,f35362,f35366,f35370,f36098,f36741,f36746,f36751,f37050,f37055,f37060,f37065,f37070,f37076,f37081,f37086,f37092,f37097,f37624,f37629,f37634,f37640,f37645,f37650,f37656,f37661,f37666,f37671,f37675,f37698,f37703,f37727,f37734,f37740,f37745,f37750,f37754,f37758,f37762,f37766,f37770,f37774,f37778,f37782,f37786,f37790,f37794,f37798,f37923,f37927,f37931,f37935,f37939,f37943,f38122,f41453,f41468,f41495,f41665,f41704,f41722,f41726,f41775,f41776,f41796,f41803,f41806,f42137,f42324,f42336,f42337,f42531,f42667,f44121,f44127,f44331,f44360,f44528,f44947,f44999,f45033,f45066,f45074,f45148,f45159,f45899,f46130,f46481,f46670,f46685,f46691,f46700,f46702,f47449,f49210,f49619,f49661,f49696,f49747,f49809,f51469,f52693,f52730,f52850,f52912,f52916,f52920,f52924,f52928,f52932,f52936,f52940,f52946,f52950,f52956,f52961,f52965,f52978,f52991,f52995,f53004,f53158,f53298,f53307,f53461,f53603,f53892,f54020,f54024,f54028,f54032,f54036,f54040,f54044,f54180,f54185,f54190,f54195,f54200,f54205,f54210,f54215,f54222,f54229,f54232,f54433,f54450,f54463,f54489,f54506,f54510,f54514,f54518,f54522,f54526,f54530,f54534,f54538,f54539]) ).
fof(f54539,plain,
( ~ spl0_567
| spl0_4
| ~ spl0_539
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f54175,f53890,f8422,f223,f9421]) ).
fof(f9421,plain,
( spl0_567
<=> y = domain_of(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f223,plain,
( spl0_4
<=> y = domain_of(intersection(x,cross_product(y,y))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f8422,plain,
( spl0_539
<=> ! [X0] : y = intersection(X0,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f53890,plain,
( spl0_1291
<=> ! [X0] : y = cross_product(X0,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f54175,plain,
( y != domain_of(y)
| spl0_4
| ~ spl0_539
| ~ spl0_1291 ),
inference(forward_demodulation,[],[f54129,f8423]) ).
fof(f8423,plain,
( ! [X0] : y = intersection(X0,y)
| ~ spl0_539 ),
inference(avatar_component_clause,[],[f8422]) ).
fof(f54129,plain,
( y != domain_of(intersection(x,y))
| spl0_4
| ~ spl0_1291 ),
inference(superposition,[],[f225,f53891]) ).
fof(f53891,plain,
( ! [X0] : y = cross_product(X0,y)
| ~ spl0_1291 ),
inference(avatar_component_clause,[],[f53890]) ).
fof(f225,plain,
( y != domain_of(intersection(x,cross_product(y,y)))
| spl0_4 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f54538,plain,
( spl0_1325
| ~ spl0_280
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6181,f6111,f2980,f54536]) ).
fof(f54536,plain,
( spl0_1325
<=> ! [X0,X1] :
( ~ member(regular(intersection(X0,X1)),singleton_relation)
| ~ subclass(X0,compose(element_relation,complement(identity_relation)))
| intersection(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f2980,plain,
( spl0_280
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f6111,plain,
( spl0_445
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f6181,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X0,X1)),singleton_relation)
| ~ subclass(X0,compose(element_relation,complement(identity_relation)))
| intersection(X0,X1) = y )
| ~ spl0_280
| ~ spl0_445 ),
inference(resolution,[],[f6112,f2981]) ).
fof(f2981,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,X1)),X2)
| ~ subclass(X0,X2)
| intersection(X0,X1) = y )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2980]) ).
fof(f6112,plain,
( ! [X0] :
( ~ member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,singleton_relation) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f6111]) ).
fof(f54534,plain,
( spl0_1324
| ~ spl0_282
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6180,f6111,f2988,f54532]) ).
fof(f54532,plain,
( spl0_1324
<=> ! [X0,X1] :
( ~ member(regular(intersection(X0,X1)),singleton_relation)
| ~ subclass(X1,compose(element_relation,complement(identity_relation)))
| intersection(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f2988,plain,
( spl0_282
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f6180,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X0,X1)),singleton_relation)
| ~ subclass(X1,compose(element_relation,complement(identity_relation)))
| intersection(X0,X1) = y )
| ~ spl0_282
| ~ spl0_445 ),
inference(resolution,[],[f6112,f2989]) ).
fof(f2989,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,X1)),X2)
| ~ subclass(X1,X2)
| intersection(X0,X1) = y )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f2988]) ).
fof(f54530,plain,
( spl0_1323
| ~ spl0_112
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6166,f6111,f856,f54528]) ).
fof(f54528,plain,
( spl0_1323
<=> ! [X0] :
( ~ member(regular(intersection(X0,compose(element_relation,complement(identity_relation)))),singleton_relation)
| y = intersection(X0,compose(element_relation,complement(identity_relation))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f856,plain,
( spl0_112
<=> ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f6166,plain,
( ! [X0] :
( ~ member(regular(intersection(X0,compose(element_relation,complement(identity_relation)))),singleton_relation)
| y = intersection(X0,compose(element_relation,complement(identity_relation))) )
| ~ spl0_112
| ~ spl0_445 ),
inference(resolution,[],[f6112,f857]) ).
fof(f857,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = y )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f54526,plain,
( spl0_1322
| ~ spl0_111
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6154,f6111,f852,f54524]) ).
fof(f54524,plain,
( spl0_1322
<=> ! [X0] :
( ~ member(regular(intersection(compose(element_relation,complement(identity_relation)),X0)),singleton_relation)
| y = intersection(compose(element_relation,complement(identity_relation)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f852,plain,
( spl0_111
<=> ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f6154,plain,
( ! [X0] :
( ~ member(regular(intersection(compose(element_relation,complement(identity_relation)),X0)),singleton_relation)
| y = intersection(compose(element_relation,complement(identity_relation)),X0) )
| ~ spl0_111
| ~ spl0_445 ),
inference(resolution,[],[f6112,f853]) ).
fof(f853,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = y )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f54522,plain,
( spl0_1321
| ~ spl0_160
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f5154,f5023,f1347,f54520]) ).
fof(f54520,plain,
( spl0_1321
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(X0,regular(X0)),X1),y)
| subclass(intersection(X0,regular(X0)),X1)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f1347,plain,
( spl0_160
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f5023,plain,
( spl0_381
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,regular(X1)),X2)
| member(not_subclass_element(intersection(X0,regular(X1)),X2),y)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f5154,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,regular(X0)),X1),y)
| subclass(intersection(X0,regular(X0)),X1)
| y = X0 )
| ~ spl0_160
| ~ spl0_381 ),
inference(duplicate_literal_removal,[],[f5121]) ).
fof(f5121,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,regular(X0)),X1),y)
| subclass(intersection(X0,regular(X0)),X1)
| y = X0
| subclass(intersection(X0,regular(X0)),X1) )
| ~ spl0_160
| ~ spl0_381 ),
inference(resolution,[],[f5024,f1348]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f5024,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| member(not_subclass_element(intersection(X0,regular(X1)),X2),y)
| subclass(intersection(X0,regular(X1)),X2)
| y = X1 )
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f5023]) ).
fof(f54518,plain,
( spl0_1320
| ~ spl0_161
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f5110,f5015,f1351,f54516]) ).
fof(f54516,plain,
( spl0_1320
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(regular(X0),X0),X1),y)
| subclass(intersection(regular(X0),X0),X1)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f1351,plain,
( spl0_161
<=> ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f5015,plain,
( spl0_379
<=> ! [X2,X0,X1] :
( subclass(intersection(regular(X0),X1),X2)
| member(not_subclass_element(intersection(regular(X0),X1),X2),y)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f5110,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(regular(X0),X0),X1),y)
| subclass(intersection(regular(X0),X0),X1)
| y = X0 )
| ~ spl0_161
| ~ spl0_379 ),
inference(duplicate_literal_removal,[],[f5080]) ).
fof(f5080,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(regular(X0),X0),X1),y)
| subclass(intersection(regular(X0),X0),X1)
| y = X0
| subclass(intersection(regular(X0),X0),X1) )
| ~ spl0_161
| ~ spl0_379 ),
inference(resolution,[],[f5016,f1352]) ).
fof(f1352,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f5016,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| member(not_subclass_element(intersection(regular(X0),X1),X2),y)
| subclass(intersection(regular(X0),X1),X2)
| y = X0 )
| ~ spl0_379 ),
inference(avatar_component_clause,[],[f5015]) ).
fof(f54514,plain,
( spl0_1319
| ~ spl0_302
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4409,f4287,f3434,f54512]) ).
fof(f54512,plain,
( spl0_1319
<=> ! [X0,X1] :
( member(X0,y)
| ~ member(X0,X0)
| y = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f3434,plain,
( spl0_302
<=> ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f4287,plain,
( spl0_349
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,y)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f4409,plain,
( ! [X0,X1] :
( member(X0,y)
| ~ member(X0,X0)
| y = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_302
| ~ spl0_349 ),
inference(duplicate_literal_removal,[],[f4363]) ).
fof(f4363,plain,
( ! [X0,X1] :
( member(X0,y)
| ~ member(X0,X0)
| y = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1
| y = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_302
| ~ spl0_349 ),
inference(resolution,[],[f4288,f3435]) ).
fof(f3435,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_302 ),
inference(avatar_component_clause,[],[f3434]) ).
fof(f4288,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| member(X2,y)
| ~ member(X2,X1)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f4287]) ).
fof(f54510,plain,
( spl0_1318
| ~ spl0_301
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4355,f4283,f3430,f54508]) ).
fof(f54508,plain,
( spl0_1318
<=> ! [X0,X1] :
( member(X0,y)
| ~ member(X0,X0)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f3430,plain,
( spl0_301
<=> ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f4283,plain,
( spl0_348
<=> ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,y)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f4355,plain,
( ! [X0,X1] :
( member(X0,y)
| ~ member(X0,X0)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_301
| ~ spl0_348 ),
inference(duplicate_literal_removal,[],[f4306]) ).
fof(f4306,plain,
( ! [X0,X1] :
( member(X0,y)
| ~ member(X0,X0)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_301
| ~ spl0_348 ),
inference(resolution,[],[f4284,f3431]) ).
fof(f3431,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f3430]) ).
fof(f4284,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| member(X2,y)
| ~ member(X2,X0)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f4283]) ).
fof(f54506,plain,
( spl0_1317
| ~ spl0_154
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4066,f4021,f1287,f54504]) ).
fof(f54504,plain,
( spl0_1317
<=> ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),y)
| y = X0
| subclass(regular(X0),X1)
| ~ subclass(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f1287,plain,
( spl0_154
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f4021,plain,
( spl0_333
<=> ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),y)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| y = X0
| subclass(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4066,plain,
( ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),y)
| y = X0
| subclass(regular(X0),X1)
| ~ subclass(regular(X0),X0) )
| ~ spl0_154
| ~ spl0_333 ),
inference(duplicate_literal_removal,[],[f4053]) ).
fof(f4053,plain,
( ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),y)
| y = X0
| subclass(regular(X0),X1)
| ~ subclass(regular(X0),X0)
| subclass(regular(X0),X1) )
| ~ spl0_154
| ~ spl0_333 ),
inference(resolution,[],[f4022,f1288]) ).
fof(f1288,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(X0,X2),X1)
| ~ subclass(X0,X1)
| subclass(X0,X2) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f4022,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(regular(X0),X1),X0)
| member(not_subclass_element(regular(X0),X1),y)
| y = X0
| subclass(regular(X0),X1) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f4021]) ).
fof(f54489,plain,
( ~ spl0_1314
| spl0_882
| ~ spl0_1315
| spl0_1316
| ~ spl0_19
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f3975,f3826,f292,f54486,f54482,f21901,f54478]) ).
fof(f54478,plain,
( spl0_1314
<=> inductive(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f21901,plain,
( spl0_882
<=> omega = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f54482,plain,
( spl0_1315
<=> member(regular(omega),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f54486,plain,
( spl0_1316
<=> member(regular(omega),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f292,plain,
( spl0_19
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f3826,plain,
( spl0_331
<=> ! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f3975,plain,
( member(regular(omega),identity_relation)
| ~ member(regular(omega),subset_relation)
| omega = y
| ~ inductive(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_19
| ~ spl0_331 ),
inference(resolution,[],[f3827,f293]) ).
fof(f293,plain,
( ! [X1] :
( subclass(omega,X1)
| ~ inductive(X1) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f3827,plain,
( ! [X0] :
( ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| member(regular(X0),identity_relation)
| ~ member(regular(X0),subset_relation)
| y = X0 )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f3826]) ).
fof(f54463,plain,
( ~ spl0_1311
| spl0_882
| ~ spl0_1312
| spl0_1313
| ~ spl0_19
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f3970,f3822,f292,f54460,f54456,f21901,f54452]) ).
fof(f54452,plain,
( spl0_1311
<=> inductive(complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f54456,plain,
( spl0_1312
<=> member(regular(omega),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f54460,plain,
( spl0_1313
<=> member(regular(omega),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f3822,plain,
( spl0_330
<=> ! [X0] :
( ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f3970,plain,
( member(regular(omega),singleton_relation)
| ~ member(regular(omega),element_relation)
| omega = y
| ~ inductive(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_19
| ~ spl0_330 ),
inference(resolution,[],[f3823,f293]) ).
fof(f3823,plain,
( ! [X0] :
( ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| member(regular(X0),singleton_relation)
| ~ member(regular(X0),element_relation)
| y = X0 )
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f3822]) ).
fof(f54450,plain,
( spl0_1310
| ~ spl0_109
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3889,f3810,f831,f54448]) ).
fof(f54448,plain,
( spl0_1310
<=> ! [X0,X1] :
( member(regular(X0),y)
| y = X1
| ~ subclass(X0,regular(X1))
| y = X0
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f831,plain,
( spl0_109
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f3810,plain,
( spl0_327
<=> ! [X0,X1] :
( member(regular(X0),y)
| ~ member(regular(X0),X1)
| y = X1
| ~ subclass(X0,regular(X1))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f3889,plain,
( ! [X0,X1] :
( member(regular(X0),y)
| y = X1
| ~ subclass(X0,regular(X1))
| y = X0
| ~ subclass(X0,X1) )
| ~ spl0_109
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3833]) ).
fof(f3833,plain,
( ! [X0,X1] :
( member(regular(X0),y)
| y = X1
| ~ subclass(X0,regular(X1))
| y = X0
| ~ subclass(X0,X1)
| y = X0 )
| ~ spl0_109
| ~ spl0_327 ),
inference(resolution,[],[f3811,f832]) ).
fof(f832,plain,
( ! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| y = X0 )
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f3811,plain,
( ! [X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),y)
| y = X1
| ~ subclass(X0,regular(X1))
| y = X0 )
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f3810]) ).
fof(f54433,plain,
( spl0_1258
| spl0_1309
| ~ spl0_245
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3876,f3810,f2422,f54431,f49612]) ).
fof(f49612,plain,
( spl0_1258
<=> element_relation = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f54431,plain,
( spl0_1309
<=> ! [X0] :
( member(regular(X0),y)
| ~ subclass(X0,singleton_relation)
| y = X0
| ~ subclass(X0,regular(element_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f2422,plain,
( spl0_245
<=> ! [X0] :
( member(regular(X0),element_relation)
| ~ subclass(X0,singleton_relation)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3876,plain,
( ! [X0] :
( member(regular(X0),y)
| element_relation = y
| ~ subclass(X0,regular(element_relation))
| y = X0
| ~ subclass(X0,singleton_relation) )
| ~ spl0_245
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3851]) ).
fof(f3851,plain,
( ! [X0] :
( member(regular(X0),y)
| element_relation = y
| ~ subclass(X0,regular(element_relation))
| y = X0
| ~ subclass(X0,singleton_relation)
| y = X0 )
| ~ spl0_245
| ~ spl0_327 ),
inference(resolution,[],[f3811,f2423]) ).
fof(f2423,plain,
( ! [X0] :
( member(regular(X0),element_relation)
| ~ subclass(X0,singleton_relation)
| y = X0 )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2422]) ).
fof(f54232,plain,
( spl0_168
| ~ spl0_1217
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f54045,f53890,f37756,f1428]) ).
fof(f1428,plain,
( spl0_168
<=> singleton_relation = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f37756,plain,
( spl0_1217
<=> ! [X0] : singleton_relation = cross_product(singleton_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f54045,plain,
( singleton_relation = y
| ~ spl0_1217
| ~ spl0_1291 ),
inference(superposition,[],[f53891,f37757]) ).
fof(f37757,plain,
( ! [X0] : singleton_relation = cross_product(singleton_relation,X0)
| ~ spl0_1217 ),
inference(avatar_component_clause,[],[f37756]) ).
fof(f54229,plain,
( spl0_238
| spl0_1308
| ~ spl0_246
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3873,f3810,f2426,f54227,f2279]) ).
fof(f2279,plain,
( spl0_238
<=> subset_relation = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f54227,plain,
( spl0_1308
<=> ! [X0] :
( member(regular(X0),y)
| ~ subclass(X0,identity_relation)
| y = X0
| ~ subclass(X0,regular(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f2426,plain,
( spl0_246
<=> ! [X0] :
( member(regular(X0),subset_relation)
| ~ subclass(X0,identity_relation)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f3873,plain,
( ! [X0] :
( member(regular(X0),y)
| subset_relation = y
| ~ subclass(X0,regular(subset_relation))
| y = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_246
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3864]) ).
fof(f3864,plain,
( ! [X0] :
( member(regular(X0),y)
| subset_relation = y
| ~ subclass(X0,regular(subset_relation))
| y = X0
| ~ subclass(X0,identity_relation)
| y = X0 )
| ~ spl0_246
| ~ spl0_327 ),
inference(resolution,[],[f3811,f2427]) ).
fof(f2427,plain,
( ! [X0] :
( member(regular(X0),subset_relation)
| ~ subclass(X0,identity_relation)
| y = X0 )
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f2426]) ).
fof(f54222,plain,
( spl0_1307
| ~ spl0_160
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3799,f3634,f1347,f54220]) ).
fof(f54220,plain,
( spl0_1307
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),y),X0)
| subclass(intersection(regular(X0),X1),y)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f3634,plain,
( spl0_323
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X1,y),regular(X0))
| ~ member(not_subclass_element(X1,y),X0)
| subclass(X1,y)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f3799,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),y),X0)
| subclass(intersection(regular(X0),X1),y)
| y = X0 )
| ~ spl0_160
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3782]) ).
fof(f3782,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(regular(X0),X1),y),X0)
| subclass(intersection(regular(X0),X1),y)
| y = X0
| subclass(intersection(regular(X0),X1),y) )
| ~ spl0_160
| ~ spl0_323 ),
inference(resolution,[],[f3635,f1348]) ).
fof(f3635,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X1,y),regular(X0))
| ~ member(not_subclass_element(X1,y),X0)
| subclass(X1,y)
| y = X0 )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f3634]) ).
fof(f54215,plain,
( spl0_1306
| ~ spl0_161
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3798,f3634,f1351,f54213]) ).
fof(f54213,plain,
( spl0_1306
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),y),X1)
| subclass(intersection(X0,regular(X1)),y)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f3798,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),y),X1)
| subclass(intersection(X0,regular(X1)),y)
| y = X1 )
| ~ spl0_161
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3783]) ).
fof(f3783,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,regular(X1)),y),X1)
| subclass(intersection(X0,regular(X1)),y)
| y = X1
| subclass(intersection(X0,regular(X1)),y) )
| ~ spl0_161
| ~ spl0_323 ),
inference(resolution,[],[f3635,f1352]) ).
fof(f54210,plain,
( spl0_1305
| ~ spl0_39
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3401,f3235,f381,f54208]) ).
fof(f54208,plain,
( spl0_1305
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,y),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,y),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f381,plain,
( spl0_39
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f3235,plain,
( spl0_298
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,y),X1)
| member(not_subclass_element(intersection(X0,y),X1),X2)
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f3401,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,y),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,y),X1),X2) )
| ~ spl0_39
| ~ spl0_298 ),
inference(resolution,[],[f3236,f382]) ).
fof(f382,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f3236,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,y),X1),X2)
| subclass(intersection(X0,y),X1)
| y = X2 )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f3235]) ).
fof(f54205,plain,
( spl0_1304
| ~ spl0_40
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3400,f3235,f385,f54203]) ).
fof(f54203,plain,
( spl0_1304
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,y),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,y),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f385,plain,
( spl0_40
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f3400,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,y),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(X0,y),X1),X3) )
| ~ spl0_40
| ~ spl0_298 ),
inference(resolution,[],[f3236,f386]) ).
fof(f386,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f54200,plain,
( spl0_1303
| ~ spl0_39
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3372,f3231,f381,f54198]) ).
fof(f54198,plain,
( spl0_1303
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(y,X0),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(y,X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f3231,plain,
( spl0_297
<=> ! [X2,X0,X1] :
( subclass(intersection(y,X0),X1)
| member(not_subclass_element(intersection(y,X0),X1),X2)
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f3372,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(y,X0),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(y,X0),X1),X2) )
| ~ spl0_39
| ~ spl0_297 ),
inference(resolution,[],[f3232,f382]) ).
fof(f3232,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(y,X0),X1),X2)
| subclass(intersection(y,X0),X1)
| y = X2 )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f3231]) ).
fof(f54195,plain,
( spl0_1302
| ~ spl0_40
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3371,f3231,f385,f54193]) ).
fof(f54193,plain,
( spl0_1302
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(y,X0),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(y,X0),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f3371,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(y,X0),X1)
| y = intersection(X2,X3)
| member(not_subclass_element(intersection(y,X0),X1),X3) )
| ~ spl0_40
| ~ spl0_297 ),
inference(resolution,[],[f3232,f386]) ).
fof(f54190,plain,
( spl0_1301
| ~ spl0_29
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3334,f3209,f334,f54188]) ).
fof(f54188,plain,
( spl0_1301
<=> ! [X2,X0,X1] :
( y = intersection(X0,intersection(complement(X1),X2))
| ~ member(regular(intersection(X0,intersection(complement(X1),X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f334,plain,
( spl0_29
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f3209,plain,
( spl0_292
<=> ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f3334,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(complement(X1),X2))
| ~ member(regular(intersection(X0,intersection(complement(X1),X2))),X1) )
| ~ spl0_29
| ~ spl0_292 ),
inference(resolution,[],[f3210,f335]) ).
fof(f335,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f3210,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,intersection(X1,X2))),X1)
| y = intersection(X0,intersection(X1,X2)) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f3209]) ).
fof(f54185,plain,
( spl0_1300
| ~ spl0_29
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3305,f3205,f334,f54183]) ).
fof(f54183,plain,
( spl0_1300
<=> ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,complement(X2)))
| ~ member(regular(intersection(X0,intersection(X1,complement(X2)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f3205,plain,
( spl0_291
<=> ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f3305,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,complement(X2)))
| ~ member(regular(intersection(X0,intersection(X1,complement(X2)))),X2) )
| ~ spl0_29
| ~ spl0_291 ),
inference(resolution,[],[f3206,f335]) ).
fof(f3206,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,intersection(X1,X2))),X2)
| y = intersection(X0,intersection(X1,X2)) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f3205]) ).
fof(f54180,plain,
( spl0_1299
| ~ spl0_29
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3276,f3201,f334,f54178]) ).
fof(f54178,plain,
( spl0_1299
<=> ! [X2,X0,X1] :
( y = intersection(intersection(complement(X0),X1),X2)
| ~ member(regular(intersection(intersection(complement(X0),X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f3201,plain,
( spl0_290
<=> ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f3276,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(complement(X0),X1),X2)
| ~ member(regular(intersection(intersection(complement(X0),X1),X2)),X0) )
| ~ spl0_29
| ~ spl0_290 ),
inference(resolution,[],[f3202,f335]) ).
fof(f3202,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(intersection(X0,X1),X2)),X0)
| y = intersection(intersection(X0,X1),X2) )
| ~ spl0_290 ),
inference(avatar_component_clause,[],[f3201]) ).
fof(f54044,plain,
( spl0_1298
| ~ spl0_29
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3247,f3197,f334,f54042]) ).
fof(f54042,plain,
( spl0_1298
<=> ! [X2,X0,X1] :
( y = intersection(intersection(X0,complement(X1)),X2)
| ~ member(regular(intersection(intersection(X0,complement(X1)),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f3197,plain,
( spl0_289
<=> ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3247,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(X0,complement(X1)),X2)
| ~ member(regular(intersection(intersection(X0,complement(X1)),X2)),X1) )
| ~ spl0_29
| ~ spl0_289 ),
inference(resolution,[],[f3198,f335]) ).
fof(f3198,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(intersection(X0,X1),X2)),X1)
| y = intersection(intersection(X0,X1),X2) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3197]) ).
fof(f54040,plain,
( spl0_1297
| ~ spl0_46
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3148,f3019,f424,f54038]) ).
fof(f54038,plain,
( spl0_1297
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,X0)
| y = cross_product(X1,X2)
| ~ subclass(X0,X3)
| member(regular(cross_product(X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f424,plain,
( spl0_46
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f3019,plain,
( spl0_286
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f3148,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| y = cross_product(X1,X2)
| ~ subclass(X0,X3)
| member(regular(cross_product(X1,X2)),X3) )
| ~ spl0_46
| ~ spl0_286 ),
inference(resolution,[],[f3020,f425]) ).
fof(f425,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f3020,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = y )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f3019]) ).
fof(f54036,plain,
( spl0_1296
| ~ spl0_46
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3091,f2988,f424,f54034]) ).
fof(f54034,plain,
( spl0_1296
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| y = intersection(X2,X0)
| ~ subclass(X1,X3)
| member(regular(intersection(X2,X0)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f3091,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X2,X0)
| ~ subclass(X1,X3)
| member(regular(intersection(X2,X0)),X3) )
| ~ spl0_46
| ~ spl0_282 ),
inference(resolution,[],[f2989,f425]) ).
fof(f54032,plain,
( spl0_1295
| ~ spl0_46
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3038,f2980,f424,f54030]) ).
fof(f54030,plain,
( spl0_1295
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,X2)
| ~ subclass(X1,X3)
| member(regular(intersection(X0,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f3038,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,X2)
| ~ subclass(X1,X3)
| member(regular(intersection(X0,X2)),X3) )
| ~ spl0_46
| ~ spl0_280 ),
inference(resolution,[],[f2981,f425]) ).
fof(f54028,plain,
( spl0_1294
| ~ spl0_139
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2950,f2838,f1089,f54026]) ).
fof(f54026,plain,
( spl0_1294
<=> ! [X0] :
( y = intersection(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1089,plain,
( spl0_139
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f2838,plain,
( spl0_275
<=> ! [X0,X1] :
( y = intersection(X0,complement(X1))
| ~ member(regular(intersection(X0,complement(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2950,plain,
( ! [X0] :
( y = intersection(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(intersection(X0,complement(cross_product(universal_class,universal_class)))),subset_relation) )
| ~ spl0_139
| ~ spl0_275 ),
inference(resolution,[],[f2839,f1090]) ).
fof(f1090,plain,
( ! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,subset_relation) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1089]) ).
fof(f2839,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X0,complement(X1))),X1)
| y = intersection(X0,complement(X1)) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2838]) ).
fof(f54024,plain,
( spl0_1293
| ~ spl0_139
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2922,f2834,f1089,f54022]) ).
fof(f54022,plain,
( spl0_1293
<=> ! [X0] :
( y = intersection(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f2834,plain,
( spl0_274
<=> ! [X0,X1] :
( y = intersection(complement(X0),X1)
| ~ member(regular(intersection(complement(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2922,plain,
( ! [X0] :
( y = intersection(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(regular(intersection(complement(cross_product(universal_class,universal_class)),X0)),subset_relation) )
| ~ spl0_139
| ~ spl0_274 ),
inference(resolution,[],[f2835,f1090]) ).
fof(f2835,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(complement(X0),X1)),X0)
| y = intersection(complement(X0),X1) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2834]) ).
fof(f54020,plain,
( spl0_1292
| ~ spl0_56
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2661,f2450,f496,f54018]) ).
fof(f54018,plain,
( spl0_1292
<=> ! [X2,X0,X1] :
( y = X0
| ~ subclass(X0,complement(intersection(X1,X2)))
| ~ member(regular(X0),X2)
| ~ member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f496,plain,
( spl0_56
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f2450,plain,
( spl0_248
<=> ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| y = X0
| ~ member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2661,plain,
( ! [X2,X0,X1] :
( y = X0
| ~ subclass(X0,complement(intersection(X1,X2)))
| ~ member(regular(X0),X2)
| ~ member(regular(X0),X1) )
| ~ spl0_56
| ~ spl0_248 ),
inference(resolution,[],[f2451,f497]) ).
fof(f497,plain,
( ! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f2451,plain,
( ! [X0,X1] :
( ~ member(regular(X0),X1)
| y = X0
| ~ subclass(X0,complement(X1)) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2450]) ).
fof(f53892,plain,
( spl0_1291
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f46544,f33974,f9421,f8731,f53890]) ).
fof(f8731,plain,
( spl0_550
<=> ! [X0] : ~ member(X0,domain_of(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f33974,plain,
( spl0_1105
<=> ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f46544,plain,
( ! [X0] : y = cross_product(X0,y)
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1105 ),
inference(forward_demodulation,[],[f46516,f9423]) ).
fof(f9423,plain,
( y = domain_of(y)
| ~ spl0_567 ),
inference(avatar_component_clause,[],[f9421]) ).
fof(f46516,plain,
( ! [X0] : y = cross_product(X0,domain_of(y))
| ~ spl0_550
| ~ spl0_1105 ),
inference(resolution,[],[f33975,f8732]) ).
fof(f8732,plain,
( ! [X0] : ~ member(X0,domain_of(y))
| ~ spl0_550 ),
inference(avatar_component_clause,[],[f8731]) ).
fof(f33975,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = y )
| ~ spl0_1105 ),
inference(avatar_component_clause,[],[f33974]) ).
fof(f53603,plain,
( spl0_1290
| ~ spl0_10
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f17595,f11827,f251,f53601]) ).
fof(f53601,plain,
( spl0_1290
<=> ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f251,plain,
( spl0_10
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f11827,plain,
( spl0_639
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f17595,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_10
| ~ spl0_639 ),
inference(resolution,[],[f11828,f252]) ).
fof(f252,plain,
( ! [X1] : subclass(X1,X1)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f11828,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_639 ),
inference(avatar_component_clause,[],[f11827]) ).
fof(f53461,plain,
( spl0_1288
| spl0_1258
| spl0_1289
| ~ spl0_252
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4885,f4449,f2522,f53458,f49612,f53454]) ).
fof(f53454,plain,
( spl0_1288
<=> y = intersection(singleton_relation,regular(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f53458,plain,
( spl0_1289
<=> member(regular(intersection(singleton_relation,regular(element_relation))),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f2522,plain,
( spl0_252
<=> ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| y = intersection(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f4449,plain,
( spl0_358
<=> ! [X0,X1] :
( member(regular(intersection(X0,regular(X1))),y)
| ~ member(regular(intersection(X0,regular(X1))),X1)
| y = X1
| y = intersection(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f4885,plain,
( member(regular(intersection(singleton_relation,regular(element_relation))),y)
| element_relation = y
| y = intersection(singleton_relation,regular(element_relation))
| ~ spl0_252
| ~ spl0_358 ),
inference(duplicate_literal_removal,[],[f4851]) ).
fof(f4851,plain,
( member(regular(intersection(singleton_relation,regular(element_relation))),y)
| element_relation = y
| y = intersection(singleton_relation,regular(element_relation))
| y = intersection(singleton_relation,regular(element_relation))
| ~ spl0_252
| ~ spl0_358 ),
inference(resolution,[],[f4450,f2523]) ).
fof(f2523,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| y = intersection(singleton_relation,X0) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2522]) ).
fof(f4450,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(X0,regular(X1))),X1)
| member(regular(intersection(X0,regular(X1))),y)
| y = X1
| y = intersection(X0,regular(X1)) )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f4449]) ).
fof(f53307,plain,
( spl0_1286
| spl0_238
| spl0_1287
| ~ spl0_254
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4883,f4449,f2532,f53304,f2279,f53300]) ).
fof(f53300,plain,
( spl0_1286
<=> y = intersection(identity_relation,regular(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f53304,plain,
( spl0_1287
<=> member(regular(intersection(identity_relation,regular(subset_relation))),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f2532,plain,
( spl0_254
<=> ! [X0] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| y = intersection(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f4883,plain,
( member(regular(intersection(identity_relation,regular(subset_relation))),y)
| subset_relation = y
| y = intersection(identity_relation,regular(subset_relation))
| ~ spl0_254
| ~ spl0_358 ),
inference(duplicate_literal_removal,[],[f4860]) ).
fof(f4860,plain,
( member(regular(intersection(identity_relation,regular(subset_relation))),y)
| subset_relation = y
| y = intersection(identity_relation,regular(subset_relation))
| y = intersection(identity_relation,regular(subset_relation))
| ~ spl0_254
| ~ spl0_358 ),
inference(resolution,[],[f4450,f2533]) ).
fof(f2533,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| y = intersection(identity_relation,X0) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2532]) ).
fof(f53298,plain,
( spl0_1285
| ~ spl0_112
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f4840,f4445,f856,f53296]) ).
fof(f53296,plain,
( spl0_1285
<=> ! [X0] :
( member(regular(intersection(regular(X0),X0)),y)
| y = X0
| y = intersection(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f4445,plain,
( spl0_357
<=> ! [X0,X1] :
( member(regular(intersection(regular(X0),X1)),y)
| ~ member(regular(intersection(regular(X0),X1)),X0)
| y = X0
| y = intersection(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f4840,plain,
( ! [X0] :
( member(regular(intersection(regular(X0),X0)),y)
| y = X0
| y = intersection(regular(X0),X0) )
| ~ spl0_112
| ~ spl0_357 ),
inference(duplicate_literal_removal,[],[f4791]) ).
fof(f4791,plain,
( ! [X0] :
( member(regular(intersection(regular(X0),X0)),y)
| y = X0
| y = intersection(regular(X0),X0)
| y = intersection(regular(X0),X0) )
| ~ spl0_112
| ~ spl0_357 ),
inference(resolution,[],[f4446,f857]) ).
fof(f4446,plain,
( ! [X0,X1] :
( ~ member(regular(intersection(regular(X0),X1)),X0)
| member(regular(intersection(regular(X0),X1)),y)
| y = X0
| y = intersection(regular(X0),X1) )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f4445]) ).
fof(f53158,plain,
( spl0_1283
| spl0_1258
| spl0_1284
| ~ spl0_253
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f4832,f4445,f2527,f53155,f49612,f53151]) ).
fof(f53151,plain,
( spl0_1283
<=> y = intersection(regular(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f53155,plain,
( spl0_1284
<=> member(regular(intersection(regular(element_relation),singleton_relation)),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f2527,plain,
( spl0_253
<=> ! [X0] :
( member(regular(intersection(X0,singleton_relation)),element_relation)
| y = intersection(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f4832,plain,
( member(regular(intersection(regular(element_relation),singleton_relation)),y)
| element_relation = y
| y = intersection(regular(element_relation),singleton_relation)
| ~ spl0_253
| ~ spl0_357 ),
inference(duplicate_literal_removal,[],[f4800]) ).
fof(f4800,plain,
( member(regular(intersection(regular(element_relation),singleton_relation)),y)
| element_relation = y
| y = intersection(regular(element_relation),singleton_relation)
| y = intersection(regular(element_relation),singleton_relation)
| ~ spl0_253
| ~ spl0_357 ),
inference(resolution,[],[f4446,f2528]) ).
fof(f2528,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),element_relation)
| y = intersection(X0,singleton_relation) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2527]) ).
fof(f53004,plain,
( spl0_1281
| spl0_238
| spl0_1282
| ~ spl0_255
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f4830,f4445,f2537,f53001,f2279,f52997]) ).
fof(f52997,plain,
( spl0_1281
<=> y = intersection(regular(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f53001,plain,
( spl0_1282
<=> member(regular(intersection(regular(subset_relation),identity_relation)),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f2537,plain,
( spl0_255
<=> ! [X0] :
( member(regular(intersection(X0,identity_relation)),subset_relation)
| y = intersection(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f4830,plain,
( member(regular(intersection(regular(subset_relation),identity_relation)),y)
| subset_relation = y
| y = intersection(regular(subset_relation),identity_relation)
| ~ spl0_255
| ~ spl0_357 ),
inference(duplicate_literal_removal,[],[f4809]) ).
fof(f4809,plain,
( member(regular(intersection(regular(subset_relation),identity_relation)),y)
| subset_relation = y
| y = intersection(regular(subset_relation),identity_relation)
| y = intersection(regular(subset_relation),identity_relation)
| ~ spl0_255
| ~ spl0_357 ),
inference(resolution,[],[f4446,f2538]) ).
fof(f2538,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),subset_relation)
| y = intersection(X0,identity_relation) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2537]) ).
fof(f52995,plain,
( spl0_1280
| ~ spl0_109
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3660,f3596,f831,f52993]) ).
fof(f52993,plain,
( spl0_1280
<=> ! [X0] :
( member(regular(regular(X0)),y)
| y = X0
| regular(X0) = y
| ~ subclass(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f3596,plain,
( spl0_315
<=> ! [X0] :
( member(regular(regular(X0)),y)
| ~ member(regular(regular(X0)),X0)
| y = X0
| regular(X0) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3660,plain,
( ! [X0] :
( member(regular(regular(X0)),y)
| y = X0
| regular(X0) = y
| ~ subclass(regular(X0),X0) )
| ~ spl0_109
| ~ spl0_315 ),
inference(duplicate_literal_removal,[],[f3643]) ).
fof(f3643,plain,
( ! [X0] :
( member(regular(regular(X0)),y)
| y = X0
| regular(X0) = y
| ~ subclass(regular(X0),X0)
| regular(X0) = y )
| ~ spl0_109
| ~ spl0_315 ),
inference(resolution,[],[f3597,f832]) ).
fof(f3597,plain,
( ! [X0] :
( ~ member(regular(regular(X0)),X0)
| member(regular(regular(X0)),y)
| y = X0
| regular(X0) = y )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3596]) ).
fof(f52991,plain,
( ~ spl0_1277
| spl0_1278
| spl0_1258
| spl0_1279
| ~ spl0_245
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3659,f3596,f2422,f52988,f49612,f52984,f52980]) ).
fof(f52980,plain,
( spl0_1277
<=> subclass(regular(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f52984,plain,
( spl0_1278
<=> y = regular(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f52988,plain,
( spl0_1279
<=> member(regular(regular(element_relation)),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f3659,plain,
( member(regular(regular(element_relation)),y)
| element_relation = y
| y = regular(element_relation)
| ~ subclass(regular(element_relation),singleton_relation)
| ~ spl0_245
| ~ spl0_315 ),
inference(duplicate_literal_removal,[],[f3645]) ).
fof(f3645,plain,
( member(regular(regular(element_relation)),y)
| element_relation = y
| y = regular(element_relation)
| ~ subclass(regular(element_relation),singleton_relation)
| y = regular(element_relation)
| ~ spl0_245
| ~ spl0_315 ),
inference(resolution,[],[f3597,f2423]) ).
fof(f52978,plain,
( ~ spl0_1274
| spl0_1275
| spl0_238
| spl0_1276
| ~ spl0_246
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3658,f3596,f2426,f52975,f2279,f52971,f52967]) ).
fof(f52967,plain,
( spl0_1274
<=> subclass(regular(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f52971,plain,
( spl0_1275
<=> y = regular(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f52975,plain,
( spl0_1276
<=> member(regular(regular(subset_relation)),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f3658,plain,
( member(regular(regular(subset_relation)),y)
| subset_relation = y
| y = regular(subset_relation)
| ~ subclass(regular(subset_relation),identity_relation)
| ~ spl0_246
| ~ spl0_315 ),
inference(duplicate_literal_removal,[],[f3653]) ).
fof(f3653,plain,
( member(regular(regular(subset_relation)),y)
| subset_relation = y
| y = regular(subset_relation)
| ~ subclass(regular(subset_relation),identity_relation)
| y = regular(subset_relation)
| ~ spl0_246
| ~ spl0_315 ),
inference(resolution,[],[f3597,f2427]) ).
fof(f52965,plain,
( spl0_1273
| ~ spl0_109
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f3640,f3592,f831,f52963]) ).
fof(f52963,plain,
( spl0_1273
<=> ! [X0] :
( member(regular(complement(complement(X0))),X0)
| y = complement(complement(X0))
| ~ subclass(complement(complement(X0)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f3592,plain,
( spl0_314
<=> ! [X0] :
( y = complement(complement(X0))
| member(regular(complement(complement(X0))),X0)
| ~ member(regular(complement(complement(X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f3640,plain,
( ! [X0] :
( member(regular(complement(complement(X0))),X0)
| y = complement(complement(X0))
| ~ subclass(complement(complement(X0)),universal_class) )
| ~ spl0_109
| ~ spl0_314 ),
inference(duplicate_literal_removal,[],[f3638]) ).
fof(f3638,plain,
( ! [X0] :
( member(regular(complement(complement(X0))),X0)
| y = complement(complement(X0))
| ~ subclass(complement(complement(X0)),universal_class)
| y = complement(complement(X0)) )
| ~ spl0_109
| ~ spl0_314 ),
inference(resolution,[],[f3593,f832]) ).
fof(f3593,plain,
( ! [X0] :
( ~ member(regular(complement(complement(X0))),universal_class)
| member(regular(complement(complement(X0))),X0)
| y = complement(complement(X0)) )
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f3592]) ).
fof(f52961,plain,
( spl0_321
| ~ spl0_1272
| ~ spl0_109
| spl0_322 ),
inference(avatar_split_clause,[],[f3632,f3627,f831,f52958,f3623]) ).
fof(f3623,plain,
( spl0_321
<=> y = complement(domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f52958,plain,
( spl0_1272
<=> subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f3627,plain,
( spl0_322
<=> member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f3632,plain,
( ~ subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| y = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_109
| spl0_322 ),
inference(resolution,[],[f3629,f832]) ).
fof(f3629,plain,
( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| spl0_322 ),
inference(avatar_component_clause,[],[f3627]) ).
fof(f52956,plain,
( spl0_319
| ~ spl0_1271
| ~ spl0_109
| spl0_320 ),
inference(avatar_split_clause,[],[f3621,f3616,f831,f52953,f3612]) ).
fof(f3612,plain,
( spl0_319
<=> y = complement(complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f52953,plain,
( spl0_1271
<=> subclass(complement(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f3616,plain,
( spl0_320
<=> member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3621,plain,
( ~ subclass(complement(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| y = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_109
| spl0_320 ),
inference(resolution,[],[f3618,f832]) ).
fof(f3618,plain,
( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| spl0_320 ),
inference(avatar_component_clause,[],[f3616]) ).
fof(f52950,plain,
( spl0_1270
| ~ spl0_29
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3403,f3235,f334,f52948]) ).
fof(f52948,plain,
( spl0_1270
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,y),X1)
| y = complement(X2)
| ~ member(not_subclass_element(intersection(X0,y),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f3403,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,y),X1)
| y = complement(X2)
| ~ member(not_subclass_element(intersection(X0,y),X1),X2) )
| ~ spl0_29
| ~ spl0_298 ),
inference(resolution,[],[f3236,f335]) ).
fof(f52946,plain,
( ~ spl0_1269
| spl0_1010
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f52734,f37756,f32244,f52943]) ).
fof(f52943,plain,
( spl0_1269
<=> operation(domain_of(flip(singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f32244,plain,
( spl0_1010
<=> operation(domain_of(flip(cross_product(singleton_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f52734,plain,
( ~ operation(domain_of(flip(singleton_relation)))
| spl0_1010
| ~ spl0_1217 ),
inference(superposition,[],[f32246,f37757]) ).
fof(f32246,plain,
( ~ operation(domain_of(flip(cross_product(singleton_relation,universal_class))))
| spl0_1010 ),
inference(avatar_component_clause,[],[f32244]) ).
fof(f52940,plain,
( spl0_1268
| ~ spl0_29
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3374,f3231,f334,f52938]) ).
fof(f52938,plain,
( spl0_1268
<=> ! [X2,X0,X1] :
( subclass(intersection(y,X0),X1)
| y = complement(X2)
| ~ member(not_subclass_element(intersection(y,X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f3374,plain,
( ! [X2,X0,X1] :
( subclass(intersection(y,X0),X1)
| y = complement(X2)
| ~ member(not_subclass_element(intersection(y,X0),X1),X2) )
| ~ spl0_29
| ~ spl0_297 ),
inference(resolution,[],[f3232,f335]) ).
fof(f52936,plain,
( spl0_1267
| ~ spl0_39
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3152,f3019,f381,f52934]) ).
fof(f52934,plain,
( spl0_1267
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| y = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f3152,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| y = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X0) )
| ~ spl0_39
| ~ spl0_286 ),
inference(resolution,[],[f3020,f382]) ).
fof(f52932,plain,
( spl0_1266
| ~ spl0_40
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3151,f3019,f385,f52930]) ).
fof(f52930,plain,
( spl0_1266
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| y = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f3151,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| y = cross_product(X2,X3)
| member(regular(cross_product(X2,X3)),X1) )
| ~ spl0_40
| ~ spl0_286 ),
inference(resolution,[],[f3020,f386]) ).
fof(f52928,plain,
( spl0_1265
| ~ spl0_39
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3095,f2988,f381,f52926]) ).
fof(f52926,plain,
( spl0_1265
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f3095,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X1) )
| ~ spl0_39
| ~ spl0_282 ),
inference(resolution,[],[f2989,f382]) ).
fof(f52924,plain,
( spl0_1264
| ~ spl0_40
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3094,f2988,f385,f52922]) ).
fof(f52922,plain,
( spl0_1264
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f3094,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X3,X0)
| member(regular(intersection(X3,X0)),X2) )
| ~ spl0_40
| ~ spl0_282 ),
inference(resolution,[],[f2989,f386]) ).
fof(f52920,plain,
( spl0_1263
| ~ spl0_39
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3042,f2980,f381,f52918]) ).
fof(f52918,plain,
( spl0_1263
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f3042,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X1) )
| ~ spl0_39
| ~ spl0_280 ),
inference(resolution,[],[f2981,f382]) ).
fof(f52916,plain,
( spl0_1262
| ~ spl0_40
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3041,f2980,f385,f52914]) ).
fof(f52914,plain,
( spl0_1262
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f3041,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = intersection(X0,X3)
| member(regular(intersection(X0,X3)),X2) )
| ~ spl0_40
| ~ spl0_280 ),
inference(resolution,[],[f2981,f386]) ).
fof(f52912,plain,
( spl0_1261
| ~ spl0_51
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2664,f2450,f472,f52910]) ).
fof(f52910,plain,
( spl0_1261
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(complement(X1)))
| member(regular(X0),X1)
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f472,plain,
( spl0_51
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f2664,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(complement(X1)))
| member(regular(X0),X1)
| ~ member(regular(X0),universal_class) )
| ~ spl0_51
| ~ spl0_248 ),
inference(resolution,[],[f2451,f473]) ).
fof(f473,plain,
( ! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f52850,plain,
( spl0_1163
| ~ spl0_1217 ),
inference(avatar_contradiction_clause,[],[f52849]) ).
fof(f52849,plain,
( $false
| spl0_1163
| ~ spl0_1217 ),
inference(trivial_inequality_removal,[],[f52739]) ).
fof(f52739,plain,
( singleton_relation != singleton_relation
| spl0_1163
| ~ spl0_1217 ),
inference(superposition,[],[f35279,f37757]) ).
fof(f35279,plain,
( singleton_relation != cross_product(singleton_relation,universal_class)
| spl0_1163 ),
inference(avatar_component_clause,[],[f35277]) ).
fof(f35277,plain,
( spl0_1163
<=> singleton_relation = cross_product(singleton_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f52730,plain,
( spl0_1200
| ~ spl0_130
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f44100,f3205,f1005,f37632]) ).
fof(f37632,plain,
( spl0_1200
<=> ! [X0,X1] :
( y = intersection(X0,intersection(X1,singleton_relation))
| member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1005,plain,
( spl0_130
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f44100,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation)
| y = intersection(X0,intersection(X1,singleton_relation)) )
| ~ spl0_130
| ~ spl0_291 ),
inference(resolution,[],[f1006,f3206]) ).
fof(f1006,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f52693,plain,
( spl0_1192
| ~ spl0_130
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f44081,f3197,f1005,f37068]) ).
fof(f37068,plain,
( spl0_1192
<=> ! [X0,X1] :
( y = intersection(intersection(X0,singleton_relation),X1)
| member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f44081,plain,
( ! [X0,X1] :
( member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation)
| y = intersection(intersection(X0,singleton_relation),X1) )
| ~ spl0_130
| ~ spl0_289 ),
inference(resolution,[],[f1006,f3198]) ).
fof(f51469,plain,
( spl0_1001
| ~ spl0_343
| ~ spl0_1251 ),
inference(avatar_split_clause,[],[f50354,f46479,f4186,f31968]) ).
fof(f31968,plain,
( spl0_1001
<=> ! [X0] : subclass(singleton_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f4186,plain,
( spl0_343
<=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f46479,plain,
( spl0_1251
<=> ! [X0] : singleton_relation = intersection(X0,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f50354,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_343
| ~ spl0_1251 ),
inference(superposition,[],[f4187,f46480]) ).
fof(f46480,plain,
( ! [X0] : singleton_relation = intersection(X0,y)
| ~ spl0_1251 ),
inference(avatar_component_clause,[],[f46479]) ).
fof(f4187,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl0_343 ),
inference(avatar_component_clause,[],[f4186]) ).
fof(f49809,plain,
( spl0_1260
| ~ spl0_152
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2665,f2450,f1260,f49807]) ).
fof(f49807,plain,
( spl0_1260
<=> ! [X0] :
( y = X0
| ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(regular(X0),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f1260,plain,
( spl0_152
<=> ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f2665,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(regular(X0),singleton_relation) )
| ~ spl0_152
| ~ spl0_248 ),
inference(resolution,[],[f2451,f1261]) ).
fof(f1261,plain,
( ! [X0] :
( member(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,singleton_relation) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1260]) ).
fof(f49747,plain,
( spl0_1145
| ~ spl0_130
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f44099,f2980,f1005,f35129]) ).
fof(f35129,plain,
( spl0_1145
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| intersection(X0,X1) = y
| member(regular(intersection(X0,X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f44099,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),element_relation)
| ~ subclass(X0,singleton_relation)
| intersection(X0,X1) = y )
| ~ spl0_130
| ~ spl0_280 ),
inference(resolution,[],[f1006,f2981]) ).
fof(f49696,plain,
( spl0_1149
| ~ spl0_130
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f44098,f2988,f1005,f35149]) ).
fof(f35149,plain,
( spl0_1149
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| y = intersection(X1,X0)
| member(regular(intersection(X1,X0)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f44098,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),element_relation)
| ~ subclass(X1,singleton_relation)
| intersection(X0,X1) = y )
| ~ spl0_130
| ~ spl0_282 ),
inference(resolution,[],[f1006,f2989]) ).
fof(f49661,plain,
( spl0_1140
| ~ spl0_31
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f42016,f2826,f342,f35104]) ).
fof(f35104,plain,
( spl0_1140
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f342,plain,
( spl0_31
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f2826,plain,
( spl0_272
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = X0
| ~ subclass(X1,X2)
| member(regular(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f42016,plain,
( ! [X0,X1] :
( ~ function(X0)
| y = X1
| ~ subclass(X1,X0)
| member(regular(X1),cross_product(universal_class,universal_class)) )
| ~ spl0_31
| ~ spl0_272 ),
inference(resolution,[],[f343,f2827]) ).
fof(f2827,plain,
( ! [X2,X0,X1] :
( ~ subclass(X1,X2)
| y = X0
| ~ subclass(X0,X1)
| member(regular(X0),X2) )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f2826]) ).
fof(f343,plain,
( ! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f49619,plain,
( spl0_168
| ~ spl0_1257
| spl0_1258
| spl0_1259
| ~ spl0_169
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f41445,f3810,f1432,f49616,f49612,f49608,f1428]) ).
fof(f49608,plain,
( spl0_1257
<=> subclass(singleton_relation,regular(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f49616,plain,
( spl0_1259
<=> member(regular(singleton_relation),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f1432,plain,
( spl0_169
<=> member(regular(singleton_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f41445,plain,
( member(regular(singleton_relation),y)
| element_relation = y
| ~ subclass(singleton_relation,regular(element_relation))
| singleton_relation = y
| ~ spl0_169
| ~ spl0_327 ),
inference(resolution,[],[f1434,f3811]) ).
fof(f1434,plain,
( member(regular(singleton_relation),element_relation)
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1432]) ).
fof(f49210,plain,
( spl0_1001
| ~ spl0_344
| ~ spl0_1250 ),
inference(avatar_split_clause,[],[f48057,f46128,f4190,f31968]) ).
fof(f4190,plain,
( spl0_344
<=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f46128,plain,
( spl0_1250
<=> ! [X0] : singleton_relation = intersection(y,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f48057,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_344
| ~ spl0_1250 ),
inference(superposition,[],[f4191,f46129]) ).
fof(f46129,plain,
( ! [X0] : singleton_relation = intersection(y,X0)
| ~ spl0_1250 ),
inference(avatar_component_clause,[],[f46128]) ).
fof(f4191,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f4190]) ).
fof(f47449,plain,
( spl0_168
| ~ spl0_585
| ~ spl0_1106
| ~ spl0_1116 ),
inference(avatar_split_clause,[],[f46658,f34034,f33979,f9669,f1428]) ).
fof(f9669,plain,
( spl0_585
<=> ! [X0] : ~ member(X0,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f33979,plain,
( spl0_1106
<=> ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f34034,plain,
( spl0_1116
<=> ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(first(regular(cross_product(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f46658,plain,
( singleton_relation = y
| ~ spl0_585
| ~ spl0_1106
| ~ spl0_1116 ),
inference(forward_demodulation,[],[f46599,f34585]) ).
fof(f34585,plain,
( ! [X0] : singleton_relation = cross_product(y,X0)
| ~ spl0_585
| ~ spl0_1116 ),
inference(resolution,[],[f34035,f9670]) ).
fof(f9670,plain,
( ! [X0] : ~ member(X0,y)
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f9669]) ).
fof(f34035,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = singleton_relation )
| ~ spl0_1116 ),
inference(avatar_component_clause,[],[f34034]) ).
fof(f46599,plain,
( ! [X0] : y = cross_product(y,X0)
| ~ spl0_585
| ~ spl0_1106 ),
inference(resolution,[],[f33980,f9670]) ).
fof(f33980,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = y )
| ~ spl0_1106 ),
inference(avatar_component_clause,[],[f33979]) ).
fof(f46702,plain,
( spl0_168
| ~ spl0_550
| ~ spl0_567
| ~ spl0_585
| ~ spl0_1105
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f46545,f34030,f33974,f9669,f9421,f8731,f1428]) ).
fof(f34030,plain,
( spl0_1115
<=> ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(second(regular(cross_product(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f46545,plain,
( singleton_relation = y
| ~ spl0_550
| ~ spl0_567
| ~ spl0_585
| ~ spl0_1105
| ~ spl0_1115 ),
inference(forward_demodulation,[],[f46544,f34513]) ).
fof(f34513,plain,
( ! [X0] : singleton_relation = cross_product(X0,y)
| ~ spl0_585
| ~ spl0_1115 ),
inference(resolution,[],[f34031,f9670]) ).
fof(f34031,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = singleton_relation )
| ~ spl0_1115 ),
inference(avatar_component_clause,[],[f34030]) ).
fof(f46700,plain,
( spl0_1256
| ~ spl0_109
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6165,f6111,f831,f46698]) ).
fof(f46698,plain,
( spl0_1256
<=> ! [X0] :
( ~ member(regular(X0),singleton_relation)
| ~ subclass(X0,compose(element_relation,complement(identity_relation)))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f6165,plain,
( ! [X0] :
( ~ member(regular(X0),singleton_relation)
| ~ subclass(X0,compose(element_relation,complement(identity_relation)))
| y = X0 )
| ~ spl0_109
| ~ spl0_445 ),
inference(resolution,[],[f6112,f832]) ).
fof(f46691,plain,
( ~ spl0_1255
| ~ spl0_550
| ~ spl0_567
| ~ spl0_585
| ~ spl0_1105
| ~ spl0_1115
| spl0_1253 ),
inference(avatar_split_clause,[],[f46686,f46678,f34030,f33974,f9669,f9421,f8731,f46688]) ).
fof(f46688,plain,
( spl0_1255
<=> compose(element_relation,complement(identity_relation)) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f46678,plain,
( spl0_1253
<=> compose(element_relation,complement(identity_relation)) = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f46686,plain,
( compose(element_relation,complement(identity_relation)) != singleton_relation
| ~ spl0_550
| ~ spl0_567
| ~ spl0_585
| ~ spl0_1105
| ~ spl0_1115
| spl0_1253 ),
inference(forward_demodulation,[],[f46679,f46545]) ).
fof(f46679,plain,
( compose(element_relation,complement(identity_relation)) != y
| spl0_1253 ),
inference(avatar_component_clause,[],[f46678]) ).
fof(f46685,plain,
( spl0_1253
| ~ spl0_1254
| ~ spl0_2
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f6153,f6111,f213,f46682,f46678]) ).
fof(f46682,plain,
( spl0_1254
<=> member(regular(compose(element_relation,complement(identity_relation))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f213,plain,
( spl0_2
<=> ! [X0] :
( y = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f6153,plain,
( ~ member(regular(compose(element_relation,complement(identity_relation))),singleton_relation)
| compose(element_relation,complement(identity_relation)) = y
| ~ spl0_2
| ~ spl0_445 ),
inference(resolution,[],[f6112,f214]) ).
fof(f214,plain,
( ! [X0] :
( member(regular(X0),X0)
| y = X0 )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f46670,plain,
( spl0_1252
| ~ spl0_49
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4229,f4190,f436,f46667]) ).
fof(f46667,plain,
( spl0_1252
<=> subclass(singleton_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f436,plain,
( spl0_49
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f4229,plain,
( subclass(singleton_relation,element_relation)
| ~ spl0_49
| ~ spl0_344 ),
inference(superposition,[],[f4191,f438]) ).
fof(f438,plain,
( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f46481,plain,
( spl0_1251
| ~ spl0_8
| ~ spl0_236
| ~ spl0_1062 ),
inference(avatar_split_clause,[],[f33521,f33336,f2269,f242,f46479]) ).
fof(f242,plain,
( spl0_8
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f2269,plain,
( spl0_236
<=> y = complement(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f33336,plain,
( spl0_1062
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,complement(X0))
| ~ subclass(complement(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f33521,plain,
( ! [X0] : singleton_relation = intersection(X0,y)
| ~ spl0_8
| ~ spl0_236
| ~ spl0_1062 ),
inference(forward_demodulation,[],[f33516,f2271]) ).
fof(f2271,plain,
( y = complement(universal_class)
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f2269]) ).
fof(f33516,plain,
( ! [X0] : singleton_relation = intersection(X0,complement(universal_class))
| ~ spl0_8
| ~ spl0_1062 ),
inference(resolution,[],[f33337,f243]) ).
fof(f243,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f33337,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| singleton_relation = intersection(X1,complement(X0)) )
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f33336]) ).
fof(f46130,plain,
( spl0_1250
| ~ spl0_8
| ~ spl0_236
| ~ spl0_1061 ),
inference(avatar_split_clause,[],[f33511,f33332,f2269,f242,f46128]) ).
fof(f33332,plain,
( spl0_1061
<=> ! [X0,X1] :
( singleton_relation = intersection(complement(X0),X1)
| ~ subclass(complement(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f33511,plain,
( ! [X0] : singleton_relation = intersection(y,X0)
| ~ spl0_8
| ~ spl0_236
| ~ spl0_1061 ),
inference(forward_demodulation,[],[f33506,f2271]) ).
fof(f33506,plain,
( ! [X0] : singleton_relation = intersection(complement(universal_class),X0)
| ~ spl0_8
| ~ spl0_1061 ),
inference(resolution,[],[f33333,f243]) ).
fof(f33333,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| singleton_relation = intersection(complement(X0),X1) )
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f33332]) ).
fof(f45899,plain,
( ~ spl0_1249
| spl0_168
| ~ spl0_248
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2663,f2454,f2450,f1428,f45896]) ).
fof(f45896,plain,
( spl0_1249
<=> subclass(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f2454,plain,
( spl0_249
<=> member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2663,plain,
( singleton_relation = y
| ~ subclass(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation)))))
| ~ spl0_248
| ~ spl0_249 ),
inference(resolution,[],[f2451,f2456]) ).
fof(f2456,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2454]) ).
fof(f45159,plain,
( spl0_412
| ~ spl0_34
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f44045,f1005,f361,f5648]) ).
fof(f5648,plain,
( spl0_412
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f361,plain,
( spl0_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f44045,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_34
| ~ spl0_130 ),
inference(resolution,[],[f1006,f362]) ).
fof(f362,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f45148,plain,
( spl0_168
| ~ spl0_375
| spl0_1248
| ~ spl0_49
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f23050,f1139,f436,f45145,f4993,f1428]) ).
fof(f4993,plain,
( spl0_375
<=> member(singleton_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f45145,plain,
( spl0_1248
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f1139,plain,
( spl0_140
<=> ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f23050,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),complement(compose(element_relation,complement(identity_relation))))
| ~ member(singleton_relation,universal_class)
| singleton_relation = y
| ~ spl0_49
| ~ spl0_140 ),
inference(superposition,[],[f1140,f438]) ).
fof(f1140,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f45074,plain,
( spl0_168
| ~ spl0_1022
| ~ spl0_1037 ),
inference(avatar_split_clause,[],[f40087,f32492,f32367,f1428]) ).
fof(f32367,plain,
( spl0_1022
<=> ! [X0,X1] : y = intersection(complement(X0),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f32492,plain,
( spl0_1037
<=> ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f40087,plain,
( singleton_relation = y
| ~ spl0_1022
| ~ spl0_1037 ),
inference(forward_demodulation,[],[f32368,f32493]) ).
fof(f32493,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_1037 ),
inference(avatar_component_clause,[],[f32492]) ).
fof(f32368,plain,
( ! [X0,X1] : y = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_1022 ),
inference(avatar_component_clause,[],[f32367]) ).
fof(f45066,plain,
( spl0_168
| ~ spl0_1021
| ~ spl0_1036 ),
inference(avatar_split_clause,[],[f40088,f32486,f32362,f1428]) ).
fof(f32362,plain,
( spl0_1021
<=> ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f32486,plain,
( spl0_1036
<=> ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f40088,plain,
( singleton_relation = y
| ~ spl0_1021
| ~ spl0_1036 ),
inference(forward_demodulation,[],[f32363,f32487]) ).
fof(f32487,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_1036 ),
inference(avatar_component_clause,[],[f32486]) ).
fof(f32363,plain,
( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_1021 ),
inference(avatar_component_clause,[],[f32362]) ).
fof(f45033,plain,
( spl0_168
| ~ spl0_343
| ~ spl0_1023
| ~ spl0_1048 ),
inference(avatar_split_clause,[],[f45000,f33180,f32372,f4186,f1428]) ).
fof(f32372,plain,
( spl0_1023
<=> ! [X0,X1] : y = intersection(complement(X0),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f33180,plain,
( spl0_1048
<=> ! [X0,X1] :
( singleton_relation = intersection(complement(X1),X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f45000,plain,
( singleton_relation = y
| ~ spl0_343
| ~ spl0_1023
| ~ spl0_1048 ),
inference(forward_demodulation,[],[f32373,f33233]) ).
fof(f33233,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_343
| ~ spl0_1048 ),
inference(resolution,[],[f33181,f4187]) ).
fof(f33181,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| singleton_relation = intersection(complement(X1),X0) )
| ~ spl0_1048 ),
inference(avatar_component_clause,[],[f33180]) ).
fof(f32373,plain,
( ! [X0,X1] : y = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_1023 ),
inference(avatar_component_clause,[],[f32372]) ).
fof(f44999,plain,
( spl0_168
| ~ spl0_344
| ~ spl0_1020
| ~ spl0_1047 ),
inference(avatar_split_clause,[],[f44964,f33176,f32357,f4190,f1428]) ).
fof(f32357,plain,
( spl0_1020
<=> ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f33176,plain,
( spl0_1047
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,complement(X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f44964,plain,
( singleton_relation = y
| ~ spl0_344
| ~ spl0_1020
| ~ spl0_1047 ),
inference(forward_demodulation,[],[f32358,f33194]) ).
fof(f33194,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_344
| ~ spl0_1047 ),
inference(resolution,[],[f33177,f4191]) ).
fof(f33177,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| singleton_relation = intersection(X0,complement(X1)) )
| ~ spl0_1047 ),
inference(avatar_component_clause,[],[f33176]) ).
fof(f32358,plain,
( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_1020 ),
inference(avatar_component_clause,[],[f32357]) ).
fof(f44947,plain,
( spl0_168
| ~ spl0_1023
| ~ spl0_1038 ),
inference(avatar_split_clause,[],[f40086,f32496,f32372,f1428]) ).
fof(f32496,plain,
( spl0_1038
<=> ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f40086,plain,
( singleton_relation = y
| ~ spl0_1023
| ~ spl0_1038 ),
inference(forward_demodulation,[],[f32373,f32497]) ).
fof(f32497,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_1038 ),
inference(avatar_component_clause,[],[f32496]) ).
fof(f44528,plain,
( spl0_168
| ~ spl0_1020
| ~ spl0_1035 ),
inference(avatar_split_clause,[],[f40089,f32482,f32357,f1428]) ).
fof(f32482,plain,
( spl0_1035
<=> ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f40089,plain,
( singleton_relation = y
| ~ spl0_1020
| ~ spl0_1035 ),
inference(forward_demodulation,[],[f32358,f32483]) ).
fof(f32483,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_1035 ),
inference(avatar_component_clause,[],[f32482]) ).
fof(f44360,plain,
( spl0_1247
| ~ spl0_939
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f41265,f37756,f28126,f44358]) ).
fof(f44358,plain,
( spl0_1247
<=> ! [X2,X0,X1] :
( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
| member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f28126,plain,
( spl0_939
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
| singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f41265,plain,
( ! [X2,X0,X1] :
( ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
| member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y )
| ~ spl0_939
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f28127,f37757]) ).
fof(f28127,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
| singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y )
| ~ spl0_939 ),
inference(avatar_component_clause,[],[f28126]) ).
fof(f44331,plain,
( spl0_551
| ~ spl0_116
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f42269,f1746,f912,f8860]) ).
fof(f8860,plain,
( spl0_551
<=> ! [X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ member(X1,universal_class)
| y = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f912,plain,
( spl0_116
<=> ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1746,plain,
( spl0_196
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f42269,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ member(X1,universal_class)
| y = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) )
| ~ spl0_116
| ~ spl0_196 ),
inference(resolution,[],[f1747,f913]) ).
fof(f913,plain,
( ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f1747,plain,
( ! [X2,X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| ~ member(X0,universal_class) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f1746]) ).
fof(f44127,plain,
( spl0_439
| ~ spl0_113
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f42273,f1746,f888,f5872]) ).
fof(f5872,plain,
( spl0_439
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),y)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f888,plain,
( spl0_113
<=> ! [X0,X1] :
( member(X1,y)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f42273,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),y)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| y = X1 )
| ~ spl0_113
| ~ spl0_196 ),
inference(resolution,[],[f1747,f889]) ).
fof(f889,plain,
( ! [X0,X1] :
( ~ member(X1,regular(X0))
| member(X1,y)
| ~ member(X1,X0)
| y = X0 )
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f44121,plain,
( spl0_339
| ~ spl0_31
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f42047,f953,f342,f4092]) ).
fof(f4092,plain,
( spl0_339
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ function(domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f953,plain,
( spl0_119
<=> ! [X2,X0,X1] :
( ~ subclass(domain_of(X0),X1)
| member(X2,X1)
| ~ member(X2,universal_class)
| y = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f42047,plain,
( ! [X0,X1] :
( ~ function(domain_of(X0))
| member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),X0) )
| ~ spl0_31
| ~ spl0_119 ),
inference(resolution,[],[f343,f954]) ).
fof(f954,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_of(X0),X1)
| member(X2,X1)
| ~ member(X2,universal_class)
| y = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f42667,plain,
( spl0_1001
| ~ spl0_343
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f37130,f36096,f4186,f31968]) ).
fof(f36096,plain,
( spl0_1184
<=> ! [X0] : singleton_relation = intersection(X0,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f37130,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_343
| ~ spl0_1184 ),
inference(superposition,[],[f4187,f36097]) ).
fof(f36097,plain,
( ! [X0] : singleton_relation = intersection(X0,singleton_relation)
| ~ spl0_1184 ),
inference(avatar_component_clause,[],[f36096]) ).
fof(f42531,plain,
( spl0_1246
| ~ spl0_531
| ~ spl0_551
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f41865,f36096,f8860,f8328,f42529]) ).
fof(f42529,plain,
( spl0_1246
<=> ! [X0,X1] :
( singleton_relation = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ function(X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f8328,plain,
( spl0_531
<=> ! [X0] : y = intersection(y,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f41865,plain,
( ! [X0,X1] :
( singleton_relation = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ function(X0)
| ~ member(X1,universal_class) )
| ~ spl0_531
| ~ spl0_551
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f8861,f37352]) ).
fof(f37352,plain,
( singleton_relation = y
| ~ spl0_531
| ~ spl0_1184 ),
inference(superposition,[],[f8329,f36097]) ).
fof(f8329,plain,
( ! [X0] : y = intersection(y,X0)
| ~ spl0_531 ),
inference(avatar_component_clause,[],[f8328]) ).
fof(f8861,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ function(X0)
| ~ member(X1,universal_class)
| y = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) )
| ~ spl0_551 ),
inference(avatar_component_clause,[],[f8860]) ).
fof(f42337,plain,
( spl0_1001
| ~ spl0_344
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f36784,f35368,f4190,f31968]) ).
fof(f35368,plain,
( spl0_1183
<=> ! [X0] : singleton_relation = intersection(singleton_relation,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f36784,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_344
| ~ spl0_1183 ),
inference(superposition,[],[f4191,f35369]) ).
fof(f35369,plain,
( ! [X0] : singleton_relation = intersection(singleton_relation,X0)
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f35368]) ).
fof(f42336,plain,
( spl0_1245
| ~ spl0_439
| ~ spl0_531
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f41823,f36096,f8328,f5872,f42334]) ).
fof(f42334,plain,
( spl0_1245
<=> ! [X2,X0,X1] :
( singleton_relation = X1
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f41823,plain,
( ! [X2,X0,X1] :
( singleton_relation = X1
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| ~ function(X0) )
| ~ spl0_439
| ~ spl0_531
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f41822,f37352]) ).
fof(f41822,plain,
( ! [X2,X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),singleton_relation)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| ~ function(X0)
| y = X1 )
| ~ spl0_439
| ~ spl0_531
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f5873,f37352]) ).
fof(f5873,plain,
( ! [X2,X0,X1] :
( ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),y)
| ~ function(X0)
| y = X1 )
| ~ spl0_439 ),
inference(avatar_component_clause,[],[f5872]) ).
fof(f42324,plain,
( spl0_1244
| ~ spl0_339
| ~ spl0_531
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f41989,f36096,f8328,f4092,f42322]) ).
fof(f42322,plain,
( spl0_1244
<=> ! [X0,X1] :
( singleton_relation = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ function(domain_of(X1))
| ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f41989,plain,
( ! [X0,X1] :
( singleton_relation = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ function(domain_of(X1))
| ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_339
| ~ spl0_531
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f4093,f37352]) ).
fof(f4093,plain,
( ! [X0,X1] :
( ~ function(domain_of(X1))
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f4092]) ).
fof(f42137,plain,
( spl0_1243
| ~ spl0_122
| ~ spl0_531
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f41996,f36096,f8328,f970,f42135]) ).
fof(f42135,plain,
( spl0_1243
<=> ! [X0] :
( singleton_relation = cross_product(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class)))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f970,plain,
( spl0_122
<=> ! [X0] :
( ~ member(X0,universal_class)
| y = cross_product(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f41996,plain,
( ! [X0] :
( singleton_relation = cross_product(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class)))
| ~ member(X0,universal_class) )
| ~ spl0_122
| ~ spl0_531
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f971,f37352]) ).
fof(f971,plain,
( ! [X0] :
( ~ function(regular(cross_product(X0,universal_class)))
| y = cross_product(X0,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f41806,plain,
( ~ spl0_6
| ~ spl0_1241 ),
inference(avatar_contradiction_clause,[],[f41804]) ).
fof(f41804,plain,
( $false
| ~ spl0_6
| ~ spl0_1241 ),
inference(resolution,[],[f41799,f235]) ).
fof(f235,plain,
( function(choice)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f233,plain,
( spl0_6
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f41799,plain,
( ! [X1] : ~ function(X1)
| ~ spl0_1241 ),
inference(avatar_component_clause,[],[f41798]) ).
fof(f41798,plain,
( spl0_1241
<=> ! [X1] : ~ function(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f41803,plain,
( spl0_1241
| spl0_1242
| ~ spl0_375
| ~ spl0_675
| ~ spl0_1183
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f41669,f37756,f35368,f13560,f4993,f41801,f41798]) ).
fof(f41801,plain,
( spl0_1242
<=> ! [X2,X0] :
( member(domain_of(domain_of(flip(singleton_relation))),X2)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f13560,plain,
( spl0_675
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,X1)
| ~ member(X2,universal_class)
| ~ subclass(X1,X3)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f41669,plain,
( ! [X2,X0,X1] :
( member(domain_of(domain_of(flip(singleton_relation))),X2)
| ~ subclass(universal_class,X0)
| ~ function(X1)
| ~ subclass(X0,X2) )
| ~ spl0_375
| ~ spl0_675
| ~ spl0_1183
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41668,f37757]) ).
fof(f41668,plain,
( ! [X2,X0,X1] :
( member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),X2)
| ~ subclass(universal_class,X0)
| ~ function(X1)
| ~ subclass(X0,X2) )
| ~ spl0_375
| ~ spl0_675
| ~ spl0_1183
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41667,f35369]) ).
fof(f41667,plain,
( ! [X2,X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(singleton_relation,X1),universal_class)))),X2)
| ~ subclass(universal_class,X0)
| ~ function(X1)
| ~ subclass(X0,X2) )
| ~ spl0_375
| ~ spl0_675
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f29535,f37757]) ).
fof(f29535,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ function(X1)
| ~ subclass(X0,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(singleton_relation,universal_class),X1),universal_class)))),X2) )
| ~ spl0_375
| ~ spl0_675 ),
inference(resolution,[],[f4994,f13561]) ).
fof(f13561,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,universal_class)
| ~ subclass(universal_class,X1)
| ~ function(X0)
| ~ subclass(X1,X3)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) )
| ~ spl0_675 ),
inference(avatar_component_clause,[],[f13560]) ).
fof(f4994,plain,
( member(singleton_relation,universal_class)
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f4993]) ).
fof(f41796,plain,
( spl0_1240
| ~ spl0_531
| ~ spl0_1145
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f39160,f36096,f35129,f8328,f41794]) ).
fof(f41794,plain,
( spl0_1240
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X0,X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f39160,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X0,X1)),element_relation) )
| ~ spl0_531
| ~ spl0_1145
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f35130,f37352]) ).
fof(f35130,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),element_relation)
| intersection(X0,X1) = y
| ~ subclass(X0,singleton_relation) )
| ~ spl0_1145 ),
inference(avatar_component_clause,[],[f35129]) ).
fof(f41776,plain,
( spl0_375
| ~ spl0_8
| ~ spl0_1011 ),
inference(avatar_split_clause,[],[f32254,f32249,f242,f4993]) ).
fof(f32249,plain,
( spl0_1011
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f32254,plain,
( member(singleton_relation,universal_class)
| ~ spl0_8
| ~ spl0_1011 ),
inference(resolution,[],[f32250,f243]) ).
fof(f32250,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(singleton_relation,X0) )
| ~ spl0_1011 ),
inference(avatar_component_clause,[],[f32249]) ).
fof(f41775,plain,
( spl0_1239
| ~ spl0_531
| ~ spl0_1149
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f39157,f36096,f35149,f8328,f41773]) ).
fof(f41773,plain,
( spl0_1239
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X1,X0)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f39157,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,singleton_relation)
| member(regular(intersection(X1,X0)),element_relation) )
| ~ spl0_531
| ~ spl0_1149
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f35150,f37352]) ).
fof(f35150,plain,
( ! [X0,X1] :
( member(regular(intersection(X1,X0)),element_relation)
| y = intersection(X1,X0)
| ~ subclass(X0,singleton_relation) )
| ~ spl0_1149 ),
inference(avatar_component_clause,[],[f35149]) ).
fof(f41726,plain,
( spl0_1238
| ~ spl0_531
| ~ spl0_1094
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f39656,f36096,f33921,f8328,f41724]) ).
fof(f41724,plain,
( spl0_1238
<=> ! [X0] :
( singleton_relation = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f33921,plain,
( spl0_1094
<=> ! [X0] :
( y = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f39656,plain,
( ! [X0] :
( singleton_relation = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
| ~ spl0_531
| ~ spl0_1094
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f33922,f37352]) ).
fof(f33922,plain,
( ! [X0] :
( ~ subclass(intersection(complement(element_relation),X0),singleton_relation)
| y = intersection(complement(element_relation),X0) )
| ~ spl0_1094 ),
inference(avatar_component_clause,[],[f33921]) ).
fof(f41722,plain,
( spl0_1237
| ~ spl0_531
| ~ spl0_1097
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f39653,f36096,f33936,f8328,f41720]) ).
fof(f41720,plain,
( spl0_1237
<=> ! [X0] :
( singleton_relation = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f33936,plain,
( spl0_1097
<=> ! [X0] :
( y = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f39653,plain,
( ! [X0] :
( singleton_relation = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
| ~ spl0_531
| ~ spl0_1097
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f33937,f37352]) ).
fof(f33937,plain,
( ! [X0] :
( ~ subclass(intersection(X0,complement(element_relation)),singleton_relation)
| y = intersection(X0,complement(element_relation)) )
| ~ spl0_1097 ),
inference(avatar_component_clause,[],[f33936]) ).
fof(f41704,plain,
( spl0_1236
| ~ spl0_531
| ~ spl0_1050
| ~ spl0_1184 ),
inference(avatar_split_clause,[],[f39822,f36096,f33271,f8328,f41702]) ).
fof(f41702,plain,
( spl0_1236
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f33271,plain,
( spl0_1050
<=> ! [X0] :
( y = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f39822,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_531
| ~ spl0_1050
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f33272,f37352]) ).
fof(f33272,plain,
( ! [X0] :
( ~ subclass(X0,complement(element_relation))
| y = X0
| ~ subclass(X0,singleton_relation) )
| ~ spl0_1050 ),
inference(avatar_component_clause,[],[f33271]) ).
fof(f41665,plain,
( ~ spl0_22
| spl0_375
| ~ spl0_1006 ),
inference(avatar_split_clause,[],[f41444,f32159,f4993,f305]) ).
fof(f305,plain,
( spl0_22
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f32159,plain,
( spl0_1006
<=> ! [X0] :
( member(singleton_relation,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f41444,plain,
( ~ inductive(universal_class)
| spl0_375
| ~ spl0_1006 ),
inference(resolution,[],[f4995,f32160]) ).
fof(f32160,plain,
( ! [X0] :
( member(singleton_relation,X0)
| ~ inductive(X0) )
| ~ spl0_1006 ),
inference(avatar_component_clause,[],[f32159]) ).
fof(f4995,plain,
( ~ member(singleton_relation,universal_class)
| spl0_375 ),
inference(avatar_component_clause,[],[f4993]) ).
fof(f41495,plain,
( ~ spl0_928
| ~ spl0_1056 ),
inference(avatar_contradiction_clause,[],[f41491]) ).
fof(f41491,plain,
( $false
| ~ spl0_928
| ~ spl0_1056 ),
inference(resolution,[],[f27611,f33302]) ).
fof(f33302,plain,
( ! [X0] : ~ member(X0,singleton_relation)
| ~ spl0_1056 ),
inference(avatar_component_clause,[],[f33301]) ).
fof(f33301,plain,
( spl0_1056
<=> ! [X0] : ~ member(X0,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f27611,plain,
( member(regular(singleton_relation),singleton_relation)
| ~ spl0_928 ),
inference(avatar_component_clause,[],[f27609]) ).
fof(f27609,plain,
( spl0_928
<=> member(regular(singleton_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f41468,plain,
( spl0_1235
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f41108,f37756,f36096,f29875,f8328,f41466]) ).
fof(f41466,plain,
( spl0_1235
<=> ! [X0,X3,X2,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f29875,plain,
( spl0_952
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f41108,plain,
( ! [X2,X3,X0,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41107,f37352]) ).
fof(f41107,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41106,f37757]) ).
fof(f41106,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41105,f37352]) ).
fof(f41105,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41104,f37757]) ).
fof(f41104,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41103,f37352]) ).
fof(f41103,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41102,f37757]) ).
fof(f41102,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41101,f37352]) ).
fof(f41101,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41100,f37757]) ).
fof(f41100,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41099,f37352]) ).
fof(f41099,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41098,f37757]) ).
fof(f41098,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_531
| ~ spl0_952
| ~ spl0_1184 ),
inference(forward_demodulation,[],[f29876,f37352]) ).
fof(f29876,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_952 ),
inference(avatar_component_clause,[],[f29875]) ).
fof(f41453,plain,
( spl0_1234
| ~ spl0_531
| ~ spl0_939
| ~ spl0_1184
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f41266,f37756,f36096,f28126,f8328,f41451]) ).
fof(f41451,plain,
( spl0_1234
<=> ! [X2,X0,X1] :
( cross_product(X0,X1) = singleton_relation
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
| member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f41266,plain,
( ! [X2,X0,X1] :
( cross_product(X0,X1) = singleton_relation
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(singleton_relation))),universal_class),X2),universal_class)))))
| member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class)) )
| ~ spl0_531
| ~ spl0_939
| ~ spl0_1184
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f41265,f37352]) ).
fof(f38122,plain,
( ~ spl0_1098
| spl0_1017
| ~ spl0_1184
| ~ spl0_1208 ),
inference(avatar_split_clause,[],[f37919,f37673,f36096,f32287,f33941]) ).
fof(f33941,plain,
( spl0_1098
<=> singleton_relation = domain_of(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f32287,plain,
( spl0_1017
<=> singleton_relation = domain_of(intersection(x,cross_product(singleton_relation,singleton_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f37673,plain,
( spl0_1208
<=> ! [X0] : singleton_relation = cross_product(X0,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f37919,plain,
( singleton_relation != domain_of(singleton_relation)
| spl0_1017
| ~ spl0_1184
| ~ spl0_1208 ),
inference(forward_demodulation,[],[f37877,f36097]) ).
fof(f37877,plain,
( singleton_relation != domain_of(intersection(x,singleton_relation))
| spl0_1017
| ~ spl0_1208 ),
inference(superposition,[],[f32289,f37674]) ).
fof(f37674,plain,
( ! [X0] : singleton_relation = cross_product(X0,singleton_relation)
| ~ spl0_1208 ),
inference(avatar_component_clause,[],[f37673]) ).
fof(f32289,plain,
( singleton_relation != domain_of(intersection(x,cross_product(singleton_relation,singleton_relation)))
| spl0_1017 ),
inference(avatar_component_clause,[],[f32287]) ).
fof(f37943,plain,
( spl0_1233
| ~ spl0_168
| ~ spl0_1212 ),
inference(avatar_split_clause,[],[f37736,f37732,f1428,f37941]) ).
fof(f37941,plain,
( spl0_1233
<=> ! [X0,X1] :
( singleton_relation = X0
| member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1)
| ~ subclass(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f37732,plain,
( spl0_1212
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),y)
| ~ subclass(X0,regular(X0))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f37736,plain,
( ! [X0,X1] :
( singleton_relation = X0
| member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1)
| ~ subclass(X0,regular(X0)) )
| ~ spl0_168
| ~ spl0_1212 ),
inference(forward_demodulation,[],[f37735,f1430]) ).
fof(f1430,plain,
( singleton_relation = y
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f37735,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),singleton_relation)
| subclass(X0,X1)
| ~ subclass(X0,regular(X0))
| y = X0 )
| ~ spl0_168
| ~ spl0_1212 ),
inference(forward_demodulation,[],[f37733,f1430]) ).
fof(f37733,plain,
( ! [X0,X1] :
( ~ subclass(X0,regular(X0))
| member(not_subclass_element(X0,X1),y)
| subclass(X0,X1)
| y = X0 )
| ~ spl0_1212 ),
inference(avatar_component_clause,[],[f37732]) ).
fof(f37939,plain,
( spl0_1232
| ~ spl0_168
| ~ spl0_1211 ),
inference(avatar_split_clause,[],[f37730,f37725,f1428,f37937]) ).
fof(f37937,plain,
( spl0_1232
<=> ! [X0,X1] :
( singleton_relation = X1
| subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),X1)
| ~ subclass(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f37725,plain,
( spl0_1211
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,y),X1)
| subclass(X0,y)
| y = X1
| ~ subclass(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f37730,plain,
( ! [X0,X1] :
( singleton_relation = X1
| subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),X1)
| ~ subclass(X0,regular(X1)) )
| ~ spl0_168
| ~ spl0_1211 ),
inference(forward_demodulation,[],[f37729,f1430]) ).
fof(f37729,plain,
( ! [X0,X1] :
( subclass(X0,singleton_relation)
| ~ member(not_subclass_element(X0,singleton_relation),X1)
| y = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_168
| ~ spl0_1211 ),
inference(forward_demodulation,[],[f37728,f1430]) ).
fof(f37728,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,singleton_relation),X1)
| subclass(X0,y)
| y = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_168
| ~ spl0_1211 ),
inference(forward_demodulation,[],[f37726,f1430]) ).
fof(f37726,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,y),X1)
| subclass(X0,y)
| y = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_1211 ),
inference(avatar_component_clause,[],[f37725]) ).
fof(f37935,plain,
( spl0_1231
| ~ spl0_168
| ~ spl0_1206 ),
inference(avatar_split_clause,[],[f37667,f37664,f1428,f37933]) ).
fof(f37933,plain,
( spl0_1231
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f37664,plain,
( spl0_1206
<=> ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f37667,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
| ~ spl0_168
| ~ spl0_1206 ),
inference(forward_demodulation,[],[f37665,f1430]) ).
fof(f37665,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1))
| y = intersection(X0,intersection(X1,X2)) )
| ~ spl0_1206 ),
inference(avatar_component_clause,[],[f37664]) ).
fof(f37931,plain,
( spl0_1230
| ~ spl0_168
| ~ spl0_1205 ),
inference(avatar_split_clause,[],[f37662,f37659,f1428,f37929]) ).
fof(f37929,plain,
( spl0_1230
<=> ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f37659,plain,
( spl0_1205
<=> ! [X0] :
( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
| y = intersection(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f37662,plain,
( ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_168
| ~ spl0_1205 ),
inference(forward_demodulation,[],[f37660,f1430]) ).
fof(f37660,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
| y = intersection(X0,identity_relation) )
| ~ spl0_1205 ),
inference(avatar_component_clause,[],[f37659]) ).
fof(f37927,plain,
( spl0_1229
| ~ spl0_168
| ~ spl0_1202 ),
inference(avatar_split_clause,[],[f37646,f37643,f1428,f37925]) ).
fof(f37925,plain,
( spl0_1229
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f37643,plain,
( spl0_1202
<=> ! [X0,X1] :
( y = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f37646,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
| ~ spl0_168
| ~ spl0_1202 ),
inference(forward_demodulation,[],[f37644,f1430]) ).
fof(f37644,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation)
| y = intersection(X0,intersection(identity_relation,X1)) )
| ~ spl0_1202 ),
inference(avatar_component_clause,[],[f37643]) ).
fof(f37923,plain,
( spl0_1228
| ~ spl0_168
| ~ spl0_1201 ),
inference(avatar_split_clause,[],[f37641,f37638,f1428,f37921]) ).
fof(f37921,plain,
( spl0_1228
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f37638,plain,
( spl0_1201
<=> ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f37641,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
| ~ spl0_168
| ~ spl0_1201 ),
inference(forward_demodulation,[],[f37639,f1430]) ).
fof(f37639,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2))
| y = intersection(X0,intersection(X1,X2)) )
| ~ spl0_1201 ),
inference(avatar_component_clause,[],[f37638]) ).
fof(f37798,plain,
( spl0_1227
| ~ spl0_168
| ~ spl0_1199 ),
inference(avatar_split_clause,[],[f37630,f37627,f1428,f37796]) ).
fof(f37796,plain,
( spl0_1227
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f37627,plain,
( spl0_1199
<=> ! [X0,X1] :
( y = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f37630,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
| ~ spl0_168
| ~ spl0_1199 ),
inference(forward_demodulation,[],[f37628,f1430]) ).
fof(f37628,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation)
| y = intersection(X0,intersection(X1,identity_relation)) )
| ~ spl0_1199 ),
inference(avatar_component_clause,[],[f37627]) ).
fof(f37794,plain,
( spl0_1226
| ~ spl0_168
| ~ spl0_1198 ),
inference(avatar_split_clause,[],[f37625,f37622,f1428,f37792]) ).
fof(f37792,plain,
( spl0_1226
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f37622,plain,
( spl0_1198
<=> ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f37625,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
| ~ spl0_168
| ~ spl0_1198 ),
inference(forward_demodulation,[],[f37623,f1430]) ).
fof(f37623,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(intersection(X0,X1),X2),complement(X0))
| y = intersection(intersection(X0,X1),X2) )
| ~ spl0_1198 ),
inference(avatar_component_clause,[],[f37622]) ).
fof(f37790,plain,
( spl0_1225
| ~ spl0_168
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f37098,f37095,f1428,f37788]) ).
fof(f37788,plain,
( spl0_1225
<=> ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f37095,plain,
( spl0_1197
<=> ! [X0] :
( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
| y = intersection(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f37098,plain,
( ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_168
| ~ spl0_1197 ),
inference(forward_demodulation,[],[f37096,f1430]) ).
fof(f37096,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
| y = intersection(identity_relation,X0) )
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f37095]) ).
fof(f37786,plain,
( spl0_1224
| ~ spl0_168
| ~ spl0_1194 ),
inference(avatar_split_clause,[],[f37082,f37079,f1428,f37784]) ).
fof(f37784,plain,
( spl0_1224
<=> ! [X0,X1] :
( singleton_relation = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f37079,plain,
( spl0_1194
<=> ! [X0,X1] :
( y = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f37082,plain,
( ! [X0,X1] :
( singleton_relation = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
| ~ spl0_168
| ~ spl0_1194 ),
inference(forward_demodulation,[],[f37080,f1430]) ).
fof(f37080,plain,
( ! [X0,X1] :
( member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation)
| y = intersection(intersection(identity_relation,X0),X1) )
| ~ spl0_1194 ),
inference(avatar_component_clause,[],[f37079]) ).
fof(f37782,plain,
( spl0_1223
| ~ spl0_168
| ~ spl0_1193 ),
inference(avatar_split_clause,[],[f37077,f37074,f1428,f37780]) ).
fof(f37780,plain,
( spl0_1223
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f37074,plain,
( spl0_1193
<=> ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f37077,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
| ~ spl0_168
| ~ spl0_1193 ),
inference(forward_demodulation,[],[f37075,f1430]) ).
fof(f37075,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(intersection(X0,X1),X2),complement(X1))
| y = intersection(intersection(X0,X1),X2) )
| ~ spl0_1193 ),
inference(avatar_component_clause,[],[f37074]) ).
fof(f37778,plain,
( spl0_1222
| ~ spl0_168
| ~ spl0_1191 ),
inference(avatar_split_clause,[],[f37066,f37063,f1428,f37776]) ).
fof(f37776,plain,
( spl0_1222
<=> ! [X0,X1] :
( singleton_relation = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f37063,plain,
( spl0_1191
<=> ! [X0,X1] :
( y = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f37066,plain,
( ! [X0,X1] :
( singleton_relation = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
| ~ spl0_168
| ~ spl0_1191 ),
inference(forward_demodulation,[],[f37064,f1430]) ).
fof(f37064,plain,
( ! [X0,X1] :
( member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation)
| y = intersection(intersection(X0,identity_relation),X1) )
| ~ spl0_1191 ),
inference(avatar_component_clause,[],[f37063]) ).
fof(f37774,plain,
( spl0_1221
| ~ spl0_168
| ~ spl0_1190 ),
inference(avatar_split_clause,[],[f37061,f37058,f1428,f37772]) ).
fof(f37772,plain,
( spl0_1221
<=> ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,complement(X0))
| ~ member(regular(cross_product(X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f37058,plain,
( spl0_1190
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| y = cross_product(X1,X2)
| ~ member(regular(cross_product(X1,X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f37061,plain,
( ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,complement(X0))
| ~ member(regular(cross_product(X1,X2)),X0) )
| ~ spl0_168
| ~ spl0_1190 ),
inference(forward_demodulation,[],[f37059,f1430]) ).
fof(f37059,plain,
( ! [X2,X0,X1] :
( ~ member(regular(cross_product(X1,X2)),X0)
| y = cross_product(X1,X2)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl0_1190 ),
inference(avatar_component_clause,[],[f37058]) ).
fof(f37770,plain,
( spl0_1220
| ~ spl0_168
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f37056,f37053,f1428,f37768]) ).
fof(f37768,plain,
( spl0_1220
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X2,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f37053,plain,
( spl0_1189
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| y = intersection(X2,X0)
| ~ member(regular(intersection(X2,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f37056,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X2,X0)),X1) )
| ~ spl0_168
| ~ spl0_1189 ),
inference(forward_demodulation,[],[f37054,f1430]) ).
fof(f37054,plain,
( ! [X2,X0,X1] :
( ~ member(regular(intersection(X2,X0)),X1)
| y = intersection(X2,X0)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f37053]) ).
fof(f37766,plain,
( spl0_1219
| ~ spl0_168
| ~ spl0_1188 ),
inference(avatar_split_clause,[],[f37051,f37048,f1428,f37764]) ).
fof(f37764,plain,
( spl0_1219
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f37048,plain,
( spl0_1188
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| y = intersection(X0,X2)
| ~ member(regular(intersection(X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f37051,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,complement(X1))
| ~ member(regular(intersection(X0,X2)),X1) )
| ~ spl0_168
| ~ spl0_1188 ),
inference(forward_demodulation,[],[f37049,f1430]) ).
fof(f37049,plain,
( ! [X2,X0,X1] :
( ~ member(regular(intersection(X0,X2)),X1)
| y = intersection(X0,X2)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_1188 ),
inference(avatar_component_clause,[],[f37048]) ).
fof(f37762,plain,
( spl0_1218
| ~ spl0_168
| ~ spl0_1187 ),
inference(avatar_split_clause,[],[f36752,f36749,f1428,f37760]) ).
fof(f37760,plain,
( spl0_1218
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f36749,plain,
( spl0_1187
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f36752,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_168
| ~ spl0_1187 ),
inference(forward_demodulation,[],[f36750,f1430]) ).
fof(f36750,plain,
( ! [X0,X1] :
( ~ subclass(X0,flip(X1))
| y = X0
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_1187 ),
inference(avatar_component_clause,[],[f36749]) ).
fof(f37758,plain,
( spl0_1217
| ~ spl0_168
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1116 ),
inference(avatar_split_clause,[],[f34601,f34034,f9421,f8731,f1428,f37756]) ).
fof(f34601,plain,
( ! [X0] : singleton_relation = cross_product(singleton_relation,X0)
| ~ spl0_168
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1116 ),
inference(forward_demodulation,[],[f34600,f1430]) ).
fof(f34600,plain,
( ! [X0] : singleton_relation = cross_product(y,X0)
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1116 ),
inference(forward_demodulation,[],[f34576,f9423]) ).
fof(f34576,plain,
( ! [X0] : singleton_relation = cross_product(domain_of(y),X0)
| ~ spl0_550
| ~ spl0_1116 ),
inference(resolution,[],[f34035,f8732]) ).
fof(f37754,plain,
( spl0_1216
| ~ spl0_168
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f36747,f36744,f1428,f37752]) ).
fof(f37752,plain,
( spl0_1216
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f36744,plain,
( spl0_1186
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f36747,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_168
| ~ spl0_1186 ),
inference(forward_demodulation,[],[f36745,f1430]) ).
fof(f36745,plain,
( ! [X0,X1] :
( ~ subclass(X0,rotate(X1))
| y = X0
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_1186 ),
inference(avatar_component_clause,[],[f36744]) ).
fof(f37750,plain,
( spl0_1215
| ~ spl0_168
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f36742,f36739,f1428,f37748]) ).
fof(f37748,plain,
( spl0_1215
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f36739,plain,
( spl0_1185
<=> ! [X0] :
( y = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f36742,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) )
| ~ spl0_168
| ~ spl0_1185 ),
inference(forward_demodulation,[],[f36740,f1430]) ).
fof(f36740,plain,
( ! [X0] :
( ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| y = X0
| ~ member(regular(X0),identity_relation) )
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f36739]) ).
fof(f37745,plain,
( spl0_1214
| ~ spl0_16
| ~ spl0_523 ),
inference(avatar_split_clause,[],[f8214,f8088,f278,f37743]) ).
fof(f37743,plain,
( spl0_1214
<=> ! [X2,X0,X1] :
( member(regular(intersection(X0,cross_product(X1,X2))),universal_class)
| y = intersection(X0,cross_product(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f278,plain,
( spl0_16
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f8088,plain,
( spl0_523
<=> ! [X2,X0,X1] :
( y = intersection(X0,cross_product(X1,X2))
| regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f8214,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(X0,cross_product(X1,X2))),universal_class)
| y = intersection(X0,cross_product(X1,X2)) )
| ~ spl0_16
| ~ spl0_523 ),
inference(superposition,[],[f279,f8089]) ).
fof(f8089,plain,
( ! [X2,X0,X1] :
( regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2)))))))
| y = intersection(X0,cross_product(X1,X2)) )
| ~ spl0_523 ),
inference(avatar_component_clause,[],[f8088]) ).
fof(f279,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f37740,plain,
( spl0_1213
| ~ spl0_16
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f8145,f8084,f278,f37738]) ).
fof(f37738,plain,
( spl0_1213
<=> ! [X2,X0,X1] :
( member(regular(intersection(cross_product(X0,X1),X2)),universal_class)
| y = intersection(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f8084,plain,
( spl0_522
<=> ! [X2,X0,X1] :
( y = intersection(cross_product(X0,X1),X2)
| regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f8145,plain,
( ! [X2,X0,X1] :
( member(regular(intersection(cross_product(X0,X1),X2)),universal_class)
| y = intersection(cross_product(X0,X1),X2) )
| ~ spl0_16
| ~ spl0_522 ),
inference(superposition,[],[f279,f8085]) ).
fof(f8085,plain,
( ! [X2,X0,X1] :
( regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2))))))
| y = intersection(cross_product(X0,X1),X2) )
| ~ spl0_522 ),
inference(avatar_component_clause,[],[f8084]) ).
fof(f37734,plain,
( spl0_1212
| ~ spl0_34
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4184,f4104,f361,f37732]) ).
fof(f4104,plain,
( spl0_342
<=> ! [X2,X0,X1] :
( ~ subclass(X0,regular(X1))
| subclass(X0,X2)
| member(not_subclass_element(X0,X2),y)
| ~ member(not_subclass_element(X0,X2),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f4184,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),y)
| ~ subclass(X0,regular(X0))
| y = X0 )
| ~ spl0_34
| ~ spl0_342 ),
inference(duplicate_literal_removal,[],[f4153]) ).
fof(f4153,plain,
( ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),y)
| ~ subclass(X0,regular(X0))
| y = X0
| subclass(X0,X1) )
| ~ spl0_34
| ~ spl0_342 ),
inference(resolution,[],[f4105,f362]) ).
fof(f4105,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2)
| member(not_subclass_element(X0,X2),y)
| ~ subclass(X0,regular(X1))
| y = X1 )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4104]) ).
fof(f37727,plain,
( spl0_1211
| ~ spl0_154
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3795,f3634,f1287,f37725]) ).
fof(f3795,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,y),X1)
| subclass(X0,y)
| y = X1
| ~ subclass(X0,regular(X1)) )
| ~ spl0_154
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3786]) ).
fof(f3786,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,y),X1)
| subclass(X0,y)
| y = X1
| ~ subclass(X0,regular(X1))
| subclass(X0,y) )
| ~ spl0_154
| ~ spl0_323 ),
inference(resolution,[],[f3635,f1288]) ).
fof(f37703,plain,
( spl0_1210
| ~ spl0_168
| ~ spl0_1209 ),
inference(avatar_split_clause,[],[f37699,f37696,f1428,f37701]) ).
fof(f37701,plain,
( spl0_1210
<=> ! [X2] :
( singleton_relation = X2
| ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f37696,plain,
( spl0_1209
<=> ! [X2] :
( ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2)
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f37699,plain,
( ! [X2] :
( singleton_relation = X2
| ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2) )
| ~ spl0_168
| ~ spl0_1209 ),
inference(forward_demodulation,[],[f37697,f1430]) ).
fof(f37697,plain,
( ! [X2] :
( ~ subclass(universal_class,regular(X2))
| ~ subclass(universal_class,X2)
| y = X2 )
| ~ spl0_1209 ),
inference(avatar_component_clause,[],[f37696]) ).
fof(f37698,plain,
( spl0_1209
| spl0_1102
| ~ spl0_137
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3750,f3608,f1078,f33959,f37696]) ).
fof(f33959,plain,
( spl0_1102
<=> ! [X0,X1] : member(unordered_pair(X0,X1),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1078,plain,
( spl0_137
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f3608,plain,
( spl0_318
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,regular(X0))
| member(unordered_pair(X1,X2),y)
| ~ member(unordered_pair(X1,X2),X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f3750,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),y)
| ~ subclass(universal_class,regular(X2))
| y = X2
| ~ subclass(universal_class,X2) )
| ~ spl0_137
| ~ spl0_318 ),
inference(resolution,[],[f3609,f1079]) ).
fof(f1079,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f3609,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| member(unordered_pair(X1,X2),y)
| ~ subclass(universal_class,regular(X0))
| y = X0 )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f3608]) ).
fof(f37675,plain,
( spl0_1208
| ~ spl0_168
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f34535,f34030,f9421,f8731,f1428,f37673]) ).
fof(f34535,plain,
( ! [X0] : singleton_relation = cross_product(X0,singleton_relation)
| ~ spl0_168
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1115 ),
inference(forward_demodulation,[],[f34534,f1430]) ).
fof(f34534,plain,
( ! [X0] : singleton_relation = cross_product(X0,y)
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1115 ),
inference(forward_demodulation,[],[f34504,f9423]) ).
fof(f34504,plain,
( ! [X0] : singleton_relation = cross_product(X0,domain_of(y))
| ~ spl0_550
| ~ spl0_1115 ),
inference(resolution,[],[f34031,f8732]) ).
fof(f37671,plain,
( spl0_1207
| spl0_882
| ~ spl0_19
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3501,f3426,f292,f21901,f37669]) ).
fof(f37669,plain,
( spl0_1207
<=> ! [X0,X1] :
( regular(omega) = X0
| ~ inductive(unordered_pair(X0,X1))
| regular(omega) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f3426,plain,
( spl0_300
<=> ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| y = X0
| regular(X0) = X1
| regular(X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3501,plain,
( ! [X0,X1] :
( omega = y
| regular(omega) = X0
| regular(omega) = X1
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_19
| ~ spl0_300 ),
inference(resolution,[],[f3427,f293]) ).
fof(f3427,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| y = X0
| regular(X0) = X1
| regular(X0) = X2 )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f3426]) ).
fof(f37666,plain,
( spl0_1206
| ~ spl0_248
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3352,f3209,f2450,f37664]) ).
fof(f3352,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
| ~ spl0_248
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f3326]) ).
fof(f3326,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| y = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X1)) )
| ~ spl0_248
| ~ spl0_292 ),
inference(resolution,[],[f3210,f2451]) ).
fof(f37661,plain,
( spl0_1205
| ~ spl0_50
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3349,f3209,f441,f37659]) ).
fof(f441,plain,
( spl0_50
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f3349,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),domain_of(flip(cross_product(subset_relation,universal_class))))
| y = intersection(X0,identity_relation) )
| ~ spl0_50
| ~ spl0_292 ),
inference(superposition,[],[f3210,f443]) ).
fof(f443,plain,
( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f37656,plain,
( spl0_1204
| ~ spl0_49
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3348,f3209,f436,f37654]) ).
fof(f37654,plain,
( spl0_1204
<=> ! [X0] :
( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(identity_relation))))
| y = intersection(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f3348,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),complement(compose(element_relation,complement(identity_relation))))
| y = intersection(X0,singleton_relation) )
| ~ spl0_49
| ~ spl0_292 ),
inference(superposition,[],[f3210,f438]) ).
fof(f37650,plain,
( spl0_1203
| ~ spl0_130
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3342,f3209,f1005,f37648]) ).
fof(f37648,plain,
( spl0_1203
<=> ! [X0,X1] :
( y = intersection(X0,intersection(singleton_relation,X1))
| member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f3342,plain,
( ! [X0,X1] :
( y = intersection(X0,intersection(singleton_relation,X1))
| member(regular(intersection(X0,intersection(singleton_relation,X1))),element_relation) )
| ~ spl0_130
| ~ spl0_292 ),
inference(resolution,[],[f3210,f1006]) ).
fof(f37645,plain,
( spl0_1202
| ~ spl0_131
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3340,f3209,f1009,f37643]) ).
fof(f1009,plain,
( spl0_131
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f3340,plain,
( ! [X0,X1] :
( y = intersection(X0,intersection(identity_relation,X1))
| member(regular(intersection(X0,intersection(identity_relation,X1))),subset_relation) )
| ~ spl0_131
| ~ spl0_292 ),
inference(resolution,[],[f3210,f1010]) ).
fof(f1010,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f37640,plain,
( spl0_1201
| ~ spl0_248
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3323,f3205,f2450,f37638]) ).
fof(f3323,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
| ~ spl0_248
| ~ spl0_291 ),
inference(duplicate_literal_removal,[],[f3297]) ).
fof(f3297,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| y = intersection(X0,intersection(X1,X2))
| ~ subclass(intersection(X0,intersection(X1,X2)),complement(X2)) )
| ~ spl0_248
| ~ spl0_291 ),
inference(resolution,[],[f3206,f2451]) ).
fof(f37634,plain,
( spl0_1200
| ~ spl0_130
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3313,f3205,f1005,f37632]) ).
fof(f3313,plain,
( ! [X0,X1] :
( y = intersection(X0,intersection(X1,singleton_relation))
| member(regular(intersection(X0,intersection(X1,singleton_relation))),element_relation) )
| ~ spl0_130
| ~ spl0_291 ),
inference(resolution,[],[f3206,f1006]) ).
fof(f37629,plain,
( spl0_1199
| ~ spl0_131
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3311,f3205,f1009,f37627]) ).
fof(f3311,plain,
( ! [X0,X1] :
( y = intersection(X0,intersection(X1,identity_relation))
| member(regular(intersection(X0,intersection(X1,identity_relation))),subset_relation) )
| ~ spl0_131
| ~ spl0_291 ),
inference(resolution,[],[f3206,f1010]) ).
fof(f37624,plain,
( spl0_1198
| ~ spl0_248
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3294,f3201,f2450,f37622]) ).
fof(f3294,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
| ~ spl0_248
| ~ spl0_290 ),
inference(duplicate_literal_removal,[],[f3268]) ).
fof(f3268,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| y = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X0)) )
| ~ spl0_248
| ~ spl0_290 ),
inference(resolution,[],[f3202,f2451]) ).
fof(f37097,plain,
( spl0_1197
| ~ spl0_50
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3291,f3201,f441,f37095]) ).
fof(f3291,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),domain_of(flip(cross_product(subset_relation,universal_class))))
| y = intersection(identity_relation,X0) )
| ~ spl0_50
| ~ spl0_290 ),
inference(superposition,[],[f3202,f443]) ).
fof(f37092,plain,
( spl0_1196
| ~ spl0_49
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3290,f3201,f436,f37090]) ).
fof(f37090,plain,
( spl0_1196
<=> ! [X0] :
( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(identity_relation))))
| y = intersection(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f3290,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),complement(compose(element_relation,complement(identity_relation))))
| y = intersection(singleton_relation,X0) )
| ~ spl0_49
| ~ spl0_290 ),
inference(superposition,[],[f3202,f438]) ).
fof(f37086,plain,
( spl0_1195
| ~ spl0_130
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3284,f3201,f1005,f37084]) ).
fof(f37084,plain,
( spl0_1195
<=> ! [X0,X1] :
( y = intersection(intersection(singleton_relation,X0),X1)
| member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f3284,plain,
( ! [X0,X1] :
( y = intersection(intersection(singleton_relation,X0),X1)
| member(regular(intersection(intersection(singleton_relation,X0),X1)),element_relation) )
| ~ spl0_130
| ~ spl0_290 ),
inference(resolution,[],[f3202,f1006]) ).
fof(f37081,plain,
( spl0_1194
| ~ spl0_131
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3282,f3201,f1009,f37079]) ).
fof(f3282,plain,
( ! [X0,X1] :
( y = intersection(intersection(identity_relation,X0),X1)
| member(regular(intersection(intersection(identity_relation,X0),X1)),subset_relation) )
| ~ spl0_131
| ~ spl0_290 ),
inference(resolution,[],[f3202,f1010]) ).
fof(f37076,plain,
( spl0_1193
| ~ spl0_248
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3265,f3197,f2450,f37074]) ).
fof(f3265,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
| ~ spl0_248
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3239]) ).
fof(f3239,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| y = intersection(intersection(X0,X1),X2)
| ~ subclass(intersection(intersection(X0,X1),X2),complement(X1)) )
| ~ spl0_248
| ~ spl0_289 ),
inference(resolution,[],[f3198,f2451]) ).
fof(f37070,plain,
( spl0_1192
| ~ spl0_130
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3255,f3197,f1005,f37068]) ).
fof(f3255,plain,
( ! [X0,X1] :
( y = intersection(intersection(X0,singleton_relation),X1)
| member(regular(intersection(intersection(X0,singleton_relation),X1)),element_relation) )
| ~ spl0_130
| ~ spl0_289 ),
inference(resolution,[],[f3198,f1006]) ).
fof(f37065,plain,
( spl0_1191
| ~ spl0_131
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3253,f3197,f1009,f37063]) ).
fof(f3253,plain,
( ! [X0,X1] :
( y = intersection(intersection(X0,identity_relation),X1)
| member(regular(intersection(intersection(X0,identity_relation),X1)),subset_relation) )
| ~ spl0_131
| ~ spl0_289 ),
inference(resolution,[],[f3198,f1010]) ).
fof(f37060,plain,
( spl0_1190
| ~ spl0_29
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3154,f3019,f334,f37058]) ).
fof(f3154,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| y = cross_product(X1,X2)
| ~ member(regular(cross_product(X1,X2)),X0) )
| ~ spl0_29
| ~ spl0_286 ),
inference(resolution,[],[f3020,f335]) ).
fof(f37055,plain,
( spl0_1189
| ~ spl0_29
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3097,f2988,f334,f37053]) ).
fof(f3097,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| y = intersection(X2,X0)
| ~ member(regular(intersection(X2,X0)),X1) )
| ~ spl0_29
| ~ spl0_282 ),
inference(resolution,[],[f2989,f335]) ).
fof(f37050,plain,
( spl0_1188
| ~ spl0_29
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3044,f2980,f334,f37048]) ).
fof(f3044,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| y = intersection(X0,X2)
| ~ member(regular(intersection(X0,X2)),X1) )
| ~ spl0_29
| ~ spl0_280 ),
inference(resolution,[],[f2981,f335]) ).
fof(f36751,plain,
( spl0_1187
| ~ spl0_42
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2882,f2826,f393,f36749]) ).
fof(f393,plain,
( spl0_42
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f2882,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,flip(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_42
| ~ spl0_272 ),
inference(resolution,[],[f2827,f394]) ).
fof(f394,plain,
( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f36746,plain,
( spl0_1186
| ~ spl0_41
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2881,f2826,f389,f36744]) ).
fof(f389,plain,
( spl0_41
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2881,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,rotate(X1))
| member(regular(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_41
| ~ spl0_272 ),
inference(resolution,[],[f2827,f390]) ).
fof(f390,plain,
( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f36741,plain,
( spl0_1185
| ~ spl0_153
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2667,f2450,f1264,f36739]) ).
fof(f1264,plain,
( spl0_153
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f2667,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(regular(X0),identity_relation) )
| ~ spl0_153
| ~ spl0_248 ),
inference(resolution,[],[f2451,f1265]) ).
fof(f1265,plain,
( ! [X0] :
( member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,identity_relation) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1264]) ).
fof(f36098,plain,
( spl0_1184
| ~ spl0_168
| ~ spl0_539 ),
inference(avatar_split_clause,[],[f13945,f8422,f1428,f36096]) ).
fof(f13945,plain,
( ! [X0] : singleton_relation = intersection(X0,singleton_relation)
| ~ spl0_168
| ~ spl0_539 ),
inference(superposition,[],[f8423,f1430]) ).
fof(f35370,plain,
( spl0_1183
| ~ spl0_168
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f13944,f8328,f1428,f35368]) ).
fof(f13944,plain,
( ! [X0] : singleton_relation = intersection(singleton_relation,X0)
| ~ spl0_168
| ~ spl0_531 ),
inference(superposition,[],[f8329,f1430]) ).
fof(f35366,plain,
( spl0_1182
| ~ spl0_168
| ~ spl0_1155 ),
inference(avatar_split_clause,[],[f35181,f35178,f1428,f35364]) ).
fof(f35364,plain,
( spl0_1182
<=> ! [X0,X1] :
( singleton_relation = unordered_pair(X1,X0)
| member(X0,universal_class)
| regular(unordered_pair(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f35178,plain,
( spl0_1155
<=> ! [X0,X1] :
( member(X0,universal_class)
| y = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f35181,plain,
( ! [X0,X1] :
( singleton_relation = unordered_pair(X1,X0)
| member(X0,universal_class)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_168
| ~ spl0_1155 ),
inference(forward_demodulation,[],[f35179,f1430]) ).
fof(f35179,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| y = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_1155 ),
inference(avatar_component_clause,[],[f35178]) ).
fof(f35362,plain,
( spl0_1181
| ~ spl0_168
| ~ spl0_1154 ),
inference(avatar_split_clause,[],[f35176,f35173,f1428,f35360]) ).
fof(f35360,plain,
( spl0_1181
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = singleton_relation
| member(X0,universal_class)
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f35173,plain,
( spl0_1154
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f35176,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = singleton_relation
| member(X0,universal_class)
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_168
| ~ spl0_1154 ),
inference(forward_demodulation,[],[f35174,f1430]) ).
fof(f35174,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_1154 ),
inference(avatar_component_clause,[],[f35173]) ).
fof(f35358,plain,
( spl0_1180
| ~ spl0_168
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f35162,f35159,f1428,f35356]) ).
fof(f35356,plain,
( spl0_1180
<=> ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,X0)
| ~ subclass(cross_product(X1,X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f35159,plain,
( spl0_1151
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| y = cross_product(X1,X2)
| ~ subclass(cross_product(X1,X2),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f35162,plain,
( ! [X2,X0,X1] :
( singleton_relation = cross_product(X1,X2)
| ~ subclass(universal_class,X0)
| ~ subclass(cross_product(X1,X2),complement(X0)) )
| ~ spl0_168
| ~ spl0_1151 ),
inference(forward_demodulation,[],[f35160,f1430]) ).
fof(f35160,plain,
( ! [X2,X0,X1] :
( ~ subclass(cross_product(X1,X2),complement(X0))
| y = cross_product(X1,X2)
| ~ subclass(universal_class,X0) )
| ~ spl0_1151 ),
inference(avatar_component_clause,[],[f35159]) ).
fof(f35354,plain,
( spl0_1179
| ~ spl0_168
| ~ spl0_1150 ),
inference(avatar_split_clause,[],[f35157,f35154,f1428,f35352]) ).
fof(f35352,plain,
( spl0_1179
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X2,X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f35154,plain,
( spl0_1150
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X2,X0)
| ~ subclass(intersection(X2,X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f35157,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X2,X0)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X2,X0),complement(X1)) )
| ~ spl0_168
| ~ spl0_1150 ),
inference(forward_demodulation,[],[f35155,f1430]) ).
fof(f35155,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X2,X0),complement(X1))
| y = intersection(X2,X0)
| ~ subclass(X0,X1) )
| ~ spl0_1150 ),
inference(avatar_component_clause,[],[f35154]) ).
fof(f35350,plain,
( spl0_1178
| ~ spl0_168
| ~ spl0_1148 ),
inference(avatar_split_clause,[],[f35147,f35144,f1428,f35348]) ).
fof(f35348,plain,
( spl0_1178
<=> ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X1,X0)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f35144,plain,
( spl0_1148
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| y = intersection(X1,X0)
| member(regular(intersection(X1,X0)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f35147,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,X0)
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X1,X0)),subset_relation) )
| ~ spl0_168
| ~ spl0_1148 ),
inference(forward_demodulation,[],[f35145,f1430]) ).
fof(f35145,plain,
( ! [X0,X1] :
( member(regular(intersection(X1,X0)),subset_relation)
| y = intersection(X1,X0)
| ~ subclass(X0,identity_relation) )
| ~ spl0_1148 ),
inference(avatar_component_clause,[],[f35144]) ).
fof(f35346,plain,
( spl0_1177
| ~ spl0_168
| ~ spl0_1147 ),
inference(avatar_split_clause,[],[f35142,f35139,f1428,f35344]) ).
fof(f35344,plain,
( spl0_1177
<=> ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X0,X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f35139,plain,
( spl0_1147
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,X2)
| ~ subclass(intersection(X0,X2),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f35142,plain,
( ! [X2,X0,X1] :
( singleton_relation = intersection(X0,X2)
| ~ subclass(X0,X1)
| ~ subclass(intersection(X0,X2),complement(X1)) )
| ~ spl0_168
| ~ spl0_1147 ),
inference(forward_demodulation,[],[f35140,f1430]) ).
fof(f35140,plain,
( ! [X2,X0,X1] :
( ~ subclass(intersection(X0,X2),complement(X1))
| y = intersection(X0,X2)
| ~ subclass(X0,X1) )
| ~ spl0_1147 ),
inference(avatar_component_clause,[],[f35139]) ).
fof(f35342,plain,
( spl0_1176
| ~ spl0_168
| ~ spl0_1144 ),
inference(avatar_split_clause,[],[f35127,f35124,f1428,f35340]) ).
fof(f35340,plain,
( spl0_1176
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X0,X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f35124,plain,
( spl0_1144
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| intersection(X0,X1) = y
| member(regular(intersection(X0,X1)),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f35127,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(X0,identity_relation)
| member(regular(intersection(X0,X1)),subset_relation) )
| ~ spl0_168
| ~ spl0_1144 ),
inference(forward_demodulation,[],[f35125,f1430]) ).
fof(f35125,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),subset_relation)
| intersection(X0,X1) = y
| ~ subclass(X0,identity_relation) )
| ~ spl0_1144 ),
inference(avatar_component_clause,[],[f35124]) ).
fof(f35338,plain,
( spl0_1175
| ~ spl0_168
| ~ spl0_1143 ),
inference(avatar_split_clause,[],[f35122,f35119,f1428,f35336]) ).
fof(f35336,plain,
( spl0_1175
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f35119,plain,
( spl0_1143
<=> ! [X0] :
( y = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f35122,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_168
| ~ spl0_1143 ),
inference(forward_demodulation,[],[f35120,f1430]) ).
fof(f35120,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ subclass(X0,application_function)
| y = X0 )
| ~ spl0_1143 ),
inference(avatar_component_clause,[],[f35119]) ).
fof(f35334,plain,
( spl0_1174
| ~ spl0_168
| ~ spl0_1142 ),
inference(avatar_split_clause,[],[f35117,f35114,f1428,f35332]) ).
fof(f35332,plain,
( spl0_1174
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f35114,plain,
( spl0_1142
<=> ! [X0] :
( y = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f35117,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_168
| ~ spl0_1142 ),
inference(forward_demodulation,[],[f35115,f1430]) ).
fof(f35115,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ subclass(X0,composition_function)
| y = X0 )
| ~ spl0_1142 ),
inference(avatar_component_clause,[],[f35114]) ).
fof(f35330,plain,
( spl0_1173
| ~ spl0_168
| ~ spl0_1141 ),
inference(avatar_split_clause,[],[f35112,f35109,f1428,f35328]) ).
fof(f35328,plain,
( spl0_1173
<=> ! [X2,X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f35109,plain,
( spl0_1141
<=> ! [X2,X0,X1] :
( y = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f35112,plain,
( ! [X2,X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1141 ),
inference(forward_demodulation,[],[f35110,f1430]) ).
fof(f35110,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,compose(X1,X2))
| y = X0
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_1141 ),
inference(avatar_component_clause,[],[f35109]) ).
fof(f35326,plain,
( spl0_1172
| ~ spl0_168
| ~ spl0_1140 ),
inference(avatar_split_clause,[],[f35107,f35104,f1428,f35324]) ).
fof(f35324,plain,
( spl0_1172
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f35107,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) )
| ~ spl0_168
| ~ spl0_1140 ),
inference(forward_demodulation,[],[f35105,f1430]) ).
fof(f35105,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = X0
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) )
| ~ spl0_1140 ),
inference(avatar_component_clause,[],[f35104]) ).
fof(f35322,plain,
( spl0_1171
| ~ spl0_168
| ~ spl0_1139 ),
inference(avatar_split_clause,[],[f35102,f35099,f1428,f35320]) ).
fof(f35320,plain,
( spl0_1171
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f35099,plain,
( spl0_1139
<=> ! [X0] :
( ~ subclass(X0,identity_relation)
| y = X0
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f35102,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_168
| ~ spl0_1139 ),
inference(forward_demodulation,[],[f35100,f1430]) ).
fof(f35100,plain,
( ! [X0] :
( member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| y = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_1139 ),
inference(avatar_component_clause,[],[f35099]) ).
fof(f35318,plain,
( spl0_1170
| ~ spl0_168
| ~ spl0_1137 ),
inference(avatar_split_clause,[],[f35092,f35089,f1428,f35316]) ).
fof(f35316,plain,
( spl0_1170
<=> ! [X0,X1] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f35089,plain,
( spl0_1137
<=> ! [X0,X1] :
( y = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f35092,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) )
| ~ spl0_168
| ~ spl0_1137 ),
inference(forward_demodulation,[],[f35090,f1430]) ).
fof(f35090,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,identity_relation)),X1)
| ~ subclass(subset_relation,X1)
| y = intersection(X0,identity_relation) )
| ~ spl0_1137 ),
inference(avatar_component_clause,[],[f35089]) ).
fof(f35314,plain,
( spl0_1169
| ~ spl0_168
| ~ spl0_1136 ),
inference(avatar_split_clause,[],[f35087,f35084,f1428,f35312]) ).
fof(f35312,plain,
( spl0_1169
<=> ! [X0,X1] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f35084,plain,
( spl0_1136
<=> ! [X0,X1] :
( y = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f35087,plain,
( ! [X0,X1] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) )
| ~ spl0_168
| ~ spl0_1136 ),
inference(forward_demodulation,[],[f35085,f1430]) ).
fof(f35085,plain,
( ! [X0,X1] :
( member(regular(intersection(identity_relation,X0)),X1)
| ~ subclass(subset_relation,X1)
| y = intersection(identity_relation,X0) )
| ~ spl0_1136 ),
inference(avatar_component_clause,[],[f35084]) ).
fof(f35310,plain,
( spl0_1168
| ~ spl0_168
| ~ spl0_1133 ),
inference(avatar_split_clause,[],[f35072,f35069,f1428,f35308]) ).
fof(f35308,plain,
( spl0_1168
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f35069,plain,
( spl0_1133
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f35072,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) )
| ~ spl0_168
| ~ spl0_1133 ),
inference(forward_demodulation,[],[f35070,f1430]) ).
fof(f35070,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| y = X0
| ~ member(regular(X0),universal_class) )
| ~ spl0_1133 ),
inference(avatar_component_clause,[],[f35069]) ).
fof(f35306,plain,
( spl0_1167
| ~ spl0_168
| ~ spl0_1132 ),
inference(avatar_split_clause,[],[f35067,f35064,f1428,f35304]) ).
fof(f35304,plain,
( spl0_1167
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f35064,plain,
( spl0_1132
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f35067,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) )
| ~ spl0_168
| ~ spl0_1132 ),
inference(forward_demodulation,[],[f35065,f1430]) ).
fof(f35065,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| y = X0
| ~ member(regular(X0),universal_class) )
| ~ spl0_1132 ),
inference(avatar_component_clause,[],[f35064]) ).
fof(f35295,plain,
( spl0_1166
| ~ spl0_168
| ~ spl0_539
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1098
| ~ spl0_1115
| ~ spl0_1165 ),
inference(avatar_split_clause,[],[f35291,f35286,f34030,f33941,f9421,f8731,f8422,f1428,f35293]) ).
fof(f35293,plain,
( spl0_1166
<=> ! [X0,X1] :
( member(singleton_relation,X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f35286,plain,
( spl0_1165
<=> ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,singleton_relation))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f35291,plain,
( ! [X0,X1] :
( member(singleton_relation,X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) )
| ~ spl0_168
| ~ spl0_539
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1098
| ~ spl0_1115
| ~ spl0_1165 ),
inference(forward_demodulation,[],[f35290,f33943]) ).
fof(f33943,plain,
( singleton_relation = domain_of(singleton_relation)
| ~ spl0_1098 ),
inference(avatar_component_clause,[],[f33941]) ).
fof(f35290,plain,
( ! [X0,X1] :
( member(domain_of(singleton_relation),X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) )
| ~ spl0_168
| ~ spl0_539
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1115
| ~ spl0_1165 ),
inference(forward_demodulation,[],[f35289,f13945]) ).
fof(f35289,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,singleton_relation)),X1)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X1) )
| ~ spl0_168
| ~ spl0_550
| ~ spl0_567
| ~ spl0_1115
| ~ spl0_1165 ),
inference(forward_demodulation,[],[f35287,f34535]) ).
fof(f35287,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,singleton_relation))),X1) )
| ~ spl0_1165 ),
inference(avatar_component_clause,[],[f35286]) ).
fof(f35288,plain,
( spl0_1165
| ~ spl0_375
| ~ spl0_607 ),
inference(avatar_split_clause,[],[f29531,f10943,f4993,f35286]) ).
fof(f10943,plain,
( spl0_607
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f29531,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,singleton_relation))),X1) )
| ~ spl0_375
| ~ spl0_607 ),
inference(resolution,[],[f4994,f10944]) ).
fof(f10944,plain,
( ! [X2,X0,X1] :
( ~ member(X1,universal_class)
| ~ subclass(universal_class,X0)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
| ~ spl0_607 ),
inference(avatar_component_clause,[],[f10943]) ).
fof(f35284,plain,
( spl0_1164
| ~ spl0_8
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f17596,f11827,f242,f35282]) ).
fof(f35282,plain,
( spl0_1164
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f17596,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = subset_relation
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_8
| ~ spl0_639 ),
inference(resolution,[],[f11828,f243]) ).
fof(f35280,plain,
( ~ spl0_1163
| ~ spl0_168
| spl0_671 ),
inference(avatar_split_clause,[],[f13959,f13527,f1428,f35277]) ).
fof(f13527,plain,
( spl0_671
<=> y = cross_product(y,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f13959,plain,
( singleton_relation != cross_product(singleton_relation,universal_class)
| ~ spl0_168
| spl0_671 ),
inference(superposition,[],[f13529,f1430]) ).
fof(f13529,plain,
( y != cross_product(y,universal_class)
| spl0_671 ),
inference(avatar_component_clause,[],[f13527]) ).
fof(f35274,plain,
( spl0_1162
| ~ spl0_21
| ~ spl0_607 ),
inference(avatar_split_clause,[],[f10969,f10943,f301,f35272]) ).
fof(f35272,plain,
( spl0_1162
<=> ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,y))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f301,plain,
( spl0_21
<=> member(y,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f10969,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,y))),X1) )
| ~ spl0_21
| ~ spl0_607 ),
inference(resolution,[],[f10944,f302]) ).
fof(f302,plain,
( member(y,universal_class)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f35269,plain,
( spl0_1161
| ~ spl0_297
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f7335,f7230,f3231,f35267]) ).
fof(f35267,plain,
( spl0_1161
<=> ! [X2,X0,X1] :
( subclass(intersection(y,X0),X1)
| ~ subclass(intersection(y,X0),complement(X2))
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f7230,plain,
( spl0_485
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f7335,plain,
( ! [X2,X0,X1] :
( subclass(intersection(y,X0),X1)
| ~ subclass(intersection(y,X0),complement(X2))
| y = X2 )
| ~ spl0_297
| ~ spl0_485 ),
inference(duplicate_literal_removal,[],[f7310]) ).
fof(f7310,plain,
( ! [X2,X0,X1] :
( subclass(intersection(y,X0),X1)
| ~ subclass(intersection(y,X0),complement(X2))
| subclass(intersection(y,X0),X1)
| y = X2 )
| ~ spl0_297
| ~ spl0_485 ),
inference(resolution,[],[f7231,f3232]) ).
fof(f7231,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2)
| ~ subclass(X0,complement(X1)) )
| ~ spl0_485 ),
inference(avatar_component_clause,[],[f7230]) ).
fof(f35264,plain,
( spl0_1160
| ~ spl0_298
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f7334,f7230,f3235,f35262]) ).
fof(f35262,plain,
( spl0_1160
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,y),X1)
| ~ subclass(intersection(X0,y),complement(X2))
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f7334,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,y),X1)
| ~ subclass(intersection(X0,y),complement(X2))
| y = X2 )
| ~ spl0_298
| ~ spl0_485 ),
inference(duplicate_literal_removal,[],[f7311]) ).
fof(f7311,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,y),X1)
| ~ subclass(intersection(X0,y),complement(X2))
| subclass(intersection(X0,y),X1)
| y = X2 )
| ~ spl0_298
| ~ spl0_485 ),
inference(resolution,[],[f7231,f3236]) ).
fof(f35260,plain,
( spl0_366
| ~ spl0_1159
| ~ spl0_109
| spl0_368 ),
inference(avatar_split_clause,[],[f4504,f4496,f831,f35257,f4488]) ).
fof(f4488,plain,
( spl0_366
<=> y = domain_of(flip(cross_product(subset_relation,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f35257,plain,
( spl0_1159
<=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f4496,plain,
( spl0_368
<=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f4504,plain,
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
| y = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_109
| spl0_368 ),
inference(resolution,[],[f4498,f832]) ).
fof(f4498,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
| spl0_368 ),
inference(avatar_component_clause,[],[f4496]) ).
fof(f35255,plain,
( spl0_366
| ~ spl0_1158
| ~ spl0_109
| spl0_367 ),
inference(avatar_split_clause,[],[f4501,f4492,f831,f35252,f4488]) ).
fof(f35252,plain,
( spl0_1158
<=> subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f4492,plain,
( spl0_367
<=> member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f4501,plain,
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),identity_relation)
| y = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_109
| spl0_367 ),
inference(resolution,[],[f4493,f832]) ).
fof(f4493,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| spl0_367 ),
inference(avatar_component_clause,[],[f4492]) ).
fof(f35250,plain,
( spl0_363
| ~ spl0_1157
| ~ spl0_109
| spl0_365 ),
inference(avatar_split_clause,[],[f4486,f4478,f831,f35247,f4470]) ).
fof(f4470,plain,
( spl0_363
<=> complement(compose(element_relation,complement(identity_relation))) = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f35247,plain,
( spl0_1157
<=> subclass(complement(compose(element_relation,complement(identity_relation))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f4478,plain,
( spl0_365
<=> member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f4486,plain,
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),element_relation)
| complement(compose(element_relation,complement(identity_relation))) = y
| ~ spl0_109
| spl0_365 ),
inference(resolution,[],[f4480,f832]) ).
fof(f4480,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
| spl0_365 ),
inference(avatar_component_clause,[],[f4478]) ).
fof(f35186,plain,
( spl0_363
| ~ spl0_1156
| ~ spl0_109
| spl0_364 ),
inference(avatar_split_clause,[],[f4483,f4474,f831,f35183,f4470]) ).
fof(f35183,plain,
( spl0_1156
<=> subclass(complement(compose(element_relation,complement(identity_relation))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f4474,plain,
( spl0_364
<=> member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f4483,plain,
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),singleton_relation)
| complement(compose(element_relation,complement(identity_relation))) = y
| ~ spl0_109
| spl0_364 ),
inference(resolution,[],[f4475,f832]) ).
fof(f4475,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| spl0_364 ),
inference(avatar_component_clause,[],[f4474]) ).
fof(f35180,plain,
( spl0_1155
| ~ spl0_8
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4075,f4032,f242,f35178]) ).
fof(f4032,plain,
( spl0_335
<=> ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f4075,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| y = unordered_pair(X1,X0)
| regular(unordered_pair(X1,X0)) = X1 )
| ~ spl0_8
| ~ spl0_335 ),
inference(resolution,[],[f4033,f243]) ).
fof(f4033,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f4032]) ).
fof(f35175,plain,
( spl0_1154
| ~ spl0_8
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4070,f4027,f242,f35173]) ).
fof(f4027,plain,
( spl0_334
<=> ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f4070,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_8
| ~ spl0_334 ),
inference(resolution,[],[f4028,f243]) ).
fof(f4028,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_334 ),
inference(avatar_component_clause,[],[f4027]) ).
fof(f35171,plain,
( spl0_186
| ~ spl0_1152
| spl0_238
| spl0_1153
| ~ spl0_187
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3863,f3810,f1605,f35168,f2279,f35164,f1601]) ).
fof(f1601,plain,
( spl0_186
<=> identity_relation = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f35164,plain,
( spl0_1152
<=> subclass(identity_relation,regular(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f35168,plain,
( spl0_1153
<=> member(regular(identity_relation),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f1605,plain,
( spl0_187
<=> member(regular(identity_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f3863,plain,
( member(regular(identity_relation),y)
| subset_relation = y
| ~ subclass(identity_relation,regular(subset_relation))
| identity_relation = y
| ~ spl0_187
| ~ spl0_327 ),
inference(resolution,[],[f3811,f1607]) ).
fof(f1607,plain,
( member(regular(identity_relation),subset_relation)
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1605]) ).
fof(f35161,plain,
( spl0_1151
| ~ spl0_248
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3165,f3019,f2450,f35159]) ).
fof(f3165,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| y = cross_product(X1,X2)
| ~ subclass(cross_product(X1,X2),complement(X0)) )
| ~ spl0_248
| ~ spl0_286 ),
inference(duplicate_literal_removal,[],[f3146]) ).
fof(f3146,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| y = cross_product(X1,X2)
| y = cross_product(X1,X2)
| ~ subclass(cross_product(X1,X2),complement(X0)) )
| ~ spl0_248
| ~ spl0_286 ),
inference(resolution,[],[f3020,f2451]) ).
fof(f35156,plain,
( spl0_1150
| ~ spl0_248
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3114,f2988,f2450,f35154]) ).
fof(f3114,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X2,X0)
| ~ subclass(intersection(X2,X0),complement(X1)) )
| ~ spl0_248
| ~ spl0_282 ),
inference(duplicate_literal_removal,[],[f3089]) ).
fof(f3089,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X2,X0)
| y = intersection(X2,X0)
| ~ subclass(intersection(X2,X0),complement(X1)) )
| ~ spl0_248
| ~ spl0_282 ),
inference(resolution,[],[f2989,f2451]) ).
fof(f35151,plain,
( spl0_1149
| ~ spl0_130
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3106,f2988,f1005,f35149]) ).
fof(f3106,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| y = intersection(X1,X0)
| member(regular(intersection(X1,X0)),element_relation) )
| ~ spl0_130
| ~ spl0_282 ),
inference(resolution,[],[f2989,f1006]) ).
fof(f35146,plain,
( spl0_1148
| ~ spl0_131
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3104,f2988,f1009,f35144]) ).
fof(f3104,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| y = intersection(X1,X0)
| member(regular(intersection(X1,X0)),subset_relation) )
| ~ spl0_131
| ~ spl0_282 ),
inference(resolution,[],[f2989,f1010]) ).
fof(f35141,plain,
( spl0_1147
| ~ spl0_248
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3061,f2980,f2450,f35139]) ).
fof(f3061,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,X2)
| ~ subclass(intersection(X0,X2),complement(X1)) )
| ~ spl0_248
| ~ spl0_280 ),
inference(duplicate_literal_removal,[],[f3036]) ).
fof(f3036,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,X2)
| y = intersection(X0,X2)
| ~ subclass(intersection(X0,X2),complement(X1)) )
| ~ spl0_248
| ~ spl0_280 ),
inference(resolution,[],[f2981,f2451]) ).
fof(f35137,plain,
( spl0_1146
| ~ spl0_168
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f13955,f11087,f1428,f35134]) ).
fof(f35134,plain,
( spl0_1146
<=> universal_class = complement(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f11087,plain,
( spl0_612
<=> universal_class = complement(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f13955,plain,
( universal_class = complement(singleton_relation)
| ~ spl0_168
| ~ spl0_612 ),
inference(superposition,[],[f11089,f1430]) ).
fof(f11089,plain,
( universal_class = complement(y)
| ~ spl0_612 ),
inference(avatar_component_clause,[],[f11087]) ).
fof(f35131,plain,
( spl0_1145
| ~ spl0_130
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3053,f2980,f1005,f35129]) ).
fof(f3053,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| intersection(X0,X1) = y
| member(regular(intersection(X0,X1)),element_relation) )
| ~ spl0_130
| ~ spl0_280 ),
inference(resolution,[],[f2981,f1006]) ).
fof(f35126,plain,
( spl0_1144
| ~ spl0_131
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3051,f2980,f1009,f35124]) ).
fof(f3051,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| intersection(X0,X1) = y
| member(regular(intersection(X0,X1)),subset_relation) )
| ~ spl0_131
| ~ spl0_280 ),
inference(resolution,[],[f2981,f1010]) ).
fof(f35121,plain,
( spl0_1143
| ~ spl0_33
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2891,f2826,f352,f35119]) ).
fof(f352,plain,
( spl0_33
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f2891,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,application_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_33
| ~ spl0_272 ),
inference(resolution,[],[f2827,f354]) ).
fof(f354,plain,
( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f35116,plain,
( spl0_1142
| ~ spl0_32
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2889,f2826,f347,f35114]) ).
fof(f347,plain,
( spl0_32
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f2889,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,composition_function)
| member(regular(X0),cross_product(universal_class,cross_product(universal_class,universal_class))) )
| ~ spl0_32
| ~ spl0_272 ),
inference(resolution,[],[f2827,f349]) ).
fof(f349,plain,
( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f35111,plain,
( spl0_1141
| ~ spl0_30
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2885,f2826,f338,f35109]) ).
fof(f338,plain,
( spl0_30
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f2885,plain,
( ! [X2,X0,X1] :
( y = X0
| ~ subclass(X0,compose(X1,X2))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_30
| ~ spl0_272 ),
inference(resolution,[],[f2827,f339]) ).
fof(f339,plain,
( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f35106,plain,
( spl0_1140
| ~ spl0_31
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2875,f2826,f342,f35104]) ).
fof(f2875,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,X1)
| member(regular(X0),cross_product(universal_class,universal_class))
| ~ function(X1) )
| ~ spl0_31
| ~ spl0_272 ),
inference(resolution,[],[f2827,f343]) ).
fof(f35101,plain,
( spl0_1139
| ~ spl0_50
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2788,f2747,f441,f35099]) ).
fof(f2747,plain,
( spl0_263
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = X0
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2788,plain,
( ! [X0] :
( ~ subclass(X0,identity_relation)
| y = X0
| member(regular(X0),domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_50
| ~ spl0_263 ),
inference(superposition,[],[f2748,f443]) ).
fof(f2748,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = X0
| member(regular(X0),X1) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2747]) ).
fof(f35096,plain,
( spl0_1138
| ~ spl0_49
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2787,f2747,f436,f35094]) ).
fof(f35094,plain,
( spl0_1138
<=> ! [X0] :
( ~ subclass(X0,singleton_relation)
| y = X0
| member(regular(X0),complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f2787,plain,
( ! [X0] :
( ~ subclass(X0,singleton_relation)
| y = X0
| member(regular(X0),complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_49
| ~ spl0_263 ),
inference(superposition,[],[f2748,f438]) ).
fof(f35091,plain,
( spl0_1137
| ~ spl0_46
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2734,f2537,f424,f35089]) ).
fof(f2734,plain,
( ! [X0,X1] :
( y = intersection(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(X0,identity_relation)),X1) )
| ~ spl0_46
| ~ spl0_255 ),
inference(resolution,[],[f2538,f425]) ).
fof(f35086,plain,
( spl0_1136
| ~ spl0_46
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2727,f2532,f424,f35084]) ).
fof(f2727,plain,
( ! [X0,X1] :
( y = intersection(identity_relation,X0)
| ~ subclass(subset_relation,X1)
| member(regular(intersection(identity_relation,X0)),X1) )
| ~ spl0_46
| ~ spl0_254 ),
inference(resolution,[],[f2533,f425]) ).
fof(f35081,plain,
( spl0_1135
| ~ spl0_46
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2722,f2527,f424,f35079]) ).
fof(f35079,plain,
( spl0_1135
<=> ! [X0,X1] :
( y = intersection(X0,singleton_relation)
| ~ subclass(element_relation,X1)
| member(regular(intersection(X0,singleton_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f2722,plain,
( ! [X0,X1] :
( y = intersection(X0,singleton_relation)
| ~ subclass(element_relation,X1)
| member(regular(intersection(X0,singleton_relation)),X1) )
| ~ spl0_46
| ~ spl0_253 ),
inference(resolution,[],[f2528,f425]) ).
fof(f35076,plain,
( spl0_1134
| ~ spl0_46
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2717,f2522,f424,f35074]) ).
fof(f35074,plain,
( spl0_1134
<=> ! [X0,X1] :
( y = intersection(singleton_relation,X0)
| ~ subclass(element_relation,X1)
| member(regular(intersection(singleton_relation,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f2717,plain,
( ! [X0,X1] :
( y = intersection(singleton_relation,X0)
| ~ subclass(element_relation,X1)
| member(regular(intersection(singleton_relation,X0)),X1) )
| ~ spl0_46
| ~ spl0_252 ),
inference(resolution,[],[f2523,f425]) ).
fof(f35071,plain,
( spl0_1133
| ~ spl0_38
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2656,f2450,f377,f35069]) ).
fof(f377,plain,
( spl0_38
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f2656,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(unordered_pair(X1,regular(X0))))
| ~ member(regular(X0),universal_class) )
| ~ spl0_38
| ~ spl0_248 ),
inference(resolution,[],[f2451,f378]) ).
fof(f378,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(X1,universal_class) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f35066,plain,
( spl0_1132
| ~ spl0_36
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2655,f2450,f369,f35064]) ).
fof(f369,plain,
( spl0_36
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f2655,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(unordered_pair(regular(X0),X1)))
| ~ member(regular(X0),universal_class) )
| ~ spl0_36
| ~ spl0_248 ),
inference(resolution,[],[f2451,f370]) ).
fof(f370,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f34764,plain,
( spl0_1131
| ~ spl0_168
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f34740,f34735,f1428,f34762]) ).
fof(f34762,plain,
( spl0_1131
<=> ! [X0] :
( singleton_relation = X0
| subclass(regular(X0),singleton_relation)
| ~ member(not_subclass_element(regular(X0),singleton_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f34735,plain,
( spl0_1125
<=> ! [X0] :
( ~ member(not_subclass_element(regular(X0),y),X0)
| subclass(regular(X0),y)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f34740,plain,
( ! [X0] :
( singleton_relation = X0
| subclass(regular(X0),singleton_relation)
| ~ member(not_subclass_element(regular(X0),singleton_relation),X0) )
| ~ spl0_168
| ~ spl0_1125 ),
inference(forward_demodulation,[],[f34739,f1430]) ).
fof(f34739,plain,
( ! [X0] :
( subclass(regular(X0),singleton_relation)
| ~ member(not_subclass_element(regular(X0),singleton_relation),X0)
| y = X0 )
| ~ spl0_168
| ~ spl0_1125 ),
inference(forward_demodulation,[],[f34738,f1430]) ).
fof(f34738,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),singleton_relation),X0)
| subclass(regular(X0),y)
| y = X0 )
| ~ spl0_168
| ~ spl0_1125 ),
inference(forward_demodulation,[],[f34736,f1430]) ).
fof(f34736,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),y),X0)
| subclass(regular(X0),y)
| y = X0 )
| ~ spl0_1125 ),
inference(avatar_component_clause,[],[f34735]) ).
fof(f34760,plain,
( spl0_1130
| ~ spl0_168
| ~ spl0_1124 ),
inference(avatar_split_clause,[],[f34733,f34730,f1428,f34758]) ).
fof(f34758,plain,
( spl0_1130
<=> ! [X0] :
( singleton_relation = intersection(X0,subset_relation)
| member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f34730,plain,
( spl0_1124
<=> ! [X0] :
( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
| y = intersection(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f34733,plain,
( ! [X0] :
( singleton_relation = intersection(X0,subset_relation)
| member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1124 ),
inference(forward_demodulation,[],[f34731,f1430]) ).
fof(f34731,plain,
( ! [X0] :
( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
| y = intersection(X0,subset_relation) )
| ~ spl0_1124 ),
inference(avatar_component_clause,[],[f34730]) ).
fof(f34756,plain,
( spl0_1129
| ~ spl0_168
| ~ spl0_1123 ),
inference(avatar_split_clause,[],[f34728,f34725,f1428,f34754]) ).
fof(f34754,plain,
( spl0_1129
<=> ! [X0] :
( singleton_relation = intersection(subset_relation,X0)
| member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f34725,plain,
( spl0_1123
<=> ! [X0] :
( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
| y = intersection(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f34728,plain,
( ! [X0] :
( singleton_relation = intersection(subset_relation,X0)
| member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1123 ),
inference(forward_demodulation,[],[f34726,f1430]) ).
fof(f34726,plain,
( ! [X0] :
( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
| y = intersection(subset_relation,X0) )
| ~ spl0_1123 ),
inference(avatar_component_clause,[],[f34725]) ).
fof(f34752,plain,
( spl0_1128
| ~ spl0_168
| ~ spl0_1122 ),
inference(avatar_split_clause,[],[f34723,f34720,f1428,f34750]) ).
fof(f34750,plain,
( spl0_1128
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f34720,plain,
( spl0_1122
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f34723,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1122 ),
inference(forward_demodulation,[],[f34721,f1430]) ).
fof(f34721,plain,
( ! [X0,X1] :
( ~ subclass(X0,compose_class(X1))
| y = X0
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_1122 ),
inference(avatar_component_clause,[],[f34720]) ).
fof(f34748,plain,
( spl0_1127
| ~ spl0_168
| ~ spl0_1121 ),
inference(avatar_split_clause,[],[f34634,f34631,f1428,f34746]) ).
fof(f34746,plain,
( spl0_1127
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f34631,plain,
( spl0_1121
<=> ! [X0] :
( y = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f34634,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) )
| ~ spl0_168
| ~ spl0_1121 ),
inference(forward_demodulation,[],[f34632,f1430]) ).
fof(f34632,plain,
( ! [X0] :
( ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| y = X0
| ~ member(regular(X0),subset_relation) )
| ~ spl0_1121 ),
inference(avatar_component_clause,[],[f34631]) ).
fof(f34744,plain,
( spl0_1126
| ~ spl0_168
| ~ spl0_1120 ),
inference(avatar_split_clause,[],[f34629,f34626,f1428,f34742]) ).
fof(f34742,plain,
( spl0_1126
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f34626,plain,
( spl0_1120
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| y = X0
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f34629,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,identity_relation)
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) )
| ~ spl0_168
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f34627,f1430]) ).
fof(f34627,plain,
( ! [X0,X1] :
( member(regular(X0),X1)
| y = X0
| ~ subclass(subset_relation,X1)
| ~ subclass(X0,identity_relation) )
| ~ spl0_1120 ),
inference(avatar_component_clause,[],[f34626]) ).
fof(f34737,plain,
( spl0_1125
| ~ spl0_34
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f3800,f3634,f361,f34735]) ).
fof(f3800,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),y),X0)
| subclass(regular(X0),y)
| y = X0 )
| ~ spl0_34
| ~ spl0_323 ),
inference(duplicate_literal_removal,[],[f3781]) ).
fof(f3781,plain,
( ! [X0] :
( ~ member(not_subclass_element(regular(X0),y),X0)
| subclass(regular(X0),y)
| y = X0
| subclass(regular(X0),y) )
| ~ spl0_34
| ~ spl0_323 ),
inference(resolution,[],[f3635,f362]) ).
fof(f34732,plain,
( spl0_1124
| ~ spl0_79
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3347,f3209,f642,f34730]) ).
fof(f642,plain,
( spl0_79
<=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f3347,plain,
( ! [X0] :
( member(regular(intersection(X0,subset_relation)),cross_product(universal_class,universal_class))
| y = intersection(X0,subset_relation) )
| ~ spl0_79
| ~ spl0_292 ),
inference(superposition,[],[f3210,f644]) ).
fof(f644,plain,
( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f34727,plain,
( spl0_1123
| ~ spl0_79
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3289,f3201,f642,f34725]) ).
fof(f3289,plain,
( ! [X0] :
( member(regular(intersection(subset_relation,X0)),cross_product(universal_class,universal_class))
| y = intersection(subset_relation,X0) )
| ~ spl0_79
| ~ spl0_290 ),
inference(superposition,[],[f3202,f644]) ).
fof(f34722,plain,
( spl0_1122
| ~ spl0_26
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2888,f2826,f322,f34720]) ).
fof(f322,plain,
( spl0_26
<=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f2888,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,compose_class(X1))
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_26
| ~ spl0_272 ),
inference(resolution,[],[f2827,f323]) ).
fof(f323,plain,
( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f34633,plain,
( spl0_1121
| ~ spl0_139
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2658,f2450,f1089,f34631]) ).
fof(f2658,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(cross_product(universal_class,universal_class)))
| ~ member(regular(X0),subset_relation) )
| ~ spl0_139
| ~ spl0_248 ),
inference(resolution,[],[f2451,f1090]) ).
fof(f34628,plain,
( spl0_1120
| ~ spl0_46
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2439,f2426,f424,f34626]) ).
fof(f2439,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| y = X0
| ~ subclass(subset_relation,X1)
| member(regular(X0),X1) )
| ~ spl0_46
| ~ spl0_246 ),
inference(resolution,[],[f2427,f425]) ).
fof(f34623,plain,
( spl0_1119
| ~ spl0_46
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2431,f2422,f424,f34621]) ).
fof(f34621,plain,
( spl0_1119
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| y = X0
| ~ subclass(element_relation,X1)
| member(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f2431,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| y = X0
| ~ subclass(element_relation,X1)
| member(regular(X0),X1) )
| ~ spl0_46
| ~ spl0_245 ),
inference(resolution,[],[f2423,f425]) ).
fof(f34613,plain,
( spl0_1118
| ~ spl0_50
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4230,f4190,f441,f34610]) ).
fof(f34610,plain,
( spl0_1118
<=> subclass(identity_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f4230,plain,
( subclass(identity_relation,subset_relation)
| ~ spl0_50
| ~ spl0_344 ),
inference(superposition,[],[f4191,f443]) ).
fof(f34177,plain,
( ~ spl0_1117
| ~ spl0_168
| spl0_800 ),
inference(avatar_split_clause,[],[f27703,f19436,f1428,f34174]) ).
fof(f34174,plain,
( spl0_1117
<=> subclass(universal_class,flip(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f19436,plain,
( spl0_800
<=> subclass(universal_class,flip(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f27703,plain,
( ~ subclass(universal_class,flip(singleton_relation))
| ~ spl0_168
| spl0_800 ),
inference(superposition,[],[f19438,f1430]) ).
fof(f19438,plain,
( ~ subclass(universal_class,flip(y))
| spl0_800 ),
inference(avatar_component_clause,[],[f19436]) ).
fof(f34036,plain,
( spl0_1116
| ~ spl0_168
| ~ spl0_1106 ),
inference(avatar_split_clause,[],[f33982,f33979,f1428,f34034]) ).
fof(f33982,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(first(regular(cross_product(X0,X1))),X0) )
| ~ spl0_168
| ~ spl0_1106 ),
inference(forward_demodulation,[],[f33980,f1430]) ).
fof(f34032,plain,
( spl0_1115
| ~ spl0_168
| ~ spl0_1105 ),
inference(avatar_split_clause,[],[f33977,f33974,f1428,f34030]) ).
fof(f33977,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = singleton_relation
| member(second(regular(cross_product(X0,X1))),X1) )
| ~ spl0_168
| ~ spl0_1105 ),
inference(forward_demodulation,[],[f33975,f1430]) ).
fof(f34017,plain,
( spl0_1114
| ~ spl0_168
| ~ spl0_1092 ),
inference(avatar_split_clause,[],[f33914,f33911,f1428,f34015]) ).
fof(f34015,plain,
( spl0_1114
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f33911,plain,
( spl0_1092
<=> ! [X0] :
( y = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f33914,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1092 ),
inference(forward_demodulation,[],[f33912,f1430]) ).
fof(f33912,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,domain_relation)
| y = X0 )
| ~ spl0_1092 ),
inference(avatar_component_clause,[],[f33911]) ).
fof(f34013,plain,
( spl0_1113
| ~ spl0_168
| ~ spl0_1091 ),
inference(avatar_split_clause,[],[f33909,f33906,f1428,f34011]) ).
fof(f34011,plain,
( spl0_1113
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f33906,plain,
( spl0_1091
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f33909,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) )
| ~ spl0_168
| ~ spl0_1091 ),
inference(forward_demodulation,[],[f33907,f1430]) ).
fof(f33907,plain,
( ! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,omega)
| y = X0
| ~ inductive(X1) )
| ~ spl0_1091 ),
inference(avatar_component_clause,[],[f33906]) ).
fof(f34009,plain,
( spl0_1112
| ~ spl0_168
| ~ spl0_1090 ),
inference(avatar_split_clause,[],[f33904,f33901,f1428,f34007]) ).
fof(f34007,plain,
( spl0_1112
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f33901,plain,
( spl0_1090
<=> ! [X0] :
( y = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f33904,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1090 ),
inference(forward_demodulation,[],[f33902,f1430]) ).
fof(f33902,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,successor_relation)
| y = X0 )
| ~ spl0_1090 ),
inference(avatar_component_clause,[],[f33901]) ).
fof(f34005,plain,
( spl0_1111
| ~ spl0_168
| ~ spl0_1089 ),
inference(avatar_split_clause,[],[f33899,f33896,f1428,f34003]) ).
fof(f34003,plain,
( spl0_1111
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f33896,plain,
( spl0_1089
<=> ! [X0] :
( y = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f33899,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1089 ),
inference(forward_demodulation,[],[f33897,f1430]) ).
fof(f33897,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,element_relation)
| y = X0 )
| ~ spl0_1089 ),
inference(avatar_component_clause,[],[f33896]) ).
fof(f34001,plain,
( spl0_1110
| ~ spl0_168
| ~ spl0_1086 ),
inference(avatar_split_clause,[],[f33884,f33881,f1428,f33999]) ).
fof(f33999,plain,
( spl0_1110
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,subset_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f33881,plain,
( spl0_1086
<=> ! [X0] :
( ~ subclass(X0,subset_relation)
| y = X0
| member(regular(X0),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f33884,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,subset_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_1086 ),
inference(forward_demodulation,[],[f33882,f1430]) ).
fof(f33882,plain,
( ! [X0] :
( member(regular(X0),cross_product(universal_class,universal_class))
| y = X0
| ~ subclass(X0,subset_relation) )
| ~ spl0_1086 ),
inference(avatar_component_clause,[],[f33881]) ).
fof(f33997,plain,
( ~ spl0_1109
| ~ spl0_168
| spl0_785 ),
inference(avatar_split_clause,[],[f27701,f18374,f1428,f33994]) ).
fof(f33994,plain,
( spl0_1109
<=> subclass(universal_class,rotate(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f18374,plain,
( spl0_785
<=> subclass(universal_class,rotate(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f27701,plain,
( ~ subclass(universal_class,rotate(singleton_relation))
| ~ spl0_168
| spl0_785 ),
inference(superposition,[],[f18376,f1430]) ).
fof(f18376,plain,
( ~ subclass(universal_class,rotate(y))
| spl0_785 ),
inference(avatar_component_clause,[],[f18374]) ).
fof(f33991,plain,
( spl0_1108
| ~ spl0_297
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f7533,f7271,f3231,f33989]) ).
fof(f33989,plain,
( spl0_1108
<=> ! [X0,X1] :
( subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f7271,plain,
( spl0_495
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f7533,plain,
( ! [X0,X1] :
( subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
| y = X1 )
| ~ spl0_297
| ~ spl0_495 ),
inference(duplicate_literal_removal,[],[f7484]) ).
fof(f7484,plain,
( ! [X0,X1] :
( subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
| subclass(intersection(y,X0),intersection(X1,intersection(y,X0)))
| y = X1 )
| ~ spl0_297
| ~ spl0_495 ),
inference(resolution,[],[f7272,f3232]) ).
fof(f7272,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f7271]) ).
fof(f33986,plain,
( spl0_1107
| ~ spl0_298
| ~ spl0_495 ),
inference(avatar_split_clause,[],[f7532,f7271,f3235,f33984]) ).
fof(f33984,plain,
( spl0_1107
<=> ! [X0,X1] :
( subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f7532,plain,
( ! [X0,X1] :
( subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
| y = X1 )
| ~ spl0_298
| ~ spl0_495 ),
inference(duplicate_literal_removal,[],[f7485]) ).
fof(f7485,plain,
( ! [X0,X1] :
( subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
| subclass(intersection(X0,y),intersection(X1,intersection(X0,y)))
| y = X1 )
| ~ spl0_298
| ~ spl0_495 ),
inference(resolution,[],[f7272,f3236]) ).
fof(f33981,plain,
( spl0_1106
| ~ spl0_2
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4152,f4100,f213,f33979]) ).
fof(f4100,plain,
( spl0_341
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f4152,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = y )
| ~ spl0_2
| ~ spl0_341 ),
inference(duplicate_literal_removal,[],[f4145]) ).
fof(f4145,plain,
( ! [X0,X1] :
( member(first(regular(cross_product(X0,X1))),X0)
| cross_product(X0,X1) = y
| cross_product(X0,X1) = y )
| ~ spl0_2
| ~ spl0_341 ),
inference(resolution,[],[f4101,f214]) ).
fof(f4101,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = y )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f4100]) ).
fof(f33976,plain,
( spl0_1105
| ~ spl0_2
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4143,f4096,f213,f33974]) ).
fof(f4096,plain,
( spl0_340
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(second(regular(cross_product(X0,X1))),X3)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f4143,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = y )
| ~ spl0_2
| ~ spl0_340 ),
inference(duplicate_literal_removal,[],[f4136]) ).
fof(f4136,plain,
( ! [X0,X1] :
( member(second(regular(cross_product(X0,X1))),X1)
| cross_product(X0,X1) = y
| cross_product(X0,X1) = y )
| ~ spl0_2
| ~ spl0_340 ),
inference(resolution,[],[f4097,f214]) ).
fof(f4097,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(second(regular(cross_product(X0,X1))),X3)
| cross_product(X0,X1) = y )
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f4096]) ).
fof(f33972,plain,
( spl0_1104
| ~ spl0_40
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4048,f3977,f385,f33969]) ).
fof(f33969,plain,
( spl0_1104
<=> member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f3977,plain,
( spl0_332
<=> member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f4048,plain,
( member(regular(subset_relation),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_40
| ~ spl0_332 ),
inference(resolution,[],[f3979,f386]) ).
fof(f3979,plain,
( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f3977]) ).
fof(f33967,plain,
( ~ spl0_1103
| ~ spl0_168
| spl0_1100 ),
inference(avatar_split_clause,[],[f33962,f33951,f1428,f33964]) ).
fof(f33964,plain,
( spl0_1103
<=> universal_class = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f33951,plain,
( spl0_1100
<=> universal_class = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f33962,plain,
( universal_class != singleton_relation
| ~ spl0_168
| spl0_1100 ),
inference(forward_demodulation,[],[f33952,f1430]) ).
fof(f33952,plain,
( universal_class != y
| spl0_1100 ),
inference(avatar_component_clause,[],[f33951]) ).
fof(f33961,plain,
( spl0_1100
| ~ spl0_1101
| spl0_1102
| ~ spl0_16
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f3753,f3608,f278,f33959,f33955,f33951]) ).
fof(f33955,plain,
( spl0_1101
<=> subclass(universal_class,regular(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f3753,plain,
( ! [X0,X1] :
( member(unordered_pair(X0,X1),y)
| ~ subclass(universal_class,regular(universal_class))
| universal_class = y )
| ~ spl0_16
| ~ spl0_318 ),
inference(resolution,[],[f3609,f279]) ).
fof(f33948,plain,
( spl0_1099
| ~ spl0_109
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2967,f2838,f831,f33946]) ).
fof(f33946,plain,
( spl0_1099
<=> ! [X0,X1] :
( y = intersection(X0,complement(X1))
| ~ subclass(intersection(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f2967,plain,
( ! [X0,X1] :
( y = intersection(X0,complement(X1))
| ~ subclass(intersection(X0,complement(X1)),X1) )
| ~ spl0_109
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f2949]) ).
fof(f2949,plain,
( ! [X0,X1] :
( y = intersection(X0,complement(X1))
| ~ subclass(intersection(X0,complement(X1)),X1)
| y = intersection(X0,complement(X1)) )
| ~ spl0_109
| ~ spl0_275 ),
inference(resolution,[],[f2839,f832]) ).
fof(f33944,plain,
( spl0_1098
| ~ spl0_168
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f13948,f9421,f1428,f33941]) ).
fof(f13948,plain,
( singleton_relation = domain_of(singleton_relation)
| ~ spl0_168
| ~ spl0_567 ),
inference(superposition,[],[f9423,f1430]) ).
fof(f33938,plain,
( spl0_1097
| ~ spl0_245
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2965,f2838,f2422,f33936]) ).
fof(f2965,plain,
( ! [X0] :
( y = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation) )
| ~ spl0_245
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f2952]) ).
fof(f2952,plain,
( ! [X0] :
( y = intersection(X0,complement(element_relation))
| ~ subclass(intersection(X0,complement(element_relation)),singleton_relation)
| y = intersection(X0,complement(element_relation)) )
| ~ spl0_245
| ~ spl0_275 ),
inference(resolution,[],[f2839,f2423]) ).
fof(f33933,plain,
( spl0_1096
| ~ spl0_246
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2963,f2838,f2426,f33931]) ).
fof(f33931,plain,
( spl0_1096
<=> ! [X0] :
( y = intersection(X0,complement(subset_relation))
| ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f2963,plain,
( ! [X0] :
( y = intersection(X0,complement(subset_relation))
| ~ subclass(intersection(X0,complement(subset_relation)),identity_relation) )
| ~ spl0_246
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f2961]) ).
fof(f2961,plain,
( ! [X0] :
( y = intersection(X0,complement(subset_relation))
| ~ subclass(intersection(X0,complement(subset_relation)),identity_relation)
| y = intersection(X0,complement(subset_relation)) )
| ~ spl0_246
| ~ spl0_275 ),
inference(resolution,[],[f2839,f2427]) ).
fof(f33928,plain,
( spl0_1095
| ~ spl0_109
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2941,f2834,f831,f33926]) ).
fof(f33926,plain,
( spl0_1095
<=> ! [X0,X1] :
( y = intersection(complement(X0),X1)
| ~ subclass(intersection(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f2941,plain,
( ! [X0,X1] :
( y = intersection(complement(X0),X1)
| ~ subclass(intersection(complement(X0),X1),X0) )
| ~ spl0_109
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2921]) ).
fof(f2921,plain,
( ! [X0,X1] :
( y = intersection(complement(X0),X1)
| ~ subclass(intersection(complement(X0),X1),X0)
| y = intersection(complement(X0),X1) )
| ~ spl0_109
| ~ spl0_274 ),
inference(resolution,[],[f2835,f832]) ).
fof(f33923,plain,
( spl0_1094
| ~ spl0_245
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2939,f2834,f2422,f33921]) ).
fof(f2939,plain,
( ! [X0] :
( y = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation) )
| ~ spl0_245
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2924]) ).
fof(f2924,plain,
( ! [X0] :
( y = intersection(complement(element_relation),X0)
| ~ subclass(intersection(complement(element_relation),X0),singleton_relation)
| y = intersection(complement(element_relation),X0) )
| ~ spl0_245
| ~ spl0_274 ),
inference(resolution,[],[f2835,f2423]) ).
fof(f33918,plain,
( spl0_1093
| ~ spl0_246
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2937,f2834,f2426,f33916]) ).
fof(f33916,plain,
( spl0_1093
<=> ! [X0] :
( y = intersection(complement(subset_relation),X0)
| ~ subclass(intersection(complement(subset_relation),X0),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f2937,plain,
( ! [X0] :
( y = intersection(complement(subset_relation),X0)
| ~ subclass(intersection(complement(subset_relation),X0),identity_relation) )
| ~ spl0_246
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2933]) ).
fof(f2933,plain,
( ! [X0] :
( y = intersection(complement(subset_relation),X0)
| ~ subclass(intersection(complement(subset_relation),X0),identity_relation)
| y = intersection(complement(subset_relation),X0) )
| ~ spl0_246
| ~ spl0_274 ),
inference(resolution,[],[f2835,f2427]) ).
fof(f33913,plain,
( spl0_1092
| ~ spl0_20
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2890,f2826,f296,f33911]) ).
fof(f296,plain,
( spl0_20
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f2890,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,domain_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_20
| ~ spl0_272 ),
inference(resolution,[],[f2827,f298]) ).
fof(f298,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f33908,plain,
( spl0_1091
| ~ spl0_19
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2884,f2826,f292,f33906]) ).
fof(f2884,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,omega)
| member(regular(X0),X1)
| ~ inductive(X1) )
| ~ spl0_19
| ~ spl0_272 ),
inference(resolution,[],[f2827,f293]) ).
fof(f33903,plain,
( spl0_1090
| ~ spl0_18
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2883,f2826,f287,f33901]) ).
fof(f287,plain,
( spl0_18
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f2883,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,successor_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_18
| ~ spl0_272 ),
inference(resolution,[],[f2827,f289]) ).
fof(f289,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f33898,plain,
( spl0_1089
| ~ spl0_17
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2878,f2826,f282,f33896]) ).
fof(f282,plain,
( spl0_17
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f2878,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,element_relation)
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_17
| ~ spl0_272 ),
inference(resolution,[],[f2827,f284]) ).
fof(f284,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f33894,plain,
( spl0_276
| ~ spl0_1088
| ~ spl0_109
| spl0_277 ),
inference(avatar_split_clause,[],[f2851,f2846,f831,f33891,f2842]) ).
fof(f2842,plain,
( spl0_276
<=> y = complement(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f33891,plain,
( spl0_1088
<=> subclass(complement(cross_product(universal_class,universal_class)),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f2846,plain,
( spl0_277
<=> member(regular(complement(cross_product(universal_class,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2851,plain,
( ~ subclass(complement(cross_product(universal_class,universal_class)),subset_relation)
| y = complement(cross_product(universal_class,universal_class))
| ~ spl0_109
| spl0_277 ),
inference(resolution,[],[f2848,f832]) ).
fof(f2848,plain,
( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
| spl0_277 ),
inference(avatar_component_clause,[],[f2846]) ).
fof(f33889,plain,
( spl0_276
| ~ spl0_1087
| ~ spl0_246
| spl0_277 ),
inference(avatar_split_clause,[],[f2850,f2846,f2426,f33886,f2842]) ).
fof(f33886,plain,
( spl0_1087
<=> subclass(complement(cross_product(universal_class,universal_class)),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f2850,plain,
( ~ subclass(complement(cross_product(universal_class,universal_class)),identity_relation)
| y = complement(cross_product(universal_class,universal_class))
| ~ spl0_246
| spl0_277 ),
inference(resolution,[],[f2848,f2427]) ).
fof(f33883,plain,
( spl0_1086
| ~ spl0_79
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2786,f2747,f642,f33881]) ).
fof(f2786,plain,
( ! [X0] :
( ~ subclass(X0,subset_relation)
| y = X0
| member(regular(X0),cross_product(universal_class,universal_class)) )
| ~ spl0_79
| ~ spl0_263 ),
inference(superposition,[],[f2748,f644]) ).
fof(f33681,plain,
( ~ spl0_1085
| ~ spl0_168
| spl0_326 ),
inference(avatar_split_clause,[],[f13936,f3804,f1428,f33678]) ).
fof(f33678,plain,
( spl0_1085
<=> member(second(singleton_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f3804,plain,
( spl0_326
<=> member(second(y),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f13936,plain,
( ~ member(second(singleton_relation),universal_class)
| ~ spl0_168
| spl0_326 ),
inference(superposition,[],[f3805,f1430]) ).
fof(f3805,plain,
( ~ member(second(y),universal_class)
| spl0_326 ),
inference(avatar_component_clause,[],[f3804]) ).
fof(f33676,plain,
( spl0_1084
| ~ spl0_168
| ~ spl0_1077 ),
inference(avatar_split_clause,[],[f33637,f33633,f1428,f33674]) ).
fof(f33674,plain,
( spl0_1084
<=> ! [X0] :
( singleton_relation = X0
| member(regular(X0),singleton_relation)
| ~ subclass(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f33633,plain,
( spl0_1077
<=> ! [X0] :
( member(regular(X0),y)
| y = X0
| ~ subclass(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f33637,plain,
( ! [X0] :
( singleton_relation = X0
| member(regular(X0),singleton_relation)
| ~ subclass(X0,regular(X0)) )
| ~ spl0_168
| ~ spl0_1077 ),
inference(forward_demodulation,[],[f33636,f1430]) ).
fof(f33636,plain,
( ! [X0] :
( member(regular(X0),singleton_relation)
| y = X0
| ~ subclass(X0,regular(X0)) )
| ~ spl0_168
| ~ spl0_1077 ),
inference(forward_demodulation,[],[f33634,f1430]) ).
fof(f33634,plain,
( ! [X0] :
( ~ subclass(X0,regular(X0))
| y = X0
| member(regular(X0),y) )
| ~ spl0_1077 ),
inference(avatar_component_clause,[],[f33633]) ).
fof(f33672,plain,
( spl0_1083
| ~ spl0_168
| ~ spl0_1076 ),
inference(avatar_split_clause,[],[f33631,f33628,f1428,f33670]) ).
fof(f33670,plain,
( spl0_1083
<=> ! [X0] :
( unordered_pair(X0,X0) = singleton_relation
| regular(unordered_pair(X0,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f33628,plain,
( spl0_1076
<=> ! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f33631,plain,
( ! [X0] :
( unordered_pair(X0,X0) = singleton_relation
| regular(unordered_pair(X0,X0)) = X0 )
| ~ spl0_168
| ~ spl0_1076 ),
inference(forward_demodulation,[],[f33629,f1430]) ).
fof(f33629,plain,
( ! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = y )
| ~ spl0_1076 ),
inference(avatar_component_clause,[],[f33628]) ).
fof(f33668,plain,
( spl0_1082
| ~ spl0_168
| ~ spl0_1073 ),
inference(avatar_split_clause,[],[f33578,f33575,f1428,f33666]) ).
fof(f33666,plain,
( spl0_1082
<=> ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f33575,plain,
( spl0_1073
<=> ! [X0] :
( y = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f33578,plain,
( ! [X0] :
( singleton_relation = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
| ~ spl0_168
| ~ spl0_1073 ),
inference(forward_demodulation,[],[f33576,f1430]) ).
fof(f33576,plain,
( ! [X0] :
( ~ subclass(intersection(X0,identity_relation),complement(subset_relation))
| y = intersection(X0,identity_relation) )
| ~ spl0_1073 ),
inference(avatar_component_clause,[],[f33575]) ).
fof(f33664,plain,
( spl0_1081
| ~ spl0_168
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f33573,f33570,f1428,f33662]) ).
fof(f33662,plain,
( spl0_1081
<=> ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f33570,plain,
( spl0_1072
<=> ! [X0] :
( y = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f33573,plain,
( ! [X0] :
( singleton_relation = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
| ~ spl0_168
| ~ spl0_1072 ),
inference(forward_demodulation,[],[f33571,f1430]) ).
fof(f33571,plain,
( ! [X0] :
( ~ subclass(intersection(identity_relation,X0),complement(subset_relation))
| y = intersection(identity_relation,X0) )
| ~ spl0_1072 ),
inference(avatar_component_clause,[],[f33570]) ).
fof(f33655,plain,
( spl0_1080
| ~ spl0_168
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f33544,f33541,f1428,f33653]) ).
fof(f33653,plain,
( spl0_1080
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f33541,plain,
( spl0_1066
<=> ! [X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(intersection(X0,X1),complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f33544,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X0)) )
| ~ spl0_168
| ~ spl0_1066 ),
inference(forward_demodulation,[],[f33542,f1430]) ).
fof(f33542,plain,
( ! [X0,X1] :
( ~ subclass(intersection(X0,X1),complement(X0))
| intersection(X0,X1) = y )
| ~ spl0_1066 ),
inference(avatar_component_clause,[],[f33541]) ).
fof(f33651,plain,
( spl0_1079
| ~ spl0_168
| ~ spl0_1065 ),
inference(avatar_split_clause,[],[f33539,f33536,f1428,f33649]) ).
fof(f33649,plain,
( spl0_1079
<=> ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f33536,plain,
( spl0_1065
<=> ! [X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(intersection(X0,X1),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f33539,plain,
( ! [X0,X1] :
( intersection(X0,X1) = singleton_relation
| ~ subclass(intersection(X0,X1),complement(X1)) )
| ~ spl0_168
| ~ spl0_1065 ),
inference(forward_demodulation,[],[f33537,f1430]) ).
fof(f33537,plain,
( ! [X0,X1] :
( ~ subclass(intersection(X0,X1),complement(X1))
| intersection(X0,X1) = y )
| ~ spl0_1065 ),
inference(avatar_component_clause,[],[f33536]) ).
fof(f33641,plain,
( spl0_1078
| ~ spl0_2
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f6189,f6115,f213,f33639]) ).
fof(f33639,plain,
( spl0_1078
<=> ! [X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),universal_class)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f6115,plain,
( spl0_446
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f6189,plain,
( ! [X0,X1] :
( ~ member(regular(X0),X1)
| member(regular(X0),universal_class)
| y = X0 )
| ~ spl0_2
| ~ spl0_446 ),
inference(resolution,[],[f6116,f214]) ).
fof(f6116,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,universal_class) )
| ~ spl0_446 ),
inference(avatar_component_clause,[],[f6115]) ).
fof(f33635,plain,
( spl0_1077
| ~ spl0_2
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3893,f3810,f213,f33633]) ).
fof(f3893,plain,
( ! [X0] :
( member(regular(X0),y)
| y = X0
| ~ subclass(X0,regular(X0)) )
| ~ spl0_2
| ~ spl0_327 ),
inference(duplicate_literal_removal,[],[f3829]) ).
fof(f3829,plain,
( ! [X0] :
( member(regular(X0),y)
| y = X0
| ~ subclass(X0,regular(X0))
| y = X0
| y = X0 )
| ~ spl0_2
| ~ spl0_327 ),
inference(resolution,[],[f3811,f214]) ).
fof(f33630,plain,
( spl0_1076
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f3140,f2996,f33628]) ).
fof(f2996,plain,
( spl0_284
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f3140,plain,
( ! [X0] :
( regular(unordered_pair(X0,X0)) = X0
| unordered_pair(X0,X0) = y )
| ~ spl0_284 ),
inference(equality_resolution,[],[f2997]) ).
fof(f2997,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f2996]) ).
fof(f33606,plain,
( spl0_1075
| spl0_882
| ~ spl0_19
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2782,f2747,f292,f21901,f33604]) ).
fof(f33604,plain,
( spl0_1075
<=> ! [X0,X1] :
( member(regular(omega),X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f2782,plain,
( ! [X0,X1] :
( omega = y
| member(regular(omega),X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl0_19
| ~ spl0_263 ),
inference(resolution,[],[f2748,f293]) ).
fof(f33582,plain,
( spl0_1074
| spl0_882
| ~ spl0_19
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2771,f2743,f292,f21901,f33580]) ).
fof(f33580,plain,
( spl0_1074
<=> ! [X0,X1] :
( member(regular(omega),X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f2743,plain,
( spl0_262
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = X0
| member(regular(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2771,plain,
( ! [X0,X1] :
( omega = y
| member(regular(omega),X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl0_19
| ~ spl0_262 ),
inference(resolution,[],[f2744,f293]) ).
fof(f2744,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = X0
| member(regular(X0),X2) )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2743]) ).
fof(f33577,plain,
( spl0_1073
| ~ spl0_248
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2736,f2537,f2450,f33575]) ).
fof(f2736,plain,
( ! [X0] :
( y = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
| ~ spl0_248
| ~ spl0_255 ),
inference(duplicate_literal_removal,[],[f2732]) ).
fof(f2732,plain,
( ! [X0] :
( y = intersection(X0,identity_relation)
| y = intersection(X0,identity_relation)
| ~ subclass(intersection(X0,identity_relation),complement(subset_relation)) )
| ~ spl0_248
| ~ spl0_255 ),
inference(resolution,[],[f2538,f2451]) ).
fof(f33572,plain,
( spl0_1072
| ~ spl0_248
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2729,f2532,f2450,f33570]) ).
fof(f2729,plain,
( ! [X0] :
( y = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
| ~ spl0_248
| ~ spl0_254 ),
inference(duplicate_literal_removal,[],[f2725]) ).
fof(f2725,plain,
( ! [X0] :
( y = intersection(identity_relation,X0)
| y = intersection(identity_relation,X0)
| ~ subclass(intersection(identity_relation,X0),complement(subset_relation)) )
| ~ spl0_248
| ~ spl0_254 ),
inference(resolution,[],[f2533,f2451]) ).
fof(f33567,plain,
( spl0_1071
| ~ spl0_248
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2724,f2527,f2450,f33565]) ).
fof(f33565,plain,
( spl0_1071
<=> ! [X0] :
( y = intersection(X0,singleton_relation)
| ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f2724,plain,
( ! [X0] :
( y = intersection(X0,singleton_relation)
| ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
| ~ spl0_248
| ~ spl0_253 ),
inference(duplicate_literal_removal,[],[f2720]) ).
fof(f2720,plain,
( ! [X0] :
( y = intersection(X0,singleton_relation)
| y = intersection(X0,singleton_relation)
| ~ subclass(intersection(X0,singleton_relation),complement(element_relation)) )
| ~ spl0_248
| ~ spl0_253 ),
inference(resolution,[],[f2528,f2451]) ).
fof(f33562,plain,
( spl0_1070
| ~ spl0_248
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2719,f2522,f2450,f33560]) ).
fof(f33560,plain,
( spl0_1070
<=> ! [X0] :
( y = intersection(singleton_relation,X0)
| ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f2719,plain,
( ! [X0] :
( y = intersection(singleton_relation,X0)
| ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
| ~ spl0_248
| ~ spl0_252 ),
inference(duplicate_literal_removal,[],[f2715]) ).
fof(f2715,plain,
( ! [X0] :
( y = intersection(singleton_relation,X0)
| y = intersection(singleton_relation,X0)
| ~ subclass(intersection(singleton_relation,X0),complement(element_relation)) )
| ~ spl0_248
| ~ spl0_252 ),
inference(resolution,[],[f2523,f2451]) ).
fof(f33558,plain,
( spl0_1069
| ~ spl0_46
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2714,f2482,f424,f33556]) ).
fof(f33556,plain,
( spl0_1069
<=> ! [X0] :
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| member(regular(identity_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f2482,plain,
( spl0_250
<=> member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2714,plain,
( ! [X0] :
( ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| member(regular(identity_relation),X0) )
| ~ spl0_46
| ~ spl0_250 ),
inference(resolution,[],[f2484,f425]) ).
fof(f2484,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2482]) ).
fof(f33554,plain,
( ~ spl0_1068
| ~ spl0_168
| spl0_745 ),
inference(avatar_split_clause,[],[f27699,f16067,f1428,f33551]) ).
fof(f33551,plain,
( spl0_1068
<=> subclass(element_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f16067,plain,
( spl0_745
<=> subclass(element_relation,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f27699,plain,
( ~ subclass(element_relation,singleton_relation)
| ~ spl0_168
| spl0_745 ),
inference(superposition,[],[f16069,f1430]) ).
fof(f16069,plain,
( ~ subclass(element_relation,y)
| spl0_745 ),
inference(avatar_component_clause,[],[f16067]) ).
fof(f33549,plain,
( ~ spl0_1067
| spl0_186
| ~ spl0_248
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2711,f2482,f2450,f1601,f33546]) ).
fof(f33546,plain,
( spl0_1067
<=> subclass(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f2711,plain,
( identity_relation = y
| ~ subclass(identity_relation,complement(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ spl0_248
| ~ spl0_250 ),
inference(resolution,[],[f2484,f2451]) ).
fof(f33543,plain,
( spl0_1066
| ~ spl0_111
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2679,f2450,f852,f33541]) ).
fof(f2679,plain,
( ! [X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(intersection(X0,X1),complement(X0)) )
| ~ spl0_111
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f2652]) ).
fof(f2652,plain,
( ! [X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(intersection(X0,X1),complement(X0))
| intersection(X0,X1) = y )
| ~ spl0_111
| ~ spl0_248 ),
inference(resolution,[],[f2451,f853]) ).
fof(f33538,plain,
( spl0_1065
| ~ spl0_112
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2677,f2450,f856,f33536]) ).
fof(f2677,plain,
( ! [X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(intersection(X0,X1),complement(X1)) )
| ~ spl0_112
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f2654]) ).
fof(f2654,plain,
( ! [X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(intersection(X0,X1),complement(X1))
| intersection(X0,X1) = y )
| ~ spl0_112
| ~ spl0_248 ),
inference(resolution,[],[f2451,f857]) ).
fof(f33534,plain,
( spl0_1064
| ~ spl0_46
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2515,f2454,f424,f33532]) ).
fof(f33532,plain,
( spl0_1064
<=> ! [X0] :
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),X0)
| member(regular(singleton_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f2515,plain,
( ! [X0] :
( ~ subclass(complement(compose(element_relation,complement(identity_relation))),X0)
| member(regular(singleton_relation),X0) )
| ~ spl0_46
| ~ spl0_249 ),
inference(resolution,[],[f2456,f425]) ).
fof(f33530,plain,
( ~ spl0_1063
| spl0_276
| ~ spl0_31
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2241,f2231,f342,f2842,f33527]) ).
fof(f33527,plain,
( spl0_1063
<=> function(complement(cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f2231,plain,
( spl0_230
<=> ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2241,plain,
( y = complement(cross_product(universal_class,universal_class))
| ~ function(complement(cross_product(universal_class,universal_class)))
| ~ spl0_31
| ~ spl0_230 ),
inference(resolution,[],[f2232,f343]) ).
fof(f2232,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = y )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2231]) ).
fof(f33338,plain,
( spl0_1062
| ~ spl0_168
| ~ spl0_1054 ),
inference(avatar_split_clause,[],[f33294,f33291,f1428,f33336]) ).
fof(f33291,plain,
( spl0_1054
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f33294,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X1,complement(X0))
| ~ subclass(complement(X0),X0) )
| ~ spl0_168
| ~ spl0_1054 ),
inference(forward_demodulation,[],[f33292,f1430]) ).
fof(f33292,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(X1,complement(X0)) )
| ~ spl0_1054 ),
inference(avatar_component_clause,[],[f33291]) ).
fof(f33334,plain,
( spl0_1061
| ~ spl0_168
| ~ spl0_1053 ),
inference(avatar_split_clause,[],[f33289,f33286,f1428,f33332]) ).
fof(f33286,plain,
( spl0_1053
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f33289,plain,
( ! [X0,X1] :
( singleton_relation = intersection(complement(X0),X1)
| ~ subclass(complement(X0),X0) )
| ~ spl0_168
| ~ spl0_1053 ),
inference(forward_demodulation,[],[f33287,f1430]) ).
fof(f33287,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(complement(X0),X1) )
| ~ spl0_1053 ),
inference(avatar_component_clause,[],[f33286]) ).
fof(f33330,plain,
( spl0_1060
| ~ spl0_168
| ~ spl0_1052 ),
inference(avatar_split_clause,[],[f33284,f33281,f1428,f33328]) ).
fof(f33328,plain,
( spl0_1060
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f33281,plain,
( spl0_1052
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f33284,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) )
| ~ spl0_168
| ~ spl0_1052 ),
inference(forward_demodulation,[],[f33282,f1430]) ).
fof(f33282,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = X0
| member(regular(X0),universal_class) )
| ~ spl0_1052 ),
inference(avatar_component_clause,[],[f33281]) ).
fof(f33326,plain,
( spl0_1059
| ~ spl0_168
| ~ spl0_1051 ),
inference(avatar_split_clause,[],[f33279,f33276,f1428,f33324]) ).
fof(f33324,plain,
( spl0_1059
<=> ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f33276,plain,
( spl0_1051
<=> ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f33279,plain,
( ! [X0,X1] :
( singleton_relation = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) )
| ~ spl0_168
| ~ spl0_1051 ),
inference(forward_demodulation,[],[f33277,f1430]) ).
fof(f33277,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| y = X0
| ~ subclass(X0,X1) )
| ~ spl0_1051 ),
inference(avatar_component_clause,[],[f33276]) ).
fof(f33322,plain,
( spl0_1058
| ~ spl0_168
| ~ spl0_1049 ),
inference(avatar_split_clause,[],[f33269,f33266,f1428,f33320]) ).
fof(f33320,plain,
( spl0_1058
<=> ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f33266,plain,
( spl0_1049
<=> ! [X0] :
( y = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f33269,plain,
( ! [X0] :
( singleton_relation = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) )
| ~ spl0_168
| ~ spl0_1049 ),
inference(forward_demodulation,[],[f33267,f1430]) ).
fof(f33267,plain,
( ! [X0] :
( ~ subclass(X0,complement(subset_relation))
| y = X0
| ~ subclass(X0,identity_relation) )
| ~ spl0_1049 ),
inference(avatar_component_clause,[],[f33266]) ).
fof(f33318,plain,
( ~ spl0_1057
| ~ spl0_168
| spl0_572 ),
inference(avatar_split_clause,[],[f13950,f9489,f1428,f33315]) ).
fof(f33315,plain,
( spl0_1057
<=> singleton_relation = cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f9489,plain,
( spl0_572
<=> y = cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f13950,plain,
( singleton_relation != cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class)
| ~ spl0_168
| spl0_572 ),
inference(superposition,[],[f9490,f1430]) ).
fof(f9490,plain,
( y != cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
| spl0_572 ),
inference(avatar_component_clause,[],[f9489]) ).
fof(f33303,plain,
( spl0_1056
| ~ spl0_168
| ~ spl0_550
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f27613,f9421,f8731,f1428,f33301]) ).
fof(f27613,plain,
( ! [X0] : ~ member(X0,singleton_relation)
| ~ spl0_168
| ~ spl0_550
| ~ spl0_567 ),
inference(forward_demodulation,[],[f13946,f13948]) ).
fof(f13946,plain,
( ! [X0] : ~ member(X0,domain_of(singleton_relation))
| ~ spl0_168
| ~ spl0_550 ),
inference(superposition,[],[f8732,f1430]) ).
fof(f33299,plain,
( ~ spl0_239
| spl0_1055
| ~ spl0_203
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4047,f3977,f1816,f33296,f2283]) ).
fof(f2283,plain,
( spl0_239
<=> member(regular(subset_relation),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f33296,plain,
( spl0_1055
<=> member(regular(subset_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f1816,plain,
( spl0_203
<=> ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f4047,plain,
( member(regular(subset_relation),subset_relation)
| ~ member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_203
| ~ spl0_332 ),
inference(resolution,[],[f3979,f1817]) ).
fof(f1817,plain,
( ! [X0] :
( ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f33293,plain,
( spl0_1054
| ~ spl0_275
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3115,f2988,f2838,f33291]) ).
fof(f3115,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(X1,complement(X0)) )
| ~ spl0_275
| ~ spl0_282 ),
inference(duplicate_literal_removal,[],[f3088]) ).
fof(f3088,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(X1,complement(X0))
| y = intersection(X1,complement(X0)) )
| ~ spl0_275
| ~ spl0_282 ),
inference(resolution,[],[f2989,f2839]) ).
fof(f33288,plain,
( spl0_1053
| ~ spl0_274
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3063,f2980,f2834,f33286]) ).
fof(f3063,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(complement(X0),X1) )
| ~ spl0_274
| ~ spl0_280 ),
inference(duplicate_literal_removal,[],[f3034]) ).
fof(f3034,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| y = intersection(complement(X0),X1)
| y = intersection(complement(X0),X1) )
| ~ spl0_274
| ~ spl0_280 ),
inference(resolution,[],[f2981,f2835]) ).
fof(f33283,plain,
( spl0_1052
| ~ spl0_8
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2873,f2826,f242,f33281]) ).
fof(f2873,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,X1)
| member(regular(X0),universal_class) )
| ~ spl0_8
| ~ spl0_272 ),
inference(resolution,[],[f2827,f243]) ).
fof(f33278,plain,
( spl0_1051
| ~ spl0_109
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2678,f2450,f831,f33276]) ).
fof(f2678,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1) )
| ~ spl0_109
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f2653]) ).
fof(f2653,plain,
( ! [X0,X1] :
( y = X0
| ~ subclass(X0,complement(X1))
| ~ subclass(X0,X1)
| y = X0 )
| ~ spl0_109
| ~ spl0_248 ),
inference(resolution,[],[f2451,f832]) ).
fof(f33273,plain,
( spl0_1050
| ~ spl0_245
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2676,f2450,f2422,f33271]) ).
fof(f2676,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation) )
| ~ spl0_245
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f2660]) ).
fof(f2660,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(element_relation))
| ~ subclass(X0,singleton_relation)
| y = X0 )
| ~ spl0_245
| ~ spl0_248 ),
inference(resolution,[],[f2451,f2423]) ).
fof(f33268,plain,
( spl0_1049
| ~ spl0_246
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2675,f2450,f2426,f33266]) ).
fof(f2675,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation) )
| ~ spl0_246
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f2670]) ).
fof(f2670,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(subset_relation))
| ~ subclass(X0,identity_relation)
| y = X0 )
| ~ spl0_246
| ~ spl0_248 ),
inference(resolution,[],[f2451,f2427]) ).
fof(f33182,plain,
( spl0_1048
| ~ spl0_168
| ~ spl0_1045 ),
inference(avatar_split_clause,[],[f33164,f33161,f1428,f33180]) ).
fof(f33161,plain,
( spl0_1045
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(complement(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f33164,plain,
( ! [X0,X1] :
( singleton_relation = intersection(complement(X1),X0)
| ~ subclass(X0,X1) )
| ~ spl0_168
| ~ spl0_1045 ),
inference(forward_demodulation,[],[f33162,f1430]) ).
fof(f33162,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(complement(X1),X0) )
| ~ spl0_1045 ),
inference(avatar_component_clause,[],[f33161]) ).
fof(f33178,plain,
( spl0_1047
| ~ spl0_168
| ~ spl0_1044 ),
inference(avatar_split_clause,[],[f33159,f33156,f1428,f33176]) ).
fof(f33156,plain,
( spl0_1044
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f33159,plain,
( ! [X0,X1] :
( singleton_relation = intersection(X0,complement(X1))
| ~ subclass(X0,X1) )
| ~ spl0_168
| ~ spl0_1044 ),
inference(forward_demodulation,[],[f33157,f1430]) ).
fof(f33157,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,complement(X1)) )
| ~ spl0_1044 ),
inference(avatar_component_clause,[],[f33156]) ).
fof(f33168,plain,
( spl0_1046
| ~ spl0_168
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f13934,f3490,f1428,f33166]) ).
fof(f33166,plain,
( spl0_1046
<=> ! [X0,X1] :
( ~ member(singleton_relation,cross_product(X0,X1))
| member(second(singleton_relation),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f3490,plain,
( spl0_306
<=> ! [X0,X1] :
( ~ member(y,cross_product(X0,X1))
| member(second(y),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f13934,plain,
( ! [X0,X1] :
( ~ member(singleton_relation,cross_product(X0,X1))
| member(second(singleton_relation),X1) )
| ~ spl0_168
| ~ spl0_306 ),
inference(superposition,[],[f3491,f1430]) ).
fof(f3491,plain,
( ! [X0,X1] :
( ~ member(y,cross_product(X0,X1))
| member(second(y),X1) )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f3490]) ).
fof(f33163,plain,
( spl0_1045
| ~ spl0_274
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f3116,f2988,f2834,f33161]) ).
fof(f3116,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(complement(X1),X0) )
| ~ spl0_274
| ~ spl0_282 ),
inference(duplicate_literal_removal,[],[f3087]) ).
fof(f3087,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(complement(X1),X0)
| y = intersection(complement(X1),X0) )
| ~ spl0_274
| ~ spl0_282 ),
inference(resolution,[],[f2989,f2835]) ).
fof(f33158,plain,
( spl0_1044
| ~ spl0_275
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3062,f2980,f2838,f33156]) ).
fof(f3062,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,complement(X1)) )
| ~ spl0_275
| ~ spl0_280 ),
inference(duplicate_literal_removal,[],[f3035]) ).
fof(f3035,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| y = intersection(X0,complement(X1))
| y = intersection(X0,complement(X1)) )
| ~ spl0_275
| ~ spl0_280 ),
inference(resolution,[],[f2981,f2839]) ).
fof(f33152,plain,
( spl0_1043
| ~ spl0_160
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2871,f2822,f1347,f33150]) ).
fof(f33150,plain,
( spl0_1043
<=> ! [X0,X1] :
( y = X0
| subclass(intersection(y,X1),regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f2822,plain,
( spl0_271
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),y)
| y = X1
| subclass(X0,regular(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2871,plain,
( ! [X0,X1] :
( y = X0
| subclass(intersection(y,X1),regular(X0)) )
| ~ spl0_160
| ~ spl0_271 ),
inference(duplicate_literal_removal,[],[f2860]) ).
fof(f2860,plain,
( ! [X0,X1] :
( y = X0
| subclass(intersection(y,X1),regular(X0))
| subclass(intersection(y,X1),regular(X0)) )
| ~ spl0_160
| ~ spl0_271 ),
inference(resolution,[],[f2823,f1348]) ).
fof(f2823,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),y)
| y = X1
| subclass(X0,regular(X1)) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2822]) ).
fof(f33146,plain,
( spl0_1042
| ~ spl0_161
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2870,f2822,f1351,f33144]) ).
fof(f33144,plain,
( spl0_1042
<=> ! [X0,X1] :
( y = X0
| subclass(intersection(X1,y),regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f2870,plain,
( ! [X0,X1] :
( y = X0
| subclass(intersection(X1,y),regular(X0)) )
| ~ spl0_161
| ~ spl0_271 ),
inference(duplicate_literal_removal,[],[f2861]) ).
fof(f2861,plain,
( ! [X0,X1] :
( y = X0
| subclass(intersection(X1,y),regular(X0))
| subclass(intersection(X1,y),regular(X0)) )
| ~ spl0_161
| ~ spl0_271 ),
inference(resolution,[],[f2823,f1352]) ).
fof(f33142,plain,
( ~ spl0_1041
| spl0_238
| ~ spl0_239
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2657,f2450,f2283,f2279,f33139]) ).
fof(f33139,plain,
( spl0_1041
<=> subclass(subset_relation,complement(cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f2657,plain,
( subset_relation = y
| ~ subclass(subset_relation,complement(cross_product(universal_class,universal_class)))
| ~ spl0_239
| ~ spl0_248 ),
inference(resolution,[],[f2451,f2285]) ).
fof(f2285,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2283]) ).
fof(f33137,plain,
( ~ spl0_1040
| ~ spl0_168
| spl0_882 ),
inference(avatar_split_clause,[],[f27706,f21901,f1428,f33134]) ).
fof(f33134,plain,
( spl0_1040
<=> omega = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f27706,plain,
( omega != singleton_relation
| ~ spl0_168
| spl0_882 ),
inference(superposition,[],[f21902,f1430]) ).
fof(f21902,plain,
( omega != y
| spl0_882 ),
inference(avatar_component_clause,[],[f21901]) ).
fof(f33132,plain,
( spl0_1039
| ~ spl0_46
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2417,f2283,f424,f33130]) ).
fof(f33130,plain,
( spl0_1039
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(regular(subset_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f2417,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(regular(subset_relation),X0) )
| ~ spl0_46
| ~ spl0_239 ),
inference(resolution,[],[f2285,f425]) ).
fof(f32498,plain,
( spl0_1038
| ~ spl0_168
| ~ spl0_1023 ),
inference(avatar_split_clause,[],[f32375,f32372,f1428,f32496]) ).
fof(f32375,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_168
| ~ spl0_1023 ),
inference(forward_demodulation,[],[f32373,f1430]) ).
fof(f32494,plain,
( spl0_1037
| ~ spl0_168
| ~ spl0_1022 ),
inference(avatar_split_clause,[],[f32370,f32367,f1428,f32492]) ).
fof(f32370,plain,
( ! [X0,X1] : singleton_relation = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_168
| ~ spl0_1022 ),
inference(forward_demodulation,[],[f32368,f1430]) ).
fof(f32490,plain,
( ~ spl0_10
| spl0_1013 ),
inference(avatar_contradiction_clause,[],[f32489]) ).
fof(f32489,plain,
( $false
| ~ spl0_10
| spl0_1013 ),
inference(resolution,[],[f32267,f252]) ).
fof(f32267,plain,
( ~ subclass(element_relation,element_relation)
| spl0_1013 ),
inference(avatar_component_clause,[],[f32265]) ).
fof(f32265,plain,
( spl0_1013
<=> subclass(element_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f32488,plain,
( spl0_1036
| ~ spl0_168
| ~ spl0_1021 ),
inference(avatar_split_clause,[],[f32365,f32362,f1428,f32486]) ).
fof(f32365,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_168
| ~ spl0_1021 ),
inference(forward_demodulation,[],[f32363,f1430]) ).
fof(f32484,plain,
( spl0_1035
| ~ spl0_168
| ~ spl0_1020 ),
inference(avatar_split_clause,[],[f32360,f32357,f1428,f32482]) ).
fof(f32360,plain,
( ! [X0,X1] : singleton_relation = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_168
| ~ spl0_1020 ),
inference(forward_demodulation,[],[f32358,f1430]) ).
fof(f32480,plain,
( ~ spl0_1034
| ~ spl0_168
| spl0_662 ),
inference(avatar_split_clause,[],[f27693,f13193,f1428,f32477]) ).
fof(f32477,plain,
( spl0_1034
<=> singleton_relation = domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f13193,plain,
( spl0_662
<=> y = domain_of(domain_of(flip(cross_product(y,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f27693,plain,
( singleton_relation != domain_of(domain_of(flip(cross_product(singleton_relation,universal_class))))
| ~ spl0_168
| spl0_662 ),
inference(superposition,[],[f13194,f1430]) ).
fof(f13194,plain,
( y != domain_of(domain_of(flip(cross_product(y,universal_class))))
| spl0_662 ),
inference(avatar_component_clause,[],[f13193]) ).
fof(f32475,plain,
( ~ spl0_1033
| ~ spl0_168
| spl0_293 ),
inference(avatar_split_clause,[],[f13928,f3213,f1428,f32472]) ).
fof(f32472,plain,
( spl0_1033
<=> inductive(domain_of(regular(cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f3213,plain,
( spl0_293
<=> inductive(domain_of(regular(cross_product(unordered_pair(y,y),universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f13928,plain,
( ~ inductive(domain_of(regular(cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class))))
| ~ spl0_168
| spl0_293 ),
inference(superposition,[],[f3215,f1430]) ).
fof(f3215,plain,
( ~ inductive(domain_of(regular(cross_product(unordered_pair(y,y),universal_class))))
| spl0_293 ),
inference(avatar_component_clause,[],[f3213]) ).
fof(f32450,plain,
( spl0_1031
| spl0_1032
| ~ spl0_332
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f12024,f6115,f3977,f32448,f32444]) ).
fof(f32444,plain,
( spl0_1031
<=> member(regular(subset_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f32448,plain,
( spl0_1032
<=> ! [X0] : ~ member(regular(subset_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f12024,plain,
( ! [X0] :
( ~ member(regular(subset_relation),X0)
| member(regular(subset_relation),universal_class) )
| ~ spl0_332
| ~ spl0_446 ),
inference(resolution,[],[f3979,f6116]) ).
fof(f32421,plain,
( spl0_1029
| spl0_1030
| ~ spl0_250
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f6256,f6115,f2482,f32419,f32415]) ).
fof(f32415,plain,
( spl0_1029
<=> member(regular(identity_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f32419,plain,
( spl0_1030
<=> ! [X0] : ~ member(regular(identity_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f6256,plain,
( ! [X0] :
( ~ member(regular(identity_relation),X0)
| member(regular(identity_relation),universal_class) )
| ~ spl0_250
| ~ spl0_446 ),
inference(resolution,[],[f6116,f2484]) ).
fof(f32397,plain,
( spl0_1027
| spl0_1028
| ~ spl0_249
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f6252,f6115,f2454,f32395,f32391]) ).
fof(f32391,plain,
( spl0_1027
<=> member(regular(singleton_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f32395,plain,
( spl0_1028
<=> ! [X0] : ~ member(regular(singleton_relation),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f6252,plain,
( ! [X0] :
( ~ member(regular(singleton_relation),X0)
| member(regular(singleton_relation),universal_class) )
| ~ spl0_249
| ~ spl0_446 ),
inference(resolution,[],[f6116,f2456]) ).
fof(f32389,plain,
( spl0_1026
| ~ spl0_45
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f3494,f2248,f405,f32387]) ).
fof(f32387,plain,
( spl0_1026
<=> ! [X0] :
( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f405,plain,
( spl0_45
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f2248,plain,
( spl0_233
<=> ! [X0] :
( ~ inductive(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f3494,plain,
( ! [X0] :
( ~ inductive(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) )
| ~ spl0_45
| ~ spl0_233 ),
inference(resolution,[],[f2249,f406]) ).
fof(f406,plain,
( ! [X8] :
( function(domain_of(flip(cross_product(X8,universal_class))))
| ~ one_to_one(X8) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f2249,plain,
( ! [X0] :
( ~ function(X0)
| ~ inductive(X0) )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2248]) ).
fof(f32384,plain,
( spl0_1025
| ~ spl0_35
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f3419,f3235,f365,f32382]) ).
fof(f32382,plain,
( spl0_1025
<=> ! [X0,X1] :
( subclass(intersection(X0,y),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f365,plain,
( spl0_35
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f3419,plain,
( ! [X0,X1] :
( subclass(intersection(X0,y),X1)
| y = X1 )
| ~ spl0_35
| ~ spl0_298 ),
inference(duplicate_literal_removal,[],[f3391]) ).
fof(f3391,plain,
( ! [X0,X1] :
( subclass(intersection(X0,y),X1)
| y = X1
| subclass(intersection(X0,y),X1) )
| ~ spl0_35
| ~ spl0_298 ),
inference(resolution,[],[f3236,f366]) ).
fof(f366,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f32379,plain,
( spl0_1024
| ~ spl0_35
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f3390,f3231,f365,f32377]) ).
fof(f32377,plain,
( spl0_1024
<=> ! [X0,X1] :
( subclass(intersection(y,X0),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f3390,plain,
( ! [X0,X1] :
( subclass(intersection(y,X0),X1)
| y = X1 )
| ~ spl0_35
| ~ spl0_297 ),
inference(duplicate_literal_removal,[],[f3362]) ).
fof(f3362,plain,
( ! [X0,X1] :
( subclass(intersection(y,X0),X1)
| y = X1
| subclass(intersection(y,X0),X1) )
| ~ spl0_35
| ~ spl0_297 ),
inference(resolution,[],[f3232,f366]) ).
fof(f32374,plain,
( spl0_1023
| ~ spl0_274
| ~ spl0_292 ),
inference(avatar_split_clause,[],[f3353,f3209,f2834,f32372]) ).
fof(f3353,plain,
( ! [X0,X1] : y = intersection(complement(X0),intersection(X0,X1))
| ~ spl0_274
| ~ spl0_292 ),
inference(duplicate_literal_removal,[],[f3325]) ).
fof(f3325,plain,
( ! [X0,X1] :
( y = intersection(complement(X0),intersection(X0,X1))
| y = intersection(complement(X0),intersection(X0,X1)) )
| ~ spl0_274
| ~ spl0_292 ),
inference(resolution,[],[f3210,f2835]) ).
fof(f32369,plain,
( spl0_1022
| ~ spl0_274
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f3324,f3205,f2834,f32367]) ).
fof(f3324,plain,
( ! [X0,X1] : y = intersection(complement(X0),intersection(X1,X0))
| ~ spl0_274
| ~ spl0_291 ),
inference(duplicate_literal_removal,[],[f3296]) ).
fof(f3296,plain,
( ! [X0,X1] :
( y = intersection(complement(X0),intersection(X1,X0))
| y = intersection(complement(X0),intersection(X1,X0)) )
| ~ spl0_274
| ~ spl0_291 ),
inference(resolution,[],[f3206,f2835]) ).
fof(f32364,plain,
( spl0_1021
| ~ spl0_275
| ~ spl0_290 ),
inference(avatar_split_clause,[],[f3295,f3201,f2838,f32362]) ).
fof(f3295,plain,
( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X0))
| ~ spl0_275
| ~ spl0_290 ),
inference(duplicate_literal_removal,[],[f3267]) ).
fof(f3267,plain,
( ! [X0,X1] :
( y = intersection(intersection(X0,X1),complement(X0))
| y = intersection(intersection(X0,X1),complement(X0)) )
| ~ spl0_275
| ~ spl0_290 ),
inference(resolution,[],[f3202,f2839]) ).
fof(f32359,plain,
( spl0_1020
| ~ spl0_275
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3266,f3197,f2838,f32357]) ).
fof(f3266,plain,
( ! [X0,X1] : y = intersection(intersection(X0,X1),complement(X1))
| ~ spl0_275
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3238]) ).
fof(f3238,plain,
( ! [X0,X1] :
( y = intersection(intersection(X0,X1),complement(X1))
| y = intersection(intersection(X0,X1),complement(X1)) )
| ~ spl0_275
| ~ spl0_289 ),
inference(resolution,[],[f3198,f2839]) ).
fof(f32347,plain,
( spl0_700
| ~ spl0_1001 ),
inference(avatar_contradiction_clause,[],[f32301]) ).
fof(f32301,plain,
( $false
| spl0_700
| ~ spl0_1001 ),
inference(resolution,[],[f31969,f14832]) ).
fof(f14832,plain,
( ~ subclass(singleton_relation,complement(element_relation))
| spl0_700 ),
inference(avatar_component_clause,[],[f14830]) ).
fof(f14830,plain,
( spl0_700
<=> subclass(singleton_relation,complement(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f31969,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_1001 ),
inference(avatar_component_clause,[],[f31968]) ).
fof(f32346,plain,
( spl0_921
| ~ spl0_1001 ),
inference(avatar_contradiction_clause,[],[f32302]) ).
fof(f32302,plain,
( $false
| spl0_921
| ~ spl0_1001 ),
inference(resolution,[],[f31969,f24325]) ).
fof(f24325,plain,
( ~ subclass(singleton_relation,identity_relation)
| spl0_921 ),
inference(avatar_component_clause,[],[f24323]) ).
fof(f24323,plain,
( spl0_921
<=> subclass(singleton_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f32345,plain,
( spl0_922
| ~ spl0_1001 ),
inference(avatar_contradiction_clause,[],[f32303]) ).
fof(f32303,plain,
( $false
| spl0_922
| ~ spl0_1001 ),
inference(resolution,[],[f31969,f25004]) ).
fof(f25004,plain,
( ~ subclass(singleton_relation,subset_relation)
| spl0_922 ),
inference(avatar_component_clause,[],[f25002]) ).
fof(f25002,plain,
( spl0_922
<=> subclass(singleton_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f32300,plain,
( spl0_1019
| ~ spl0_187
| ~ spl0_167
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2712,f2482,f1424,f1605,f32297]) ).
fof(f32297,plain,
( spl0_1019
<=> member(regular(identity_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1424,plain,
( spl0_167
<=> ! [X0] :
( member(X0,identity_relation)
| ~ member(X0,subset_relation)
| ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f2712,plain,
( ~ member(regular(identity_relation),subset_relation)
| member(regular(identity_relation),identity_relation)
| ~ spl0_167
| ~ spl0_250 ),
inference(resolution,[],[f2484,f1425]) ).
fof(f1425,plain,
( ! [X0] :
( ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,subset_relation)
| member(X0,identity_relation) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f32295,plain,
( ~ spl0_1018
| spl0_123
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2471,f1428,f973,f32292]) ).
fof(f32292,plain,
( spl0_1018
<=> member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f973,plain,
( spl0_123
<=> member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f2471,plain,
( ~ member(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class)
| spl0_123
| ~ spl0_168 ),
inference(superposition,[],[f974,f1430]) ).
fof(f974,plain,
( ~ member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
| spl0_123 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f32290,plain,
( ~ spl0_1017
| spl0_4
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2466,f1428,f223,f32287]) ).
fof(f2466,plain,
( singleton_relation != domain_of(intersection(x,cross_product(singleton_relation,singleton_relation)))
| spl0_4
| ~ spl0_168 ),
inference(superposition,[],[f225,f1430]) ).
fof(f32283,plain,
( ~ spl0_1016
| ~ spl0_168
| spl0_569 ),
inference(avatar_split_clause,[],[f13949,f9473,f1428,f32280]) ).
fof(f32280,plain,
( spl0_1016
<=> inductive(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f9473,plain,
( spl0_569
<=> inductive(domain_of(domain_of(flip(cross_product(y,universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f13949,plain,
( ~ inductive(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))))
| ~ spl0_168
| spl0_569 ),
inference(superposition,[],[f9475,f1430]) ).
fof(f9475,plain,
( ~ inductive(domain_of(domain_of(flip(cross_product(y,universal_class)))))
| spl0_569 ),
inference(avatar_component_clause,[],[f9473]) ).
fof(f32278,plain,
( ~ spl0_1015
| ~ spl0_168
| spl0_294 ),
inference(avatar_split_clause,[],[f13929,f3217,f1428,f32275]) ).
fof(f32275,plain,
( spl0_1015
<=> singleton_relation = cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f3217,plain,
( spl0_294
<=> y = cross_product(unordered_pair(y,y),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f13929,plain,
( singleton_relation != cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)
| ~ spl0_168
| spl0_294 ),
inference(superposition,[],[f3218,f1430]) ).
fof(f3218,plain,
( y != cross_product(unordered_pair(y,y),universal_class)
| spl0_294 ),
inference(avatar_component_clause,[],[f3217]) ).
fof(f32273,plain,
( ~ spl0_1014
| ~ spl0_168
| spl0_241 ),
inference(avatar_split_clause,[],[f13925,f2306,f1428,f32270]) ).
fof(f32270,plain,
( spl0_1014
<=> member(singleton_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f2306,plain,
( spl0_241
<=> member(y,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f13925,plain,
( ~ member(singleton_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_168
| spl0_241 ),
inference(superposition,[],[f2307,f1430]) ).
fof(f2307,plain,
( ~ member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
| spl0_241 ),
inference(avatar_component_clause,[],[f2306]) ).
fof(f32268,plain,
( ~ spl0_1013
| spl0_169
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f27714,f13889,f1432,f32265]) ).
fof(f13889,plain,
( spl0_691
<=> ! [X0] :
( ~ subclass(element_relation,X0)
| member(regular(singleton_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f27714,plain,
( ~ subclass(element_relation,element_relation)
| spl0_169
| ~ spl0_691 ),
inference(resolution,[],[f1433,f13890]) ).
fof(f13890,plain,
( ! [X0] :
( member(regular(singleton_relation),X0)
| ~ subclass(element_relation,X0) )
| ~ spl0_691 ),
inference(avatar_component_clause,[],[f13889]) ).
fof(f1433,plain,
( ~ member(regular(singleton_relation),element_relation)
| spl0_169 ),
inference(avatar_component_clause,[],[f1432]) ).
fof(f32263,plain,
( ~ spl0_1012
| ~ spl0_168
| spl0_235 ),
inference(avatar_split_clause,[],[f2475,f2263,f1428,f32260]) ).
fof(f32260,plain,
( spl0_1012
<=> member(singleton_relation,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f2263,plain,
( spl0_235
<=> member(y,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2475,plain,
( ~ member(singleton_relation,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl0_168
| spl0_235 ),
inference(superposition,[],[f2264,f1430]) ).
fof(f2264,plain,
( ~ member(y,cross_product(universal_class,cross_product(universal_class,universal_class)))
| spl0_235 ),
inference(avatar_component_clause,[],[f2263]) ).
fof(f32251,plain,
( spl0_1011
| ~ spl0_46
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f29539,f4993,f424,f32249]) ).
fof(f29539,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(singleton_relation,X0) )
| ~ spl0_46
| ~ spl0_375 ),
inference(resolution,[],[f4994,f425]) ).
fof(f32247,plain,
( ~ spl0_1010
| ~ spl0_168
| spl0_854 ),
inference(avatar_split_clause,[],[f27705,f21109,f1428,f32244]) ).
fof(f21109,plain,
( spl0_854
<=> operation(domain_of(flip(cross_product(y,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f27705,plain,
( ~ operation(domain_of(flip(cross_product(singleton_relation,universal_class))))
| ~ spl0_168
| spl0_854 ),
inference(superposition,[],[f21111,f1430]) ).
fof(f21111,plain,
( ~ operation(domain_of(flip(cross_product(y,universal_class))))
| spl0_854 ),
inference(avatar_component_clause,[],[f21109]) ).
fof(f32242,plain,
( ~ spl0_1009
| ~ spl0_168
| spl0_304 ),
inference(avatar_split_clause,[],[f13932,f3480,f1428,f32239]) ).
fof(f32239,plain,
( spl0_1009
<=> second(singleton_relation) = domain_of(first(singleton_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f3480,plain,
( spl0_304
<=> second(y) = domain_of(first(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f13932,plain,
( second(singleton_relation) != domain_of(first(singleton_relation))
| ~ spl0_168
| spl0_304 ),
inference(superposition,[],[f3481,f1430]) ).
fof(f3481,plain,
( second(y) != domain_of(first(y))
| spl0_304 ),
inference(avatar_component_clause,[],[f3480]) ).
fof(f32171,plain,
( ~ spl0_1008
| spl0_124
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f13920,f1428,f978,f32168]) ).
fof(f32168,plain,
( spl0_1008
<=> member(singleton_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f978,plain,
( spl0_124
<=> member(y,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f13920,plain,
( ~ member(singleton_relation,cross_product(universal_class,universal_class))
| spl0_124
| ~ spl0_168 ),
inference(superposition,[],[f980,f1430]) ).
fof(f980,plain,
( ~ member(y,cross_product(universal_class,universal_class))
| spl0_124 ),
inference(avatar_component_clause,[],[f978]) ).
fof(f32166,plain,
( ~ spl0_1007
| ~ spl0_168
| spl0_823 ),
inference(avatar_split_clause,[],[f27704,f19881,f1428,f32163]) ).
fof(f32163,plain,
( spl0_1007
<=> member(singleton_relation,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f19881,plain,
( spl0_823
<=> member(y,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f27704,plain,
( ~ member(singleton_relation,composition_function)
| ~ spl0_168
| spl0_823 ),
inference(superposition,[],[f19883,f1430]) ).
fof(f19883,plain,
( ~ member(y,composition_function)
| spl0_823 ),
inference(avatar_component_clause,[],[f19881]) ).
fof(f32161,plain,
( spl0_1006
| ~ spl0_1
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2465,f1428,f209,f32159]) ).
fof(f209,plain,
( spl0_1
<=> ! [X0] :
( ~ inductive(X0)
| member(y,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f2465,plain,
( ! [X0] :
( member(singleton_relation,X0)
| ~ inductive(X0) )
| ~ spl0_1
| ~ spl0_168 ),
inference(superposition,[],[f210,f1430]) ).
fof(f210,plain,
( ! [X0] :
( member(y,X0)
| ~ inductive(X0) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f32095,plain,
( spl0_1005
| ~ spl0_91
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1973,f1943,f710,f32093]) ).
fof(f32093,plain,
( spl0_1005
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f710,plain,
( spl0_91
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1943,plain,
( spl0_215
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1973,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_91
| ~ spl0_215 ),
inference(resolution,[],[f1944,f711]) ).
fof(f711,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| ~ operation(X10) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f1944,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f1943]) ).
fof(f32091,plain,
( spl0_1004
| ~ spl0_91
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1947,f1939,f710,f32089]) ).
fof(f32089,plain,
( spl0_1004
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1939,plain,
( spl0_214
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1947,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_91
| ~ spl0_214 ),
inference(resolution,[],[f1940,f711]) ).
fof(f1940,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f1939]) ).
fof(f32047,plain,
( spl0_1003
| ~ spl0_139
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2207,f2203,f1089,f32045]) ).
fof(f32045,plain,
( spl0_1003
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f2203,plain,
( spl0_226
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2207,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),subset_relation) )
| ~ spl0_139
| ~ spl0_226 ),
inference(resolution,[],[f2204,f1090]) ).
fof(f2204,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2203]) ).
fof(f32007,plain,
( spl0_1002
| ~ spl0_103
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2011,f1999,f778,f32005]) ).
fof(f32005,plain,
( spl0_1002
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ homomorphism(X3,X0,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f778,plain,
( spl0_103
<=> ! [X10,X11,X0,X9,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1999,plain,
( spl0_216
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f2011,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ homomorphism(X3,X0,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))))))),universal_class),X0),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) )
| ~ spl0_103
| ~ spl0_216 ),
inference(resolution,[],[f2000,f779]) ).
fof(f779,plain,
( ! [X10,X0,X11,X1,X9] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
| ~ homomorphism(X9,X10,X11)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f2000,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2)
| ~ subclass(composition_function,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_216 ),
inference(avatar_component_clause,[],[f1999]) ).
fof(f31970,plain,
( spl0_1001
| ~ spl0_168
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f13938,f5764,f1428,f31968]) ).
fof(f5764,plain,
( spl0_427
<=> ! [X0] : subclass(y,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f13938,plain,
( ! [X0] : subclass(singleton_relation,X0)
| ~ spl0_168
| ~ spl0_427 ),
inference(superposition,[],[f5765,f1430]) ).
fof(f5765,plain,
( ! [X0] : subclass(y,X0)
| ~ spl0_427 ),
inference(avatar_component_clause,[],[f5764]) ).
fof(f31966,plain,
( spl0_1000
| ~ spl0_211
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2140,f2118,f1883,f31964]) ).
fof(f31964,plain,
( spl0_1000
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1883,plain,
( spl0_211
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2118,plain,
( spl0_221
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f2140,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(successor_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),complement(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
| ~ spl0_211
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1884]) ).
fof(f1884,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f1883]) ).
fof(f2119,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2118]) ).
fof(f31920,plain,
( spl0_999
| ~ spl0_80
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2206,f2203,f647,f31918]) ).
fof(f31918,plain,
( spl0_999
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f647,plain,
( spl0_80
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f2206,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_226 ),
inference(resolution,[],[f2204,f648]) ).
fof(f648,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f31883,plain,
( spl0_998
| ~ spl0_216
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2126,f2118,f1999,f31881]) ).
fof(f31881,plain,
( spl0_998
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f2126,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl0_216
| ~ spl0_221 ),
inference(resolution,[],[f2119,f2000]) ).
fof(f31846,plain,
( spl0_997
| ~ spl0_93
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2145,f2118,f719,f31844]) ).
fof(f31844,plain,
( spl0_997
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f719,plain,
( spl0_93
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2145,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(composition_function))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0))))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_221 ),
inference(resolution,[],[f2119,f720]) ).
fof(f720,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f31824,plain,
( spl0_996
| ~ spl0_103
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1897,f1889,f778,f31822]) ).
fof(f31822,plain,
( spl0_996
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(X3))
| ~ operation(X2)
| ~ homomorphism(X4,X3,X5)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f1889,plain,
( spl0_212
<=> ! [X0,X3,X2,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1897,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(X3))
| ~ operation(X2)
| ~ homomorphism(X4,X3,X5)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class),X3),universal_class)))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),X4),universal_class))))))))))),universal_class),X5),universal_class))))))) )
| ~ spl0_103
| ~ spl0_212 ),
inference(resolution,[],[f1890,f779]) ).
fof(f1890,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| ~ operation(X0) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f1889]) ).
fof(f31820,plain,
( spl0_995
| ~ spl0_103
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1707,f1646,f778,f31818]) ).
fof(f31818,plain,
( spl0_995
<=> ! [X0,X3,X2,X1] :
( ~ subclass(domain_relation,domain_of(X0))
| ~ member(X1,universal_class)
| ~ homomorphism(X2,X0,X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1646,plain,
( spl0_192
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1707,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,domain_of(X0))
| ~ member(X1,universal_class)
| ~ homomorphism(X2,X0,X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))),universal_class),X0),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(X1),domain_of(X1)),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
| ~ spl0_103
| ~ spl0_192 ),
inference(resolution,[],[f1647,f779]) ).
fof(f1647,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
| ~ subclass(domain_relation,X1)
| ~ member(X0,universal_class) )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1646]) ).
fof(f31783,plain,
( spl0_994
| ~ spl0_57
| ~ spl0_103
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1285,f1264,f778,f500,f31781]) ).
fof(f31781,plain,
( spl0_994
<=> ! [X0,X3,X2,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f500,plain,
( spl0_57
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1285,plain,
( ! [X2,X3,X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class)),universal_class)))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3) )
| ~ spl0_57
| ~ spl0_103
| ~ spl0_153 ),
inference(forward_demodulation,[],[f1282,f501]) ).
fof(f501,plain,
( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f1282,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),identity_relation)
| ~ homomorphism(X2,flip(cross_product(subset_relation,universal_class)),X3)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),flip(cross_product(subset_relation,universal_class))),universal_class)))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class))))))))))),universal_class),X3),universal_class))))))) )
| ~ spl0_103
| ~ spl0_153 ),
inference(resolution,[],[f1265,f779]) ).
fof(f31779,plain,
( spl0_993
| ~ spl0_103
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1096,f1078,f778,f31777]) ).
fof(f31777,plain,
( spl0_993
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(X0))
| ~ homomorphism(X1,X0,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f1096,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,domain_of(X0))
| ~ homomorphism(X1,X0,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X0),universal_class)))))))),universal_class),X1),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X1),universal_class))))))))))),universal_class),X2),universal_class))))))) )
| ~ spl0_103
| ~ spl0_137 ),
inference(resolution,[],[f1079,f779]) ).
fof(f31611,plain,
( spl0_992
| ~ spl0_96
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2016,f1999,f746,f31609]) ).
fof(f31609,plain,
( spl0_992
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f746,plain,
( spl0_96
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f2016,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),unordered_pair(X1,X1))),X0) )
| ~ spl0_96
| ~ spl0_216 ),
inference(resolution,[],[f2000,f747]) ).
fof(f747,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f31607,plain,
( spl0_990
| ~ spl0_991
| ~ spl0_101
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2018,f1999,f767,f31604,f31601]) ).
fof(f31601,plain,
( spl0_990
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f31604,plain,
( spl0_991
<=> subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f767,plain,
( spl0_101
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f2018,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2),compose(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2))))))),X3) )
| ~ spl0_101
| ~ spl0_216 ),
inference(resolution,[],[f2000,f768]) ).
fof(f768,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f31566,plain,
( spl0_989
| ~ spl0_204
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2144,f2118,f1841,f31564]) ).
fof(f31564,plain,
( spl0_989
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose_class(X0)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f1841,plain,
( spl0_204
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2144,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose_class(X0)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))),unordered_pair(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(compose(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
| ~ spl0_204
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1842]) ).
fof(f1842,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f1841]) ).
fof(f31541,plain,
( spl0_988
| ~ spl0_215
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2030,f1999,f1943,f31539]) ).
fof(f31539,plain,
( spl0_988
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X0,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f2030,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X0,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_215
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1944]) ).
fof(f31537,plain,
( spl0_987
| ~ spl0_214
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2029,f1999,f1939,f31535]) ).
fof(f31535,plain,
( spl0_987
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f2029,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_214
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1940]) ).
fof(f31533,plain,
( spl0_986
| ~ spl0_94
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2028,f1999,f725,f31531]) ).
fof(f31531,plain,
( spl0_986
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f725,plain,
( spl0_94
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f2028,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(composition_function,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4))))))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))),unordered_pair(unordered_pair(X4,X4),unordered_pair(X4,unordered_pair(compose(X3,X4),compose(X3,X4)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_216 ),
inference(resolution,[],[f2000,f726]) ).
fof(f726,plain,
( ! [X1,X7,X4,X5] :
( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f31469,plain,
( spl0_985
| ~ spl0_216
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2149,f2122,f1999,f31467]) ).
fof(f31467,plain,
( spl0_985
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(X3))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f2122,plain,
( spl0_222
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f2149,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(X3))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_216
| ~ spl0_222 ),
inference(resolution,[],[f2123,f2000]) ).
fof(f2123,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f2122]) ).
fof(f31432,plain,
( spl0_984
| ~ spl0_192
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2125,f2118,f1646,f31430]) ).
fof(f31430,plain,
( spl0_984
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X2))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f2125,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X2))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
| ~ spl0_192
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1647]) ).
fof(f31368,plain,
( spl0_983
| ~ spl0_93
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2168,f2122,f719,f31366]) ).
fof(f31366,plain,
( spl0_983
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f2168,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2))))))),flip(composition_function))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_93
| ~ spl0_222 ),
inference(resolution,[],[f2123,f720]) ).
fof(f31331,plain,
( spl0_982
| ~ spl0_72
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2146,f2118,f605,f31329]) ).
fof(f31329,plain,
( spl0_982
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(domain_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f605,plain,
( spl0_72
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f2146,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(domain_relation))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class) )
| ~ spl0_72
| ~ spl0_221 ),
inference(resolution,[],[f2119,f606]) ).
fof(f606,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
| ~ member(X0,universal_class) )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f31307,plain,
( spl0_981
| ~ spl0_212
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2183,f2175,f1889,f31305]) ).
fof(f31305,plain,
( spl0_981
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(not_homomorphism1(X1,X2,X3),domain_of(X0))
| ~ member(X0,universal_class)
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),cross_product(universal_class,universal_class))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f2175,plain,
( spl0_223
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(X1))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2183,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(not_homomorphism1(X1,X2,X3),domain_of(X0))
| ~ member(X0,universal_class)
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),cross_product(universal_class,universal_class))
| ~ operation(X3) )
| ~ spl0_212
| ~ spl0_223 ),
inference(resolution,[],[f2176,f1890]) ).
fof(f2176,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
| ~ member(X0,domain_of(X1))
| ~ member(X1,universal_class) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2175]) ).
fof(f31249,plain,
( spl0_980
| ~ spl0_211
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2172,f2122,f1883,f31247]) ).
fof(f31247,plain,
( spl0_980
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f2172,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_211
| ~ spl0_222 ),
inference(duplicate_literal_removal,[],[f2163]) ).
fof(f2163,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))))))))),flip(successor_relation))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(complement(intersection(complement(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),complement(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_211
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1884]) ).
fof(f31224,plain,
( spl0_979
| ~ spl0_212
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1992,f1943,f1889,f31222]) ).
fof(f31222,plain,
( spl0_979
<=> ! [X3,X4,X0,X5,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f1992,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X5),universal_class)))),universal_class)),universal_class)))))
| ~ operation(X3) )
| ~ spl0_212
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1890]) ).
fof(f31220,plain,
( spl0_978
| ~ spl0_212
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1966,f1939,f1889,f31218]) ).
fof(f31218,plain,
( spl0_978
<=> ! [X3,X4,X0,X5,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f1966,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),compose(X4,X5))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X3),not_homomorphism1(X1,X2,X3)),unordered_pair(not_homomorphism1(X1,X2,X3),unordered_pair(not_homomorphism2(X1,X2,X3),not_homomorphism2(X1,X2,X3))))))),cross_product(universal_class,universal_class))
| ~ compatible(X1,X2,X3)
| homomorphism(X1,X2,X3)
| ~ operation(X2)
| ~ subclass(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X5,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X4),universal_class)))))
| ~ operation(X3) )
| ~ spl0_212
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1890]) ).
fof(f31216,plain,
( spl0_977
| ~ spl0_94
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1910,f1889,f725,f31214]) ).
fof(f31214,plain,
( spl0_977
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f1910,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X4),universal_class)))),universal_class),X5),universal_class)))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),compose(X5,X4))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_212 ),
inference(resolution,[],[f1890,f726]) ).
fof(f30949,plain,
( spl0_976
| ~ spl0_161
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1981,f1943,f1351,f30947]) ).
fof(f30947,plain,
( spl0_976
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f1981,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),X4) )
| ~ spl0_161
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1352]) ).
fof(f30945,plain,
( spl0_975
| ~ spl0_160
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1975,f1943,f1347,f30943]) ).
fof(f30943,plain,
( spl0_975
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f1975,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),X4) )
| ~ spl0_160
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1348]) ).
fof(f30941,plain,
( spl0_974
| ~ spl0_161
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1955,f1939,f1351,f30939]) ).
fof(f30939,plain,
( spl0_974
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f1955,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),X4) )
| ~ spl0_161
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1352]) ).
fof(f30937,plain,
( spl0_973
| ~ spl0_160
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1949,f1939,f1347,f30935]) ).
fof(f30935,plain,
( spl0_973
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f1949,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class))
| subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),X4) )
| ~ spl0_160
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1348]) ).
fof(f30933,plain,
( spl0_972
| ~ spl0_94
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1395,f1351,f725,f30931]) ).
fof(f30931,plain,
( spl0_972
<=> ! [X4,X0,X3,X2,X1] :
( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f1395,plain,
( ! [X2,X3,X0,X1,X4] :
( subclass(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4),not_subclass_element(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_161 ),
inference(resolution,[],[f1352,f726]) ).
fof(f30929,plain,
( spl0_971
| ~ spl0_94
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1374,f1347,f725,f30927]) ).
fof(f30927,plain,
( spl0_971
<=> ! [X4,X0,X3,X2,X1] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f1374,plain,
( ! [X2,X3,X0,X1,X4] :
( subclass(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4),not_subclass_element(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_160 ),
inference(resolution,[],[f1348,f726]) ).
fof(f30866,plain,
( spl0_970
| ~ spl0_34
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1974,f1943,f361,f30864]) ).
fof(f30864,plain,
( spl0_970
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f1974,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
| ~ spl0_34
| ~ spl0_215 ),
inference(resolution,[],[f1944,f362]) ).
fof(f30862,plain,
( spl0_969
| ~ spl0_34
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1948,f1939,f361,f30860]) ).
fof(f30860,plain,
( spl0_969
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f1948,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_34
| ~ spl0_214 ),
inference(resolution,[],[f1940,f362]) ).
fof(f30814,plain,
( spl0_968
| ~ spl0_139
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2190,f2186,f1089,f30812]) ).
fof(f30812,plain,
( spl0_968
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f2186,plain,
( spl0_224
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f2190,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),subset_relation) )
| ~ spl0_139
| ~ spl0_224 ),
inference(resolution,[],[f2187,f1090]) ).
fof(f2187,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2186]) ).
fof(f30651,plain,
( spl0_967
| ~ spl0_99
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2017,f1999,f759,f30649]) ).
fof(f30649,plain,
( spl0_967
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f759,plain,
( spl0_99
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2017,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3),compose(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3))))))),X0) )
| ~ spl0_99
| ~ spl0_216 ),
inference(resolution,[],[f2000,f760]) ).
fof(f760,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f30647,plain,
( spl0_965
| ~ spl0_966
| ~ spl0_101
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1714,f1646,f767,f30644,f30641]) ).
fof(f30641,plain,
( spl0_965
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f30644,plain,
( spl0_966
<=> subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f1714,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),flip(X2))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),domain_of(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))))),X2) )
| ~ spl0_101
| ~ spl0_192 ),
inference(resolution,[],[f1647,f768]) ).
fof(f30275,plain,
( spl0_964
| ~ spl0_56
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2157,f2122,f496,f30273]) ).
fof(f30273,plain,
( spl0_964
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2157,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3) )
| ~ spl0_56
| ~ spl0_222 ),
inference(resolution,[],[f2123,f497]) ).
fof(f30271,plain,
( ~ spl0_963
| ~ spl0_168
| spl0_787 ),
inference(avatar_split_clause,[],[f27702,f18712,f1428,f30268]) ).
fof(f30268,plain,
( spl0_963
<=> member(singleton_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f18712,plain,
( spl0_787
<=> member(y,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f27702,plain,
( ~ member(singleton_relation,successor_relation)
| ~ spl0_168
| spl0_787 ),
inference(superposition,[],[f18714,f1430]) ).
fof(f18714,plain,
( ~ member(y,successor_relation)
| spl0_787 ),
inference(avatar_component_clause,[],[f18712]) ).
fof(f30266,plain,
( spl0_962
| ~ spl0_56
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2134,f2118,f496,f30264]) ).
fof(f30264,plain,
( spl0_962
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2134,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X4)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3) )
| ~ spl0_56
| ~ spl0_221 ),
inference(resolution,[],[f2119,f497]) ).
fof(f30199,plain,
( spl0_961
| ~ spl0_51
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2159,f2122,f472,f30197]) ).
fof(f30197,plain,
( spl0_961
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2159,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
| ~ spl0_51
| ~ spl0_222 ),
inference(resolution,[],[f2123,f473]) ).
fof(f30195,plain,
( spl0_960
| ~ spl0_51
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2136,f2118,f472,f30193]) ).
fof(f30193,plain,
( spl0_960
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2136,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
| ~ spl0_51
| ~ spl0_221 ),
inference(resolution,[],[f2119,f473]) ).
fof(f29947,plain,
( spl0_959
| ~ spl0_38
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2153,f2122,f377,f29945]) ).
fof(f29945,plain,
( spl0_959
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2153,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
| ~ spl0_38
| ~ spl0_222 ),
inference(resolution,[],[f2123,f378]) ).
fof(f29943,plain,
( ~ spl0_958
| ~ spl0_168
| spl0_305 ),
inference(avatar_split_clause,[],[f13933,f3484,f1428,f29940]) ).
fof(f29940,plain,
( spl0_958
<=> member(singleton_relation,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f3484,plain,
( spl0_305
<=> member(y,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f13933,plain,
( ~ member(singleton_relation,domain_relation)
| ~ spl0_168
| spl0_305 ),
inference(superposition,[],[f3486,f1430]) ).
fof(f3486,plain,
( ~ member(y,domain_relation)
| spl0_305 ),
inference(avatar_component_clause,[],[f3484]) ).
fof(f29938,plain,
( spl0_957
| ~ spl0_36
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2152,f2122,f369,f29936]) ).
fof(f29936,plain,
( spl0_957
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2152,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class) )
| ~ spl0_36
| ~ spl0_222 ),
inference(resolution,[],[f2123,f370]) ).
fof(f29934,plain,
( spl0_956
| ~ spl0_38
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2130,f2118,f377,f29932]) ).
fof(f29932,plain,
( spl0_956
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f2130,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(X3,unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
| ~ spl0_38
| ~ spl0_221 ),
inference(resolution,[],[f2119,f378]) ).
fof(f29930,plain,
( spl0_955
| ~ spl0_36
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2129,f2118,f369,f29928]) ).
fof(f29928,plain,
( spl0_955
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f2129,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class) )
| ~ spl0_36
| ~ spl0_221 ),
inference(resolution,[],[f2119,f370]) ).
fof(f29908,plain,
( spl0_954
| ~ spl0_32
| ~ spl0_102
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2005,f1999,f773,f347,f29906]) ).
fof(f29906,plain,
( spl0_954
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f773,plain,
( spl0_102
<=> ! [X4,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f2005,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
| ~ spl0_102
| ~ spl0_216 ),
inference(resolution,[],[f2000,f774]) ).
fof(f774,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f29887,plain,
( spl0_953
| ~ spl0_168
| ~ spl0_952 ),
inference(avatar_split_clause,[],[f29883,f29875,f1428,f29885]) ).
fof(f29885,plain,
( spl0_953
<=> ! [X0,X3,X2,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f29883,plain,
( ! [X2,X3,X0,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3) )
| ~ spl0_168
| ~ spl0_952 ),
inference(forward_demodulation,[],[f29882,f1430]) ).
fof(f29882,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))))
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_168
| ~ spl0_952 ),
inference(forward_demodulation,[],[f29881,f1430]) ).
fof(f29881,plain,
( ! [X2,X3,X0,X1] :
( homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_168
| ~ spl0_952 ),
inference(forward_demodulation,[],[f29880,f1430]) ).
fof(f29880,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_168
| ~ spl0_952 ),
inference(forward_demodulation,[],[f29879,f1430]) ).
fof(f29879,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_168
| ~ spl0_952 ),
inference(forward_demodulation,[],[f29878,f1430]) ).
fof(f29878,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_168
| ~ spl0_952 ),
inference(forward_demodulation,[],[f29876,f1430]) ).
fof(f29877,plain,
( spl0_952
| ~ spl0_7
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2210,f2203,f238,f29875]) ).
fof(f238,plain,
( spl0_7
<=> ! [X0] :
( y = X0
| intersection(X0,regular(X0)) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f2210,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3))))))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ operation(X3)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_226 ),
inference(superposition,[],[f2204,f239]) ).
fof(f239,plain,
( ! [X0] :
( intersection(X0,regular(X0)) = y
| y = X0 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f29840,plain,
( spl0_951
| ~ spl0_139
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2179,f2175,f1089,f29838]) ).
fof(f29838,plain,
( spl0_951
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f2179,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),subset_relation) )
| ~ spl0_139
| ~ spl0_223 ),
inference(resolution,[],[f2176,f1090]) ).
fof(f29836,plain,
( ~ spl0_950
| ~ spl0_168
| spl0_268 ),
inference(avatar_split_clause,[],[f13927,f2805,f1428,f29833]) ).
fof(f29833,plain,
( spl0_950
<=> member(singleton_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2805,plain,
( spl0_268
<=> member(y,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f13927,plain,
( ~ member(singleton_relation,identity_relation)
| ~ spl0_168
| spl0_268 ),
inference(superposition,[],[f2806,f1430]) ).
fof(f2806,plain,
( ~ member(y,identity_relation)
| spl0_268 ),
inference(avatar_component_clause,[],[f2805]) ).
fof(f29788,plain,
( spl0_949
| ~ spl0_80
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2189,f2186,f647,f29786]) ).
fof(f29786,plain,
( spl0_949
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2189,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| ~ member(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_224 ),
inference(resolution,[],[f2187,f648]) ).
fof(f29526,plain,
( spl0_375
| ~ spl0_21
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f13916,f1428,f301,f4993]) ).
fof(f13916,plain,
( member(singleton_relation,universal_class)
| ~ spl0_21
| ~ spl0_168 ),
inference(superposition,[],[f302,f1430]) ).
fof(f29306,plain,
( ~ spl0_948
| ~ spl0_168
| spl0_238 ),
inference(avatar_split_clause,[],[f2476,f2279,f1428,f29303]) ).
fof(f29303,plain,
( spl0_948
<=> subset_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f2476,plain,
( subset_relation != singleton_relation
| ~ spl0_168
| spl0_238 ),
inference(superposition,[],[f2280,f1430]) ).
fof(f2280,plain,
( subset_relation != y
| spl0_238 ),
inference(avatar_component_clause,[],[f2279]) ).
fof(f29107,plain,
( ~ spl0_947
| spl0_97
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2468,f1428,f750,f29104]) ).
fof(f29104,plain,
( spl0_947
<=> member(singleton_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f750,plain,
( spl0_97
<=> member(y,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f2468,plain,
( ~ member(singleton_relation,subset_relation)
| spl0_97
| ~ spl0_168 ),
inference(superposition,[],[f751,f1430]) ).
fof(f751,plain,
( ~ member(y,subset_relation)
| spl0_97 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f28911,plain,
( ~ spl0_946
| spl0_69
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2467,f1428,f587,f28908]) ).
fof(f28908,plain,
( spl0_946
<=> member(singleton_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f587,plain,
( spl0_69
<=> member(y,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f2467,plain,
( ~ member(singleton_relation,element_relation)
| spl0_69
| ~ spl0_168 ),
inference(superposition,[],[f588,f1430]) ).
fof(f588,plain,
( ~ member(y,element_relation)
| spl0_69 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f28311,plain,
( spl0_945
| ~ spl0_171
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2460,f2118,f1497,f28309]) ).
fof(f28309,plain,
( spl0_945
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(compose(X1,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)))))
| ~ member(X3,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1497,plain,
( spl0_171
<=> ! [X2,X0,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f2460,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(compose(X1,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)))))
| ~ member(X3,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_171
| ~ spl0_221 ),
inference(resolution,[],[f1498,f2119]) ).
fof(f1498,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
| singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f28307,plain,
( spl0_944
| ~ spl0_171
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2459,f2122,f1497,f28305]) ).
fof(f28305,plain,
( spl0_944
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X0,X0))),flip(compose(X1,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)))))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f2459,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X0,X0))),flip(compose(X1,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),universal_class)))))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_171
| ~ spl0_222 ),
inference(resolution,[],[f1498,f2123]) ).
fof(f28145,plain,
( spl0_943
| ~ spl0_141
| ~ spl0_167
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1489,f1428,f1424,f1143,f28143]) ).
fof(f28143,plain,
( spl0_943
<=> ! [X0] :
( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1143,plain,
( spl0_141
<=> ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1489,plain,
( ! [X0] :
( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) )
| ~ spl0_141
| ~ spl0_167
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1476,f1430]) ).
fof(f1476,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_141
| ~ spl0_167 ),
inference(resolution,[],[f1425,f1144]) ).
fof(f1144,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f28141,plain,
( spl0_942
| ~ spl0_140
| ~ spl0_167
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1483,f1428,f1424,f1139,f28139]) ).
fof(f28139,plain,
( spl0_942
<=> ! [X0] :
( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f1483,plain,
( ! [X0] :
( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class) )
| ~ spl0_140
| ~ spl0_167
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1469,f1430]) ).
fof(f1469,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
| ~ spl0_140
| ~ spl0_167 ),
inference(resolution,[],[f1425,f1140]) ).
fof(f28137,plain,
( spl0_941
| ~ spl0_141
| ~ spl0_166
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1462,f1428,f1420,f1143,f28135]) ).
fof(f28135,plain,
( spl0_941
<=> ! [X0] :
( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1420,plain,
( spl0_166
<=> ! [X0] :
( member(X0,singleton_relation)
| ~ member(X0,element_relation)
| ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1462,plain,
( ! [X0] :
( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class) )
| ~ spl0_141
| ~ spl0_166
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1451,f1430]) ).
fof(f1451,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_141
| ~ spl0_166 ),
inference(resolution,[],[f1421,f1144]) ).
fof(f1421,plain,
( ! [X0] :
( ~ member(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,element_relation)
| member(X0,singleton_relation) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1420]) ).
fof(f28133,plain,
( spl0_940
| ~ spl0_140
| ~ spl0_166
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1456,f1428,f1420,f1139,f28131]) ).
fof(f28131,plain,
( spl0_940
<=> ! [X0] :
( singleton_relation = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1456,plain,
( ! [X0] :
( singleton_relation = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class) )
| ~ spl0_140
| ~ spl0_166
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1444,f1430]) ).
fof(f1444,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
| ~ spl0_140
| ~ spl0_166 ),
inference(resolution,[],[f1421,f1140]) ).
fof(f28128,plain,
( spl0_939
| ~ spl0_144
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2463,f1497,f1199,f28126]) ).
fof(f1199,plain,
( spl0_144
<=> ! [X0,X1] :
( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f2463,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
| singleton_relation = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_171 ),
inference(superposition,[],[f1498,f1200]) ).
fof(f1200,plain,
( ! [X0,X1] :
( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
| cross_product(X0,X1) = y )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f28018,plain,
( ~ spl0_938
| ~ spl0_168
| spl0_442 ),
inference(avatar_split_clause,[],[f13940,f5884,f1428,f28015]) ).
fof(f28015,plain,
( spl0_938
<=> function(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f5884,plain,
( spl0_442
<=> function(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f13940,plain,
( ~ function(singleton_relation)
| ~ spl0_168
| spl0_442 ),
inference(superposition,[],[f5885,f1430]) ).
fof(f5885,plain,
( ~ function(y)
| spl0_442 ),
inference(avatar_component_clause,[],[f5884]) ).
fof(f27954,plain,
( spl0_937
| ~ spl0_134
| ~ spl0_167
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1488,f1428,f1424,f1043,f27952]) ).
fof(f27952,plain,
( spl0_937
<=> ! [X0] :
( singleton_relation = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1043,plain,
( spl0_134
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| ~ member(X0,universal_class)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1488,plain,
( ! [X0] :
( singleton_relation = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class) )
| ~ spl0_134
| ~ spl0_167
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1475,f1430]) ).
fof(f1475,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| y = X0 )
| ~ spl0_134
| ~ spl0_167 ),
inference(resolution,[],[f1425,f1044]) ).
fof(f1044,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| y = X0 )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f27950,plain,
( spl0_936
| ~ spl0_134
| ~ spl0_166
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1461,f1428,f1420,f1043,f27948]) ).
fof(f27948,plain,
( spl0_936
<=> ! [X0] :
( singleton_relation = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1461,plain,
( ! [X0] :
( singleton_relation = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class) )
| ~ spl0_134
| ~ spl0_166
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1450,f1430]) ).
fof(f1450,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| y = X0 )
| ~ spl0_134
| ~ spl0_166 ),
inference(resolution,[],[f1421,f1044]) ).
fof(f27881,plain,
( spl0_935
| ~ spl0_112
| ~ spl0_167
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1487,f1428,f1424,f856,f27879]) ).
fof(f27879,plain,
( spl0_935
<=> ! [X0] :
( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
| member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1487,plain,
( ! [X0] :
( singleton_relation = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
| member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
| ~ spl0_112
| ~ spl0_167
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1474,f1430]) ).
fof(f1474,plain,
( ! [X0] :
( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
| member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_112
| ~ spl0_167 ),
inference(resolution,[],[f1425,f857]) ).
fof(f27877,plain,
( spl0_934
| ~ spl0_111
| ~ spl0_167
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1485,f1428,f1424,f852,f27875]) ).
fof(f27875,plain,
( spl0_934
<=> ! [X0] :
( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
| member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1485,plain,
( ! [X0] :
( singleton_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)
| ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
| member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation) )
| ~ spl0_111
| ~ spl0_167
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1471,f1430]) ).
fof(f1471,plain,
( ! [X0] :
( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
| member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
| y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
| ~ spl0_111
| ~ spl0_167 ),
inference(resolution,[],[f1425,f853]) ).
fof(f27873,plain,
( ~ spl0_933
| ~ spl0_168
| spl0_441 ),
inference(avatar_split_clause,[],[f13939,f5880,f1428,f27870]) ).
fof(f27870,plain,
( spl0_933
<=> single_valued_class(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f5880,plain,
( spl0_441
<=> single_valued_class(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f13939,plain,
( ~ single_valued_class(singleton_relation)
| ~ spl0_168
| spl0_441 ),
inference(superposition,[],[f5882,f1430]) ).
fof(f5882,plain,
( ~ single_valued_class(y)
| spl0_441 ),
inference(avatar_component_clause,[],[f5880]) ).
fof(f27868,plain,
( spl0_932
| ~ spl0_112
| ~ spl0_166
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1460,f1428,f1420,f856,f27866]) ).
fof(f27866,plain,
( spl0_932
<=> ! [X0] :
( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
| member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1460,plain,
( ! [X0] :
( singleton_relation = intersection(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
| member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
| ~ spl0_112
| ~ spl0_166
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1449,f1430]) ).
fof(f1449,plain,
( ! [X0] :
( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
| member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_112
| ~ spl0_166 ),
inference(resolution,[],[f1421,f857]) ).
fof(f27864,plain,
( spl0_931
| ~ spl0_111
| ~ spl0_166
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1458,f1428,f1420,f852,f27862]) ).
fof(f27862,plain,
( spl0_931
<=> ! [X0] :
( singleton_relation = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
| ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
| member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1458,plain,
( ! [X0] :
( singleton_relation = intersection(complement(compose(element_relation,complement(identity_relation))),X0)
| ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
| member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation) )
| ~ spl0_111
| ~ spl0_166
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1446,f1430]) ).
fof(f1446,plain,
( ! [X0] :
( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
| member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
| y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) )
| ~ spl0_111
| ~ spl0_166 ),
inference(resolution,[],[f1421,f853]) ).
fof(f27758,plain,
( spl0_930
| ~ spl0_12
| ~ spl0_57
| ~ spl0_167
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1481,f1428,f1424,f500,f261,f27756]) ).
fof(f27756,plain,
( spl0_930
<=> ! [X0] :
( singleton_relation = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f261,plain,
( spl0_12
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| y = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1481,plain,
( ! [X0] :
( singleton_relation = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class) )
| ~ spl0_12
| ~ spl0_57
| ~ spl0_167
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1480,f1430]) ).
fof(f1480,plain,
( ! [X0] :
( y = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class) )
| ~ spl0_12
| ~ spl0_57
| ~ spl0_167 ),
inference(forward_demodulation,[],[f1464,f501]) ).
fof(f1464,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),flip(cross_product(subset_relation,universal_class))) )
| ~ spl0_12
| ~ spl0_167 ),
inference(resolution,[],[f1425,f262]) ).
fof(f262,plain,
( ! [X0,X4] :
( member(X4,domain_of(X0))
| ~ member(X4,universal_class)
| y = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f27719,plain,
( spl0_929
| ~ spl0_109
| ~ spl0_167
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1486,f1428,f1424,f831,f27717]) ).
fof(f27717,plain,
( spl0_929
<=> ! [X0] :
( singleton_relation = X0
| ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1486,plain,
( ! [X0] :
( singleton_relation = X0
| ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_109
| ~ spl0_167
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1473,f1430]) ).
fof(f1473,plain,
( ! [X0] :
( ~ member(regular(X0),subset_relation)
| member(regular(X0),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| y = X0 )
| ~ spl0_109
| ~ spl0_167 ),
inference(resolution,[],[f1425,f832]) ).
fof(f27612,plain,
( spl0_928
| ~ spl0_169
| ~ spl0_166
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2512,f2454,f1420,f1432,f27609]) ).
fof(f2512,plain,
( ~ member(regular(singleton_relation),element_relation)
| member(regular(singleton_relation),singleton_relation)
| ~ spl0_166
| ~ spl0_249 ),
inference(resolution,[],[f2456,f1421]) ).
fof(f26653,plain,
( spl0_926
| ~ spl0_927
| ~ spl0_106
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2444,f2426,f810,f26650,f26646]) ).
fof(f26646,plain,
( spl0_926
<=> y = complement(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f26650,plain,
( spl0_927
<=> subclass(complement(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f810,plain,
( spl0_106
<=> ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2444,plain,
( ~ subclass(complement(subset_relation),identity_relation)
| y = complement(subset_relation)
| ~ spl0_106
| ~ spl0_246 ),
inference(duplicate_literal_removal,[],[f2437]) ).
fof(f2437,plain,
( ~ subclass(complement(subset_relation),identity_relation)
| y = complement(subset_relation)
| y = complement(subset_relation)
| ~ spl0_106
| ~ spl0_246 ),
inference(resolution,[],[f2427,f811]) ).
fof(f811,plain,
( ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = y )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f25843,plain,
( spl0_924
| ~ spl0_925
| ~ spl0_106
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2436,f2422,f810,f25840,f25836]) ).
fof(f25836,plain,
( spl0_924
<=> complement(element_relation) = y ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f25840,plain,
( spl0_925
<=> subclass(complement(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2436,plain,
( ~ subclass(complement(element_relation),singleton_relation)
| complement(element_relation) = y
| ~ spl0_106
| ~ spl0_245 ),
inference(duplicate_literal_removal,[],[f2429]) ).
fof(f2429,plain,
( ~ subclass(complement(element_relation),singleton_relation)
| complement(element_relation) = y
| complement(element_relation) = y
| ~ spl0_106
| ~ spl0_245 ),
inference(resolution,[],[f2423,f811]) ).
fof(f25485,plain,
( spl0_923
| ~ spl0_2
| ~ spl0_520
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8956,f8731,f7933,f213,f25483]) ).
fof(f25483,plain,
( spl0_923
<=> ! [X0] :
( subclass(X0,complement(y))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f7933,plain,
( spl0_520
<=> ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f8956,plain,
( ! [X0] :
( subclass(X0,complement(y))
| ~ subclass(X0,universal_class) )
| ~ spl0_2
| ~ spl0_520
| ~ spl0_550 ),
inference(forward_demodulation,[],[f8921,f8914]) ).
fof(f8914,plain,
( y = domain_of(y)
| ~ spl0_2
| ~ spl0_550 ),
inference(resolution,[],[f8732,f214]) ).
fof(f8921,plain,
( ! [X0] :
( subclass(X0,complement(domain_of(y)))
| ~ subclass(X0,universal_class) )
| ~ spl0_520
| ~ spl0_550 ),
inference(resolution,[],[f8732,f7934]) ).
fof(f7934,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) )
| ~ spl0_520 ),
inference(avatar_component_clause,[],[f7933]) ).
fof(f25005,plain,
( spl0_168
| ~ spl0_922
| ~ spl0_109
| spl0_911 ),
inference(avatar_split_clause,[],[f23752,f22465,f831,f25002,f1428]) ).
fof(f22465,plain,
( spl0_911
<=> member(regular(singleton_relation),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f23752,plain,
( ~ subclass(singleton_relation,subset_relation)
| singleton_relation = y
| ~ spl0_109
| spl0_911 ),
inference(resolution,[],[f22466,f832]) ).
fof(f22466,plain,
( ~ member(regular(singleton_relation),subset_relation)
| spl0_911 ),
inference(avatar_component_clause,[],[f22465]) ).
fof(f24326,plain,
( spl0_168
| ~ spl0_921
| ~ spl0_246
| spl0_911 ),
inference(avatar_split_clause,[],[f23750,f22465,f2426,f24323,f1428]) ).
fof(f23750,plain,
( ~ subclass(singleton_relation,identity_relation)
| singleton_relation = y
| ~ spl0_246
| spl0_911 ),
inference(resolution,[],[f22466,f2427]) ).
fof(f24016,plain,
( ~ spl0_920
| ~ spl0_691
| spl0_911 ),
inference(avatar_split_clause,[],[f23751,f22465,f13889,f24013]) ).
fof(f24013,plain,
( spl0_920
<=> subclass(element_relation,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f23751,plain,
( ~ subclass(element_relation,subset_relation)
| ~ spl0_691
| spl0_911 ),
inference(resolution,[],[f22466,f13890]) ).
fof(f22541,plain,
( ~ spl0_16
| ~ spl0_918 ),
inference(avatar_contradiction_clause,[],[f22500]) ).
fof(f22500,plain,
( $false
| ~ spl0_16
| ~ spl0_918 ),
inference(resolution,[],[f22495,f279]) ).
fof(f22495,plain,
( ! [X2] : ~ member(X2,universal_class)
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f22494]) ).
fof(f22494,plain,
( spl0_918
<=> ! [X2] : ~ member(X2,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f22540,plain,
( ~ spl0_9
| ~ spl0_918 ),
inference(avatar_contradiction_clause,[],[f22501]) ).
fof(f22501,plain,
( $false
| ~ spl0_9
| ~ spl0_918 ),
inference(resolution,[],[f22495,f248]) ).
fof(f248,plain,
( member(omega,universal_class)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f246,plain,
( spl0_9
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f22539,plain,
( ~ spl0_21
| ~ spl0_918 ),
inference(avatar_contradiction_clause,[],[f22503]) ).
fof(f22503,plain,
( $false
| ~ spl0_21
| ~ spl0_918 ),
inference(resolution,[],[f22495,f302]) ).
fof(f22499,plain,
( spl0_918
| spl0_919
| ~ spl0_80
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2178,f2175,f647,f22497,f22494]) ).
fof(f22497,plain,
( spl0_919
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f2178,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(X0,universal_class)
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) )
| ~ spl0_80
| ~ spl0_223 ),
inference(resolution,[],[f2176,f648]) ).
fof(f22492,plain,
( spl0_917
| ~ spl0_96
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1712,f1646,f746,f22490]) ).
fof(f22490,plain,
( spl0_917
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,rotate(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1712,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,rotate(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),unordered_pair(X1,X1))),X0) )
| ~ spl0_96
| ~ spl0_192 ),
inference(resolution,[],[f1647,f747]) ).
fof(f22488,plain,
( ~ spl0_915
| spl0_916
| ~ spl0_91
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1465,f1424,f710,f22486,f22482]) ).
fof(f22482,plain,
( spl0_915
<=> operation(flip(cross_product(subset_relation,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f22486,plain,
( spl0_916
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
| homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
| ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
| ~ operation(X1)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1465,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1)),unordered_pair(not_homomorphism1(X0,flip(cross_product(subset_relation,universal_class)),X1),unordered_pair(not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1),not_homomorphism2(X0,flip(cross_product(subset_relation,universal_class)),X1)))),identity_relation)
| ~ operation(X1)
| ~ compatible(X0,flip(cross_product(subset_relation,universal_class)),X1)
| homomorphism(X0,flip(cross_product(subset_relation,universal_class)),X1)
| ~ operation(flip(cross_product(subset_relation,universal_class))) )
| ~ spl0_91
| ~ spl0_167 ),
inference(resolution,[],[f1425,f711]) ).
fof(f22480,plain,
( spl0_913
| ~ spl0_914
| ~ spl0_203
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2025,f1999,f1816,f22477,f22474]) ).
fof(f22474,plain,
( spl0_913
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f22477,plain,
( spl0_914
<=> subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f2025,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_203
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1817]) ).
fof(f22472,plain,
( spl0_911
| ~ spl0_912
| ~ spl0_131
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f15644,f13889,f1009,f22469,f22465]) ).
fof(f22469,plain,
( spl0_912
<=> subclass(element_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f15644,plain,
( ~ subclass(element_relation,identity_relation)
| member(regular(singleton_relation),subset_relation)
| ~ spl0_131
| ~ spl0_691 ),
inference(resolution,[],[f13890,f1010]) ).
fof(f22414,plain,
( spl0_910
| ~ spl0_189
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2158,f2122,f1625,f22412]) ).
fof(f22412,plain,
( spl0_910
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1625,plain,
( spl0_189
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2158,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
| ~ spl0_189
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1626]) ).
fof(f1626,plain,
( ! [X0] :
( member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,subset_relation) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1625]) ).
fof(f22410,plain,
( spl0_909
| ~ spl0_189
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2135,f2118,f1625,f22408]) ).
fof(f22408,plain,
( spl0_909
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f2135,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
| ~ spl0_189
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1626]) ).
fof(f22385,plain,
( spl0_908
| ~ spl0_197
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1983,f1943,f1750,f22383]) ).
fof(f22383,plain,
( spl0_908
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1750,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1983,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_197
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1751]) ).
fof(f1751,plain,
( ! [X0,X1] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1750]) ).
fof(f22381,plain,
( spl0_907
| ~ spl0_197
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1957,f1939,f1750,f22379]) ).
fof(f22379,plain,
( spl0_907
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1957,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_197
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1751]) ).
fof(f22377,plain,
( spl0_906
| ~ spl0_94
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1787,f1750,f725,f22375]) ).
fof(f22375,plain,
( spl0_906
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f1787,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X3),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_197 ),
inference(resolution,[],[f1751,f726]) ).
fof(f22333,plain,
( spl0_905
| ~ spl0_204
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2171,f2122,f1841,f22331]) ).
fof(f22331,plain,
( spl0_905
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2171,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_204
| ~ spl0_222 ),
inference(duplicate_literal_removal,[],[f2167]) ).
fof(f2167,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(compose_class(X2)))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(compose(X2,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_204
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1842]) ).
fof(f22287,plain,
( spl0_904
| ~ spl0_192
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2148,f2122,f1646,f22285]) ).
fof(f22285,plain,
( spl0_904
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2148,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(X2))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_192
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1647]) ).
fof(f22259,plain,
( spl0_903
| ~ spl0_192
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1982,f1943,f1646,f22257]) ).
fof(f22257,plain,
( spl0_903
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1982,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_192
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1647]) ).
fof(f22255,plain,
( spl0_902
| ~ spl0_192
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1956,f1939,f1646,f22253]) ).
fof(f22253,plain,
( spl0_902
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f1956,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1))))))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_192
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1647]) ).
fof(f22251,plain,
( spl0_901
| ~ spl0_94
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1723,f1646,f725,f22249]) ).
fof(f22249,plain,
( spl0_901
<=> ! [X0,X3,X2,X1] :
( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f1723,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(domain_relation,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(domain_of(X3),domain_of(X3))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_192 ),
inference(resolution,[],[f1647,f726]) ).
fof(f22247,plain,
( spl0_186
| spl0_900
| ~ spl0_261
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f14305,f4465,f2706,f22244,f1601]) ).
fof(f22244,plain,
( spl0_900
<=> member(regular(y),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2706,plain,
( spl0_261
<=> ! [X0] :
( identity_relation = intersection(singleton_relation,X0)
| member(regular(intersection(singleton_relation,X0)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f4465,plain,
( spl0_362
<=> y = intersection(singleton_relation,complement(element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f14305,plain,
( member(regular(y),element_relation)
| identity_relation = y
| ~ spl0_261
| ~ spl0_362 ),
inference(superposition,[],[f2707,f4467]) ).
fof(f4467,plain,
( y = intersection(singleton_relation,complement(element_relation))
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f4465]) ).
fof(f2707,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| identity_relation = intersection(singleton_relation,X0) )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f2706]) ).
fof(f22236,plain,
( spl0_899
| ~ spl0_144
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2116,f2108,f1199,f22234]) ).
fof(f22234,plain,
( spl0_899
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| y = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2108,plain,
( spl0_220
<=> ! [X4,X0,X3,X2,X1] :
( ~ homomorphism(X0,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f2116,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(regular(cross_product(X0,X1)),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| y = intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_220 ),
inference(superposition,[],[f2109,f1200]) ).
fof(f2109,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ homomorphism(X0,X1,X2)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2108]) ).
fof(f22134,plain,
( spl0_898
| ~ spl0_153
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2162,f2122,f1264,f22132]) ).
fof(f22132,plain,
( spl0_898
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2162,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),identity_relation) )
| ~ spl0_153
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1265]) ).
fof(f22130,plain,
( spl0_897
| ~ spl0_152
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2160,f2122,f1260,f22128]) ).
fof(f22128,plain,
( spl0_897
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f2160,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),singleton_relation) )
| ~ spl0_152
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1261]) ).
fof(f22126,plain,
( spl0_896
| ~ spl0_153
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2139,f2118,f1264,f22124]) ).
fof(f22124,plain,
( spl0_896
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f2139,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),identity_relation) )
| ~ spl0_153
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1265]) ).
fof(f22122,plain,
( spl0_895
| ~ spl0_152
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2137,f2118,f1260,f22120]) ).
fof(f22120,plain,
( spl0_895
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2137,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(complement(compose(element_relation,complement(identity_relation)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),singleton_relation) )
| ~ spl0_152
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1261]) ).
fof(f22040,plain,
( spl0_894
| ~ spl0_72
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2169,f2122,f605,f22038]) ).
fof(f22038,plain,
( spl0_894
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2169,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))))))),flip(domain_relation))
| ~ member(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_72
| ~ spl0_222 ),
inference(resolution,[],[f2123,f606]) ).
fof(f22035,plain,
( spl0_892
| ~ spl0_893
| ~ spl0_167
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2032,f1999,f1424,f22032,f22029]) ).
fof(f22029,plain,
( spl0_892
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f22032,plain,
( spl0_893
<=> subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2032,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),identity_relation) )
| ~ spl0_167
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1425]) ).
fof(f22027,plain,
( spl0_890
| ~ spl0_891
| ~ spl0_166
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2027,f1999,f1420,f22024,f22021]) ).
fof(f22021,plain,
( spl0_890
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f22024,plain,
( spl0_891
<=> subclass(composition_function,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2027,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,complement(compose(element_relation,complement(identity_relation))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),singleton_relation) )
| ~ spl0_166
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1421]) ).
fof(f22019,plain,
( spl0_889
| ~ spl0_196
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1991,f1943,f1746,f22017]) ).
fof(f22017,plain,
( spl0_889
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f1991,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_196
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1747]) ).
fof(f22015,plain,
( spl0_888
| ~ spl0_196
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1965,f1939,f1746,f22013]) ).
fof(f22013,plain,
( spl0_888
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f1965,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X2),universal_class))))))),cross_product(universal_class,universal_class))
| ~ function(X2)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_196
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1747]) ).
fof(f22011,plain,
( spl0_887
| ~ spl0_94
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1769,f1746,f725,f22009]) ).
fof(f22009,plain,
( spl0_887
<=> ! [X4,X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X4,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f1769,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X4,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X4,universal_class),X0),universal_class))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_196 ),
inference(resolution,[],[f1747,f726]) ).
fof(f21958,plain,
( spl0_886
| ~ spl0_139
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2155,f2122,f1089,f21956]) ).
fof(f21956,plain,
( spl0_886
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2155,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),subset_relation) )
| ~ spl0_139
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1090]) ).
fof(f21954,plain,
( spl0_885
| ~ spl0_139
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2132,f2118,f1089,f21952]) ).
fof(f21952,plain,
( spl0_885
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f2132,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(universal_class,universal_class)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),subset_relation) )
| ~ spl0_139
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1090]) ).
fof(f21924,plain,
( spl0_884
| ~ spl0_55
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2021,f1999,f492,f21922]) ).
fof(f21922,plain,
( spl0_884
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f492,plain,
( spl0_55
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f2021,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))) = X1 )
| ~ spl0_55
| ~ spl0_216 ),
inference(resolution,[],[f2000,f493]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f21908,plain,
( spl0_883
| ~ spl0_103
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1219,f1199,f778,f21906]) ).
fof(f21906,plain,
( spl0_883
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
| ~ homomorphism(X3,X2,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f1219,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(regular(cross_product(X0,X1)),domain_of(X2))
| ~ homomorphism(X3,X2,X4)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class)))))))
| cross_product(X0,X1) = y )
| ~ spl0_103
| ~ spl0_144 ),
inference(superposition,[],[f779,f1200]) ).
fof(f21904,plain,
( ~ spl0_881
| spl0_882
| ~ spl0_19
| ~ spl0_720 ),
inference(avatar_split_clause,[],[f21752,f15431,f292,f21901,f21897]) ).
fof(f21897,plain,
( spl0_881
<=> inductive(complement(omega)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f15431,plain,
( spl0_720
<=> ! [X0] :
( y = X0
| ~ subclass(X0,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f21752,plain,
( omega = y
| ~ inductive(complement(omega))
| ~ spl0_19
| ~ spl0_720 ),
inference(resolution,[],[f15432,f293]) ).
fof(f15432,plain,
( ! [X0] :
( ~ subclass(X0,complement(X0))
| y = X0 )
| ~ spl0_720 ),
inference(avatar_component_clause,[],[f15431]) ).
fof(f21889,plain,
( spl0_880
| ~ spl0_203
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1907,f1889,f1816,f21887]) ).
fof(f21887,plain,
( spl0_880
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f1907,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),cross_product(universal_class,universal_class)) )
| ~ spl0_203
| ~ spl0_212 ),
inference(resolution,[],[f1890,f1817]) ).
fof(f21764,plain,
( spl0_879
| ~ spl0_141
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1985,f1943,f1143,f21762]) ).
fof(f21762,plain,
( spl0_879
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class)
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f1985,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))),universal_class)
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
| ~ spl0_141
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1144]) ).
fof(f21760,plain,
( spl0_878
| ~ spl0_140
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1977,f1943,f1139,f21758]) ).
fof(f21758,plain,
( spl0_878
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class)
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f1977,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3),universal_class)
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
| ~ spl0_140
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1140]) ).
fof(f21745,plain,
( spl0_877
| ~ spl0_141
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1959,f1939,f1143,f21743]) ).
fof(f21743,plain,
( spl0_877
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f1959,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_141
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1144]) ).
fof(f21741,plain,
( spl0_876
| ~ spl0_140
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1951,f1939,f1139,f21739]) ).
fof(f21739,plain,
( spl0_876
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f1951,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_140
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1140]) ).
fof(f21737,plain,
( spl0_875
| ~ spl0_94
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1169,f1143,f725,f21735]) ).
fof(f21735,plain,
( spl0_875
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| y = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f1169,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),universal_class)
| y = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))),intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_141 ),
inference(resolution,[],[f1144,f726]) ).
fof(f21733,plain,
( spl0_874
| ~ spl0_94
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1152,f1139,f725,f21731]) ).
fof(f21731,plain,
( spl0_874
<=> ! [X0,X3,X2,X1] :
( ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f1152,plain,
( ! [X2,X3,X0,X1] :
( ~ member(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),universal_class)
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_140 ),
inference(resolution,[],[f1140,f726]) ).
fof(f21700,plain,
( spl0_873
| ~ spl0_198
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2133,f2118,f1754,f21698]) ).
fof(f21698,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f1754,plain,
( spl0_198
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2133,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X0)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class) )
| ~ spl0_198
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1755]) ).
fof(f1755,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f1754]) ).
fof(f21696,plain,
( spl0_872
| ~ spl0_16
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2111,f2108,f278,f21694]) ).
fof(f21694,plain,
( spl0_872
<=> ! [X2,X4,X0,X3,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2111,plain,
( ! [X2,X3,X0,X1,X4] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2),universal_class)))))))),universal_class),X3),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X3),universal_class))))))))))),universal_class),X4),universal_class)))))))
| ~ homomorphism(X3,X2,X4)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X2) )
| ~ spl0_16
| ~ spl0_220 ),
inference(resolution,[],[f2109,f279]) ).
fof(f21663,plain,
( spl0_871
| ~ spl0_198
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2173,f2122,f1754,f21661]) ).
fof(f21661,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2173,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_198
| ~ spl0_222 ),
inference(duplicate_literal_removal,[],[f2156]) ).
fof(f2156,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(element_relation))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X2)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),universal_class) )
| ~ spl0_198
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1755]) ).
fof(f21627,plain,
( spl0_870
| ~ spl0_28
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1976,f1943,f330,f21625]) ).
fof(f21625,plain,
( spl0_870
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f330,plain,
( spl0_28
<=> ! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1976,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_28
| ~ spl0_215 ),
inference(resolution,[],[f1944,f331]) ).
fof(f331,plain,
( ! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| y = X1 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f21623,plain,
( spl0_869
| ~ spl0_28
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1950,f1939,f330,f21621]) ).
fof(f21621,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f1950,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_28
| ~ spl0_214 ),
inference(resolution,[],[f1940,f331]) ).
fof(f21591,plain,
( spl0_868
| ~ spl0_139
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2094,f2090,f1089,f21589]) ).
fof(f21589,plain,
( spl0_868
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2090,plain,
( spl0_218
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2094,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),subset_relation) )
| ~ spl0_139
| ~ spl0_218 ),
inference(resolution,[],[f2091,f1090]) ).
fof(f2091,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2090]) ).
fof(f21548,plain,
( spl0_867
| ~ spl0_179
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1986,f1943,f1537,f21546]) ).
fof(f21546,plain,
( spl0_867
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f1537,plain,
( spl0_179
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1986,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_179
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1538]) ).
fof(f1538,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f21544,plain,
( spl0_866
| ~ spl0_179
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1960,f1939,f1537,f21542]) ).
fof(f21542,plain,
( spl0_866
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f1960,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X1))),domain_of(intersection(element_relation,cross_product(universal_class,X1)))))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class) )
| ~ spl0_179
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1538]) ).
fof(f21540,plain,
( spl0_865
| ~ spl0_167
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1912,f1889,f1424,f21538]) ).
fof(f21538,plain,
( spl0_865
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1912,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),identity_relation) )
| ~ spl0_167
| ~ spl0_212 ),
inference(resolution,[],[f1890,f1425]) ).
fof(f21536,plain,
( spl0_864
| ~ spl0_166
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1909,f1889,f1420,f21534]) ).
fof(f21534,plain,
( spl0_864
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f1909,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(compose(element_relation,complement(identity_relation))))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),singleton_relation) )
| ~ spl0_166
| ~ spl0_212 ),
inference(resolution,[],[f1890,f1421]) ).
fof(f21532,plain,
( spl0_863
| ~ spl0_94
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1557,f1537,f725,f21530]) ).
fof(f21530,plain,
( spl0_863
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f1557,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X3,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X3))),domain_of(intersection(element_relation,cross_product(universal_class,X3)))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_179 ),
inference(resolution,[],[f1538,f726]) ).
fof(f21510,plain,
( spl0_862
| ~ spl0_55
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1903,f1889,f492,f21508]) ).
fof(f21508,plain,
( spl0_862
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),unordered_pair(X3,X4))
| ~ operation(X2)
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f1903,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),unordered_pair(X3,X4))
| ~ operation(X2)
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X3
| unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))) = X4 )
| ~ spl0_55
| ~ spl0_212 ),
inference(resolution,[],[f1890,f493]) ).
fof(f21448,plain,
( spl0_238
| ~ spl0_861
| ~ spl0_109
| spl0_781 ),
inference(avatar_split_clause,[],[f18044,f17228,f831,f21445,f2279]) ).
fof(f21445,plain,
( spl0_861
<=> subclass(subset_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f17228,plain,
( spl0_781
<=> member(regular(subset_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f18044,plain,
( ~ subclass(subset_relation,element_relation)
| subset_relation = y
| ~ spl0_109
| spl0_781 ),
inference(resolution,[],[f17229,f832]) ).
fof(f17229,plain,
( ~ member(regular(subset_relation),element_relation)
| spl0_781 ),
inference(avatar_component_clause,[],[f17228]) ).
fof(f21335,plain,
( spl0_860
| ~ spl0_80
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2154,f2122,f647,f21333]) ).
fof(f21333,plain,
( spl0_860
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2154,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
| ~ spl0_80
| ~ spl0_222 ),
inference(resolution,[],[f2123,f648]) ).
fof(f21331,plain,
( spl0_859
| ~ spl0_80
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2131,f2118,f647,f21329]) ).
fof(f21329,plain,
( spl0_859
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f2131,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(cross_product(X3,X4)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),X3) )
| ~ spl0_80
| ~ spl0_221 ),
inference(resolution,[],[f2119,f648]) ).
fof(f21327,plain,
( spl0_858
| ~ spl0_99
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1713,f1646,f759,f21325]) ).
fof(f21325,plain,
( spl0_858
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,flip(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1713,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,flip(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),universal_class)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X1,X1))),unordered_pair(domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),domain_of(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))))))),X0) )
| ~ spl0_99
| ~ spl0_192 ),
inference(resolution,[],[f1647,f760]) ).
fof(f21123,plain,
( spl0_857
| ~ spl0_183
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1930,f1918,f1589,f21121]) ).
fof(f21121,plain,
( spl0_857
<=> ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1589,plain,
( spl0_183
<=> ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1918,plain,
( spl0_213
<=> ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1930,plain,
( ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))))))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
| ~ spl0_183
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1590]) ).
fof(f1590,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1589]) ).
fof(f1919,plain,
( ! [X2,X0,X1] :
( subclass(cross_product(X0,X1),X2)
| not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))))) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f1918]) ).
fof(f21119,plain,
( spl0_856
| ~ spl0_182
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1929,f1918,f1585,f21117]) ).
fof(f21117,plain,
( spl0_856
<=> ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1585,plain,
( spl0_182
<=> ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1929,plain,
( ! [X0] :
( not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)))),unordered_pair(first(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),unordered_pair(second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))),second(not_subclass_element(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))))))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
| ~ spl0_182
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1586]) ).
fof(f1586,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1585]) ).
fof(f21115,plain,
( ~ spl0_854
| spl0_855
| ~ spl0_7
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2213,f2203,f238,f21113,f21109]) ).
fof(f21113,plain,
( spl0_855
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3))))))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
| homomorphism(X2,domain_of(flip(cross_product(y,universal_class))),X3)
| ~ compatible(X2,domain_of(flip(cross_product(y,universal_class))),X3)
| ~ operation(X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2213,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3)))),unordered_pair(unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3)),unordered_pair(not_homomorphism1(X2,domain_of(flip(cross_product(y,universal_class))),X3),unordered_pair(not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3),not_homomorphism2(X2,domain_of(flip(cross_product(y,universal_class))),X3))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ operation(X3)
| ~ compatible(X2,domain_of(flip(cross_product(y,universal_class))),X3)
| homomorphism(X2,domain_of(flip(cross_product(y,universal_class))),X3)
| ~ operation(domain_of(flip(cross_product(y,universal_class))))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_7
| ~ spl0_226 ),
inference(superposition,[],[f2204,f239]) ).
fof(f21091,plain,
( spl0_853
| ~ spl0_7
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2097,f2090,f238,f21089]) ).
fof(f21089,plain,
( spl0_853
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f2097,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),universal_class)),universal_class)))))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_218 ),
inference(superposition,[],[f2091,f239]) ).
fof(f21001,plain,
( spl0_852
| ~ spl0_154
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1990,f1943,f1287,f20999]) ).
fof(f20999,plain,
( spl0_852
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1990,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class)))))
| subclass(X1,X2) )
| ~ spl0_154
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1288]) ).
fof(f20997,plain,
( spl0_851
| ~ spl0_154
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1964,f1939,f1287,f20995]) ).
fof(f20995,plain,
( spl0_851
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1964,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(X1,X2),not_subclass_element(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X1,X2) )
| ~ spl0_154
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1288]) ).
fof(f20993,plain,
( spl0_850
| ~ spl0_142
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1934,f1918,f1181,f20991]) ).
fof(f20991,plain,
( spl0_850
<=> ! [X0,X1] :
( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
| function(cross_product(X0,X1))
| ~ single_valued_class(cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1181,plain,
( spl0_142
<=> ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1934,plain,
( ! [X0,X1] :
( not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class)))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),unordered_pair(second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(X0,X1),cross_product(universal_class,universal_class))))))
| function(cross_product(X0,X1))
| ~ single_valued_class(cross_product(X0,X1)) )
| ~ spl0_142
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1182]) ).
fof(f1182,plain,
( ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f20989,plain,
( spl0_849
| ~ spl0_94
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1316,f1287,f725,f20987]) ).
fof(f20987,plain,
( spl0_849
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X0,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1316,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| subclass(X0,X4)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(not_subclass_element(X0,X4),not_subclass_element(X0,X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_154 ),
inference(resolution,[],[f1288,f726]) ).
fof(f20985,plain,
( spl0_238
| ~ spl0_848
| ~ spl0_245
| spl0_781 ),
inference(avatar_split_clause,[],[f18043,f17228,f2422,f20982,f2279]) ).
fof(f20982,plain,
( spl0_848
<=> subclass(subset_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f18043,plain,
( ~ subclass(subset_relation,singleton_relation)
| subset_relation = y
| ~ spl0_245
| spl0_781 ),
inference(resolution,[],[f17229,f2423]) ).
fof(f20795,plain,
( spl0_847
| ~ spl0_173
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1924,f1918,f1511,f20793]) ).
fof(f20793,plain,
( spl0_847
<=> ! [X0,X1] :
( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
| cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f1511,plain,
( spl0_173
<=> ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1924,plain,
( ! [X0,X1] :
( not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))),second(not_subclass_element(cross_product(universal_class,universal_class),compose(X0,X1))))))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_173
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1512]) ).
fof(f1512,plain,
( ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1511]) ).
fof(f20791,plain,
( spl0_846
| ~ spl0_82
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1391,f1351,f665,f20789]) ).
fof(f20789,plain,
( spl0_846
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f665,plain,
( spl0_82
<=> ! [X4,X0,X1] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1391,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,cross_product(X1,X2)),X3)
| not_subclass_element(intersection(X0,cross_product(X1,X2)),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))),unordered_pair(first(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),unordered_pair(second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3)),second(not_subclass_element(intersection(X0,cross_product(X1,X2)),X3))))) )
| ~ spl0_82
| ~ spl0_161 ),
inference(resolution,[],[f1352,f666]) ).
fof(f666,plain,
( ! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f20787,plain,
( spl0_845
| ~ spl0_82
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1370,f1347,f665,f20785]) ).
fof(f20785,plain,
( spl0_845
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1370,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(cross_product(X0,X1),X2),X3)
| not_subclass_element(intersection(cross_product(X0,X1),X2),X3) = unordered_pair(unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))),unordered_pair(first(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),unordered_pair(second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3)),second(not_subclass_element(intersection(cross_product(X0,X1),X2),X3))))) )
| ~ spl0_82
| ~ spl0_160 ),
inference(resolution,[],[f1348,f666]) ).
fof(f20754,plain,
( spl0_844
| ~ spl0_80
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2093,f2090,f647,f20752]) ).
fof(f20752,plain,
( spl0_844
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f2093,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_218 ),
inference(resolution,[],[f2091,f648]) ).
fof(f20724,plain,
( ~ spl0_843
| ~ spl0_691
| spl0_696 ),
inference(avatar_split_clause,[],[f16788,f14688,f13889,f20721]) ).
fof(f20721,plain,
( spl0_843
<=> subclass(element_relation,compose(element_relation,complement(identity_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f14688,plain,
( spl0_696
<=> member(regular(singleton_relation),compose(element_relation,complement(identity_relation))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f16788,plain,
( ~ subclass(element_relation,compose(element_relation,complement(identity_relation)))
| ~ spl0_691
| spl0_696 ),
inference(resolution,[],[f14690,f13890]) ).
fof(f14690,plain,
( ~ member(regular(singleton_relation),compose(element_relation,complement(identity_relation)))
| spl0_696 ),
inference(avatar_component_clause,[],[f14688]) ).
fof(f20547,plain,
( spl0_842
| ~ spl0_137
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1989,f1943,f1078,f20545]) ).
fof(f20545,plain,
( spl0_842
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f1989,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X4),universal_class)))),universal_class)),universal_class))))) )
| ~ spl0_137
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1079]) ).
fof(f20543,plain,
( spl0_841
| ~ spl0_137
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1963,f1939,f1078,f20541]) ).
fof(f20541,plain,
( spl0_841
<=> ! [X4,X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1963,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),compose(X3,X4))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X4,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_137
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1079]) ).
fof(f20539,plain,
( spl0_840
| ~ spl0_202
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1931,f1918,f1809,f20537]) ).
fof(f20537,plain,
( spl0_840
<=> ! [X4,X0,X3,X2,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ member(X3,X0)
| ~ member(X4,X1)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f1809,plain,
( spl0_202
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ subclass(cross_product(X3,X1),X4)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1931,plain,
( ! [X2,X3,X0,X1,X4] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ member(X3,X0)
| ~ member(X4,X1)
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),X2) )
| ~ spl0_202
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1810]) ).
fof(f1810,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(cross_product(X3,X1),X4)
| ~ member(X2,X3)
| ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f1809]) ).
fof(f20535,plain,
( spl0_839
| ~ spl0_94
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1117,f1078,f725,f20533]) ).
fof(f20533,plain,
( spl0_839
<=> ! [X4,X0,X3,X2,X1] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f1117,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subclass(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X4)))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_137 ),
inference(resolution,[],[f1079,f726]) ).
fof(f20520,plain,
( spl0_838
| ~ spl0_190
| ~ spl0_208 ),
inference(avatar_split_clause,[],[f1863,f1860,f1638,f20518]) ).
fof(f20518,plain,
( spl0_838
<=> ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f1638,plain,
( spl0_190
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X0
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1860,plain,
( spl0_208
<=> ! [X0] :
( ~ inductive(X0)
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1863,plain,
( ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| unordered_pair(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X1
| not_subclass_element(unordered_pair(X0,X1),domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(unordered_pair(X0,X1),universal_class)),universal_class))))) = X0 )
| ~ spl0_190
| ~ spl0_208 ),
inference(resolution,[],[f1861,f1639]) ).
fof(f1639,plain,
( ! [X2,X0,X1] :
( subclass(unordered_pair(X0,X1),X2)
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0 )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1638]) ).
fof(f1861,plain,
( ! [X0] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
| ~ inductive(X0)
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f1860]) ).
fof(f20466,plain,
( spl0_244
| ~ spl0_591
| ~ spl0_612
| ~ spl0_640 ),
inference(avatar_split_clause,[],[f20338,f12137,f11087,f10596,f2322]) ).
fof(f2322,plain,
( spl0_244
<=> member(subset_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f10596,plain,
( spl0_591
<=> subclass(universal_class,complement(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f12137,plain,
( spl0_640
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f20338,plain,
( member(subset_relation,universal_class)
| ~ spl0_591
| ~ spl0_612
| ~ spl0_640 ),
inference(forward_demodulation,[],[f20333,f11089]) ).
fof(f20333,plain,
( member(subset_relation,complement(y))
| ~ spl0_591
| ~ spl0_640 ),
inference(resolution,[],[f12138,f10598]) ).
fof(f10598,plain,
( subclass(universal_class,complement(y))
| ~ spl0_591 ),
inference(avatar_component_clause,[],[f10596]) ).
fof(f12138,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(subset_relation,X0) )
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f12137]) ).
fof(f20425,plain,
( spl0_837
| ~ spl0_137
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2150,f2122,f1078,f20423]) ).
fof(f20423,plain,
( spl0_837
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f2150,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) )
| ~ spl0_137
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1079]) ).
fof(f20421,plain,
( spl0_836
| ~ spl0_137
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2127,f2118,f1078,f20419]) ).
fof(f20419,plain,
( spl0_836
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f2127,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,X3) )
| ~ spl0_137
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1079]) ).
fof(f20417,plain,
( spl0_835
| ~ spl0_189
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1678,f1642,f1625,f20415]) ).
fof(f20415,plain,
( spl0_835
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
| subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f1642,plain,
( spl0_191
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1678,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),X1)
| subclass(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) )
| ~ spl0_189
| ~ spl0_191 ),
inference(resolution,[],[f1643,f1626]) ).
fof(f1643,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1642]) ).
fof(f20391,plain,
( spl0_834
| ~ spl0_46
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2020,f1999,f424,f20389]) ).
fof(f20389,plain,
( spl0_834
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,X0)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ subclass(X0,X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2020,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,X0)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ subclass(X0,X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X3) )
| ~ spl0_46
| ~ spl0_216 ),
inference(resolution,[],[f2000,f425]) ).
fof(f20386,plain,
( spl0_833
| spl0_747
| ~ spl0_82
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1552,f1537,f665,f16075,f20384]) ).
fof(f20384,plain,
( spl0_833
<=> ! [X2] :
( ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f16075,plain,
( spl0_747
<=> ! [X0,X1] : ~ subclass(universal_class,cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f1552,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),first(domain_of(intersection(element_relation,cross_product(universal_class,X2))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,X2)))),second(domain_of(intersection(element_relation,cross_product(universal_class,X2))))))) )
| ~ spl0_82
| ~ spl0_179 ),
inference(resolution,[],[f1538,f666]) ).
fof(f20300,plain,
( spl0_832
| ~ spl0_39
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2024,f1999,f381,f20298]) ).
fof(f20298,plain,
( spl0_832
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f2024,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X0) )
| ~ spl0_39
| ~ spl0_216 ),
inference(resolution,[],[f2000,f382]) ).
fof(f20296,plain,
( spl0_831
| ~ spl0_40
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2023,f1999,f385,f20294]) ).
fof(f20294,plain,
( spl0_831
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2023,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,intersection(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3))))))),X1) )
| ~ spl0_40
| ~ spl0_216 ),
inference(resolution,[],[f2000,f386]) ).
fof(f20292,plain,
( spl0_830
| ~ spl0_90
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2013,f1999,f706,f20290]) ).
fof(f20290,plain,
( spl0_830
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,compose(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f706,plain,
( spl0_90
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f2013,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,compose(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_90
| ~ spl0_216 ),
inference(resolution,[],[f2000,f707]) ).
fof(f707,plain,
( ! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) )
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f20288,plain,
( spl0_829
| ~ spl0_85
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1895,f1889,f683,f20286]) ).
fof(f20286,plain,
( spl0_829
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f683,plain,
( spl0_85
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1895,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation)
| ~ member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
| ~ spl0_85
| ~ spl0_212 ),
inference(resolution,[],[f1890,f684]) ).
fof(f684,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f19907,plain,
( spl0_828
| ~ spl0_16
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2151,f2122,f278,f19905]) ).
fof(f19905,plain,
( spl0_828
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2151,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_16
| ~ spl0_222 ),
inference(resolution,[],[f2123,f279]) ).
fof(f19903,plain,
( spl0_827
| ~ spl0_16
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2128,f2118,f278,f19901]) ).
fof(f19901,plain,
( spl0_827
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2128,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(universal_class))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_16
| ~ spl0_221 ),
inference(resolution,[],[f2119,f279]) ).
fof(f19899,plain,
( spl0_826
| ~ spl0_29
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2026,f1999,f334,f19897]) ).
fof(f19897,plain,
( spl0_826
<=> ! [X2,X0,X1] :
( ~ subclass(composition_function,complement(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2026,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,complement(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0) )
| ~ spl0_29
| ~ spl0_216 ),
inference(resolution,[],[f2000,f335]) ).
fof(f19895,plain,
( spl0_825
| spl0_177
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1928,f1918,f1528,f19892]) ).
fof(f19892,plain,
( spl0_825
<=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f1528,plain,
( spl0_177
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1928,plain,
( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)))))
| spl0_177
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1530]) ).
fof(f1530,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| spl0_177 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f19889,plain,
( spl0_824
| ~ spl0_33
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f19801,f1515,f352,f19886]) ).
fof(f19886,plain,
( spl0_824
<=> subclass(application_function,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f1515,plain,
( spl0_174
<=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f19801,plain,
( subclass(application_function,composition_function)
| ~ spl0_33
| ~ spl0_174 ),
inference(superposition,[],[f354,f1517]) ).
fof(f1517,plain,
( composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f1515]) ).
fof(f19884,plain,
( ~ spl0_823
| ~ spl0_174
| spl0_235 ),
inference(avatar_split_clause,[],[f19805,f2263,f1515,f19881]) ).
fof(f19805,plain,
( ~ member(y,composition_function)
| ~ spl0_174
| spl0_235 ),
inference(superposition,[],[f2264,f1517]) ).
fof(f19799,plain,
( spl0_822
| spl0_175
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1927,f1918,f1519,f19796]) ).
fof(f19796,plain,
( spl0_822
<=> not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f1519,plain,
( spl0_175
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1927,plain,
( not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function))),unordered_pair(first(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),unordered_pair(second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)),second(not_subclass_element(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)))))
| spl0_175
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1521]) ).
fof(f1521,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| spl0_175 ),
inference(avatar_component_clause,[],[f1519]) ).
fof(f19794,plain,
( spl0_821
| ~ spl0_163
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1925,f1918,f1359,f19792]) ).
fof(f19792,plain,
( spl0_821
<=> ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
| cross_product(universal_class,universal_class) = compose_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f1359,plain,
( spl0_163
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1925,plain,
( ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0)))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))),second(not_subclass_element(cross_product(universal_class,universal_class),compose_class(X0))))))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_163
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1360]) ).
fof(f1360,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f19790,plain,
( spl0_819
| ~ spl0_820
| ~ spl0_130
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2035,f1999,f1005,f19787,f19784]) ).
fof(f19784,plain,
( spl0_819
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f19787,plain,
( spl0_820
<=> subclass(composition_function,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f2035,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,singleton_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),element_relation) )
| ~ spl0_130
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1006]) ).
fof(f19782,plain,
( spl0_817
| ~ spl0_818
| ~ spl0_131
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2033,f1999,f1009,f19779,f19776]) ).
fof(f19776,plain,
( spl0_817
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f19779,plain,
( spl0_818
<=> subclass(composition_function,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2033,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,identity_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),subset_relation) )
| ~ spl0_131
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1010]) ).
fof(f19748,plain,
( spl0_239
| ~ spl0_39
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4049,f3977,f381,f2283]) ).
fof(f4049,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| ~ spl0_39
| ~ spl0_332 ),
inference(resolution,[],[f3979,f382]) ).
fof(f19721,plain,
( spl0_816
| ~ spl0_48
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1933,f1918,f432,f19719]) ).
fof(f19719,plain,
( spl0_816
<=> ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ subclass(X2,cross_product(X0,X1))
| cross_product(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f432,plain,
( spl0_48
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1933,plain,
( ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| ~ subclass(X2,cross_product(X0,X1))
| cross_product(X0,X1) = X2 )
| ~ spl0_48
| ~ spl0_213 ),
inference(resolution,[],[f1919,f433]) ).
fof(f433,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f19717,plain,
( spl0_815
| ~ spl0_90
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1899,f1889,f706,f19715]) ).
fof(f19715,plain,
( spl0_815
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f1899,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_90
| ~ spl0_212 ),
inference(resolution,[],[f1890,f707]) ).
fof(f19713,plain,
( spl0_814
| ~ spl0_95
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1133,f1089,f741,f19711]) ).
fof(f19711,plain,
( spl0_814
<=> ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f741,plain,
( spl0_95
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1133,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| ~ spl0_95
| ~ spl0_139 ),
inference(resolution,[],[f1090,f742]) ).
fof(f742,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f19632,plain,
( spl0_813
| ~ spl0_57
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1969,f1939,f500,f19630]) ).
fof(f19630,plain,
( spl0_813
<=> ! [X0,X3,X2,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f1969,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),compose(X2,X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
| ~ spl0_57
| ~ spl0_214 ),
inference(superposition,[],[f1940,f501]) ).
fof(f19626,plain,
( spl0_812
| ~ spl0_162
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1921,f1918,f1355,f19624]) ).
fof(f19624,plain,
( spl0_812
<=> ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f1355,plain,
( spl0_162
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1921,plain,
( ! [X0] :
( not_subclass_element(cross_product(universal_class,universal_class),X0) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),first(not_subclass_element(cross_product(universal_class,universal_class),X0))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),X0)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),X0)),second(not_subclass_element(cross_product(universal_class,universal_class),X0)))))
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_162
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1356]) ).
fof(f1356,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1355]) ).
fof(f19622,plain,
( ~ spl0_810
| spl0_811
| ~ spl0_192
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1829,f1816,f1646,f19620,f19616]) ).
fof(f19616,plain,
( spl0_810
<=> subclass(domain_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f19620,plain,
( spl0_811
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f1829,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),cross_product(universal_class,universal_class))
| ~ subclass(domain_relation,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class) )
| ~ spl0_192
| ~ spl0_203 ),
inference(resolution,[],[f1817,f1647]) ).
fof(f19600,plain,
( spl0_809
| ~ spl0_102
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1218,f1199,f773,f19598]) ).
fof(f19598,plain,
( spl0_809
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f1218,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| cross_product(X0,X1) = y )
| ~ spl0_102
| ~ spl0_144 ),
inference(superposition,[],[f774,f1200]) ).
fof(f19593,plain,
( spl0_808
| ~ spl0_46
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1902,f1889,f424,f19591]) ).
fof(f19591,plain,
( spl0_808
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),X3)
| ~ operation(X2)
| ~ subclass(X3,X4)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f1902,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),X3)
| ~ operation(X2)
| ~ subclass(X3,X4)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
| ~ spl0_46
| ~ spl0_212 ),
inference(resolution,[],[f1890,f425]) ).
fof(f19549,plain,
( spl0_807
| ~ spl0_39
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1906,f1889,f381,f19547]) ).
fof(f19547,plain,
( spl0_807
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f1906,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
| ~ spl0_39
| ~ spl0_212 ),
inference(resolution,[],[f1890,f382]) ).
fof(f19545,plain,
( spl0_806
| ~ spl0_40
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1905,f1889,f385,f19543]) ).
fof(f19543,plain,
( spl0_806
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f1905,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),intersection(X3,X4))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X4) )
| ~ spl0_40
| ~ spl0_212 ),
inference(resolution,[],[f1890,f386]) ).
fof(f19529,plain,
( spl0_805
| ~ spl0_82
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1165,f1143,f665,f19527]) ).
fof(f19527,plain,
( spl0_805
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
| y = intersection(X0,cross_product(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f1165,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,cross_product(X1,X2)),universal_class)
| y = intersection(X0,cross_product(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,cross_product(X1,X2)),intersection(X0,cross_product(X1,X2))),universal_class)),universal_class))))))))))) )
| ~ spl0_82
| ~ spl0_141 ),
inference(resolution,[],[f1144,f666]) ).
fof(f19525,plain,
( spl0_804
| ~ spl0_82
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1148,f1139,f665,f19523]) ).
fof(f19523,plain,
( spl0_804
<=> ! [X2,X0,X1] :
( ~ member(intersection(cross_product(X0,X1),X2),universal_class)
| y = intersection(cross_product(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f1148,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(cross_product(X0,X1),X2),universal_class)
| y = intersection(cross_product(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(cross_product(X0,X1),X2),intersection(cross_product(X0,X1),X2)),universal_class)),universal_class))))))))))) )
| ~ spl0_82
| ~ spl0_140 ),
inference(resolution,[],[f1140,f666]) ).
fof(f19483,plain,
( spl0_803
| ~ spl0_29
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1908,f1889,f334,f19481]) ).
fof(f19481,plain,
( spl0_803
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(X3))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f1908,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),complement(X3))
| ~ operation(X2)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3) )
| ~ spl0_29
| ~ spl0_212 ),
inference(resolution,[],[f1890,f335]) ).
fof(f19465,plain,
( spl0_802
| ~ spl0_144
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2184,f2175,f1199,f19463]) ).
fof(f19463,plain,
( spl0_802
<=> ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| ~ member(X2,universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2184,plain,
( ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))))),unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class))))))))))))),application_function)
| ~ member(first(regular(cross_product(X0,X1))),domain_of(X2))
| ~ member(X2,universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_223 ),
inference(superposition,[],[f2176,f1200]) ).
fof(f19443,plain,
( spl0_801
| ~ spl0_130
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1915,f1889,f1005,f19441]) ).
fof(f19441,plain,
( spl0_801
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),singleton_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f1915,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),singleton_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),element_relation) )
| ~ spl0_130
| ~ spl0_212 ),
inference(resolution,[],[f1890,f1006]) ).
fof(f19439,plain,
( ~ spl0_800
| ~ spl0_550
| ~ spl0_567
| ~ spl0_776 ),
inference(avatar_split_clause,[],[f16997,f16784,f9421,f8731,f19436]) ).
fof(f16784,plain,
( spl0_776
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f16997,plain,
( ~ subclass(universal_class,flip(y))
| ~ spl0_550
| ~ spl0_567
| ~ spl0_776 ),
inference(forward_demodulation,[],[f16982,f9423]) ).
fof(f16982,plain,
( ~ subclass(universal_class,flip(domain_of(y)))
| ~ spl0_550
| ~ spl0_776 ),
inference(resolution,[],[f16785,f8732]) ).
fof(f16785,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0)
| ~ subclass(universal_class,flip(X0)) )
| ~ spl0_776 ),
inference(avatar_component_clause,[],[f16784]) ).
fof(f19434,plain,
( spl0_799
| ~ spl0_131
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1913,f1889,f1009,f19432]) ).
fof(f19432,plain,
( spl0_799
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),identity_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f1913,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),identity_relation)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),subset_relation) )
| ~ spl0_131
| ~ spl0_212 ),
inference(resolution,[],[f1890,f1010]) ).
fof(f19352,plain,
( spl0_798
| ~ spl0_46
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f1887,f1883,f424,f19350]) ).
fof(f19350,plain,
( spl0_798
<=> ! [X0,X1] :
( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class)
| ~ subclass(successor_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f1887,plain,
( ! [X0,X1] :
( ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class)
| ~ subclass(successor_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),X1) )
| ~ spl0_46
| ~ spl0_211 ),
inference(resolution,[],[f1884,f425]) ).
fof(f19246,plain,
( spl0_797
| ~ spl0_181
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2165,f2122,f1575,f19244]) ).
fof(f19244,plain,
( spl0_797
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f1575,plain,
( spl0_181
<=> ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2165,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class),X3),universal_class)))),universal_class) )
| ~ spl0_181
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1576]) ).
fof(f1576,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1575]) ).
fof(f19242,plain,
( spl0_796
| ~ spl0_12
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2161,f2122,f261,f19240]) ).
fof(f19240,plain,
( spl0_796
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2161,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),universal_class)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2)))),universal_class),X3) )
| ~ spl0_12
| ~ spl0_222 ),
inference(resolution,[],[f2123,f262]) ).
fof(f19238,plain,
( spl0_795
| ~ spl0_181
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2142,f2118,f1575,f19236]) ).
fof(f19236,plain,
( spl0_795
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2142,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class)),X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class),X3),universal_class)))),universal_class) )
| ~ spl0_181
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1576]) ).
fof(f19234,plain,
( spl0_794
| ~ spl0_12
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2138,f2118,f261,f19232]) ).
fof(f19232,plain,
( spl0_794
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2138,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(domain_of(X3)))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),universal_class)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0)))),universal_class),X3) )
| ~ spl0_12
| ~ spl0_221 ),
inference(resolution,[],[f2119,f262]) ).
fof(f18953,plain,
( spl0_793
| ~ spl0_17
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f18744,f1251,f282,f18950]) ).
fof(f18950,plain,
( spl0_793
<=> subclass(element_relation,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1251,plain,
( spl0_150
<=> cross_product(universal_class,universal_class) = domain_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f18744,plain,
( subclass(element_relation,domain_relation)
| ~ spl0_17
| ~ spl0_150 ),
inference(superposition,[],[f284,f1253]) ).
fof(f1253,plain,
( cross_product(universal_class,universal_class) = domain_relation
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f18948,plain,
( ~ spl0_792
| spl0_126
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f18762,f1251,f986,f18945]) ).
fof(f18945,plain,
( spl0_792
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(domain_relation,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f986,plain,
( spl0_126
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f18762,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(domain_relation,universal_class)),universal_class)))))
| spl0_126
| ~ spl0_150 ),
inference(superposition,[],[f988,f1253]) ).
fof(f988,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
| spl0_126 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f18943,plain,
( ~ spl0_791
| ~ spl0_150
| spl0_276 ),
inference(avatar_split_clause,[],[f18790,f2842,f1251,f18940]) ).
fof(f18940,plain,
( spl0_791
<=> y = complement(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f18790,plain,
( y != complement(domain_relation)
| ~ spl0_150
| spl0_276 ),
inference(superposition,[],[f2843,f1253]) ).
fof(f2843,plain,
( y != complement(cross_product(universal_class,universal_class))
| spl0_276 ),
inference(avatar_component_clause,[],[f2842]) ).
fof(f18743,plain,
( spl0_790
| spl0_151
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1926,f1918,f1255,f18740]) ).
fof(f18740,plain,
( spl0_790
<=> not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1255,plain,
( spl0_151
<=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1926,plain,
( not_subclass_element(cross_product(universal_class,universal_class),domain_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),domain_relation)))))
| spl0_151
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1257]) ).
fof(f1257,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| spl0_151 ),
inference(avatar_component_clause,[],[f1255]) ).
fof(f18726,plain,
( spl0_789
| ~ spl0_17
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f18516,f1242,f282,f18723]) ).
fof(f18723,plain,
( spl0_789
<=> subclass(element_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f1242,plain,
( spl0_148
<=> cross_product(universal_class,universal_class) = successor_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f18516,plain,
( subclass(element_relation,successor_relation)
| ~ spl0_17
| ~ spl0_148 ),
inference(superposition,[],[f284,f1244]) ).
fof(f1244,plain,
( cross_product(universal_class,universal_class) = successor_relation
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f18721,plain,
( ~ spl0_788
| spl0_126
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f18534,f1242,f986,f18718]) ).
fof(f18718,plain,
( spl0_788
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(successor_relation,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f18534,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(successor_relation,universal_class)),universal_class)))))
| spl0_126
| ~ spl0_148 ),
inference(superposition,[],[f988,f1244]) ).
fof(f18715,plain,
( ~ spl0_787
| spl0_124
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f18533,f1242,f978,f18712]) ).
fof(f18533,plain,
( ~ member(y,successor_relation)
| spl0_124
| ~ spl0_148 ),
inference(superposition,[],[f980,f1244]) ).
fof(f18515,plain,
( spl0_786
| spl0_149
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1923,f1918,f1246,f18512]) ).
fof(f18512,plain,
( spl0_786
<=> not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1246,plain,
( spl0_149
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1923,plain,
( not_subclass_element(cross_product(universal_class,universal_class),successor_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),successor_relation)))))
| spl0_149
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1248]) ).
fof(f1248,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| spl0_149 ),
inference(avatar_component_clause,[],[f1246]) ).
fof(f18377,plain,
( ~ spl0_785
| ~ spl0_550
| ~ spl0_567
| ~ spl0_775 ),
inference(avatar_split_clause,[],[f16893,f16780,f9421,f8731,f18374]) ).
fof(f16780,plain,
( spl0_775
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f16893,plain,
( ~ subclass(universal_class,rotate(y))
| ~ spl0_550
| ~ spl0_567
| ~ spl0_775 ),
inference(forward_demodulation,[],[f16878,f9423]) ).
fof(f16878,plain,
( ~ subclass(universal_class,rotate(domain_of(y)))
| ~ spl0_550
| ~ spl0_775 ),
inference(resolution,[],[f16781,f8732]) ).
fof(f16781,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0)
| ~ subclass(universal_class,rotate(X0)) )
| ~ spl0_775 ),
inference(avatar_component_clause,[],[f16780]) ).
fof(f17743,plain,
( spl0_238
| ~ spl0_244
| spl0_784
| ~ spl0_79
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1177,f1143,f642,f17740,f2322,f2279]) ).
fof(f17740,plain,
( spl0_784
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1177,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(subset_relation,universal_class)
| subset_relation = y
| ~ spl0_79
| ~ spl0_141 ),
inference(superposition,[],[f1144,f644]) ).
fof(f17736,plain,
( spl0_440
| ~ spl0_144
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f17347,f1754,f1199,f5876]) ).
fof(f5876,plain,
( spl0_440
<=> ! [X0,X1] :
( member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(first(regular(cross_product(X0,X1))),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f17347,plain,
( ! [X0,X1] :
( member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(first(regular(cross_product(X0,X1))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_198 ),
inference(superposition,[],[f1755,f1200]) ).
fof(f17359,plain,
( spl0_783
| ~ spl0_238
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f4035,f4032,f2279,f17357]) ).
fof(f17357,plain,
( spl0_783
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f4035,plain,
( ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_238
| ~ spl0_335 ),
inference(forward_demodulation,[],[f4033,f2281]) ).
fof(f2281,plain,
( subset_relation = y
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2279]) ).
fof(f17329,plain,
( spl0_782
| ~ spl0_18
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f17028,f1233,f287,f17326]) ).
fof(f17326,plain,
( spl0_782
<=> subclass(successor_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f1233,plain,
( spl0_146
<=> element_relation = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f17028,plain,
( subclass(successor_relation,element_relation)
| ~ spl0_18
| ~ spl0_146 ),
inference(superposition,[],[f289,f1235]) ).
fof(f1235,plain,
( element_relation = cross_product(universal_class,universal_class)
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1233]) ).
fof(f17231,plain,
( spl0_781
| ~ spl0_146
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f17071,f2283,f1233,f17228]) ).
fof(f17071,plain,
( member(regular(subset_relation),element_relation)
| ~ spl0_146
| ~ spl0_239 ),
inference(superposition,[],[f2285,f1235]) ).
fof(f17226,plain,
( ~ spl0_780
| spl0_126
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f17045,f1233,f986,f17223]) ).
fof(f17223,plain,
( spl0_780
<=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f17045,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(element_relation,universal_class)),universal_class)))))
| spl0_126
| ~ spl0_146 ),
inference(superposition,[],[f988,f1235]) ).
fof(f17026,plain,
( spl0_779
| spl0_147
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f1922,f1918,f1237,f17023]) ).
fof(f17023,plain,
( spl0_779
<=> not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1237,plain,
( spl0_147
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1922,plain,
( not_subclass_element(cross_product(universal_class,universal_class),element_relation) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),first(not_subclass_element(cross_product(universal_class,universal_class),element_relation))),unordered_pair(first(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),unordered_pair(second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)),second(not_subclass_element(cross_product(universal_class,universal_class),element_relation)))))
| spl0_147
| ~ spl0_213 ),
inference(resolution,[],[f1919,f1239]) ).
fof(f1239,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| spl0_147 ),
inference(avatar_component_clause,[],[f1237]) ).
fof(f17005,plain,
( spl0_778
| ~ spl0_144
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2170,f2122,f1199,f17003]) ).
fof(f17003,plain,
( spl0_778
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f2170,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_222 ),
inference(superposition,[],[f2123,f1200]) ).
fof(f17001,plain,
( spl0_777
| ~ spl0_116
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2031,f1999,f912,f16999]) ).
fof(f16999,plain,
( spl0_777
<=> ! [X0,X1] :
( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f2031,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))))))),universal_class) )
| ~ spl0_116
| ~ spl0_216 ),
inference(resolution,[],[f2000,f913]) ).
fof(f16786,plain,
( spl0_776
| ~ spl0_99
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1108,f1078,f759,f16784]) ).
fof(f1108,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,flip(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
| ~ spl0_99
| ~ spl0_137 ),
inference(resolution,[],[f1079,f760]) ).
fof(f16782,plain,
( spl0_775
| ~ spl0_96
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1107,f1078,f746,f16780]) ).
fof(f1107,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,rotate(X0))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),X0) )
| ~ spl0_96
| ~ spl0_137 ),
inference(resolution,[],[f1079,f747]) ).
fof(f16775,plain,
( spl0_773
| ~ spl0_774
| ~ spl0_81
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2012,f1999,f661,f16772,f16769]) ).
fof(f16769,plain,
( spl0_773
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f16772,plain,
( spl0_774
<=> subclass(composition_function,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f661,plain,
( spl0_81
<=> ! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f2012,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
| ~ spl0_81
| ~ spl0_216 ),
inference(resolution,[],[f2000,f662]) ).
fof(f662,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f16767,plain,
( spl0_772
| ~ spl0_81
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1898,f1889,f661,f16765]) ).
fof(f16765,plain,
( spl0_772
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),successor_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1898,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),successor_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = complement(intersection(complement(not_homomorphism1(X0,X1,X2)),complement(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2))))) )
| ~ spl0_81
| ~ spl0_212 ),
inference(resolution,[],[f1890,f662]) ).
fof(f16717,plain,
( spl0_771
| ~ spl0_170
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f2164,f2122,f1491,f16715]) ).
fof(f16715,plain,
( spl0_771
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1491,plain,
( spl0_170
<=> ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f2164,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),universal_class) )
| ~ spl0_170
| ~ spl0_222 ),
inference(resolution,[],[f2123,f1492]) ).
fof(f1492,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1491]) ).
fof(f16713,plain,
( spl0_770
| ~ spl0_170
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2141,f2118,f1491,f16711]) ).
fof(f16711,plain,
( spl0_770
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f2141,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(compose(X3,regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class)))))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X3),universal_class)))))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),universal_class) )
| ~ spl0_170
| ~ spl0_221 ),
inference(resolution,[],[f2119,f1492]) ).
fof(f16660,plain,
( spl0_769
| ~ spl0_101
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1217,f1199,f767,f16658]) ).
fof(f16658,plain,
( spl0_769
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f1217,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = y )
| ~ spl0_101
| ~ spl0_144 ),
inference(superposition,[],[f768,f1200]) ).
fof(f16630,plain,
( spl0_768
| ~ spl0_55
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1781,f1750,f492,f16628]) ).
fof(f16628,plain,
( spl0_768
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f1781,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X0
| complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))) = X1 )
| ~ spl0_55
| ~ spl0_197 ),
inference(resolution,[],[f1751,f493]) ).
fof(f16625,plain,
( spl0_766
| ~ spl0_767
| ~ spl0_167
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1725,f1646,f1424,f16622,f16619]) ).
fof(f16619,plain,
( spl0_766
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f16622,plain,
( spl0_767
<=> subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f1725,plain,
( ! [X0] :
( ~ subclass(domain_relation,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),identity_relation) )
| ~ spl0_167
| ~ spl0_192 ),
inference(resolution,[],[f1647,f1425]) ).
fof(f16617,plain,
( spl0_764
| ~ spl0_765
| ~ spl0_166
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1722,f1646,f1420,f16614,f16611]) ).
fof(f16611,plain,
( spl0_764
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f16614,plain,
( spl0_765
<=> subclass(domain_relation,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f1722,plain,
( ! [X0] :
( ~ subclass(domain_relation,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),singleton_relation) )
| ~ spl0_166
| ~ spl0_192 ),
inference(resolution,[],[f1647,f1421]) ).
fof(f16609,plain,
( spl0_763
| ~ spl0_82
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1312,f1287,f665,f16607]) ).
fof(f16607,plain,
( spl0_763
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1312,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = unordered_pair(unordered_pair(first(not_subclass_element(X0,X3)),first(not_subclass_element(X0,X3))),unordered_pair(first(not_subclass_element(X0,X3)),unordered_pair(second(not_subclass_element(X0,X3)),second(not_subclass_element(X0,X3))))) )
| ~ spl0_82
| ~ spl0_154 ),
inference(resolution,[],[f1288,f666]) ).
fof(f16605,plain,
( ~ spl0_762
| ~ spl0_550
| ~ spl0_567
| ~ spl0_693 ),
inference(avatar_split_clause,[],[f16439,f14096,f9421,f8731,f16602]) ).
fof(f16602,plain,
( spl0_762
<=> subclass(subset_relation,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f14096,plain,
( spl0_693
<=> ! [X0] :
( ~ subclass(subset_relation,X0)
| member(regular(identity_relation),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f16439,plain,
( ~ subclass(subset_relation,y)
| ~ spl0_550
| ~ spl0_567
| ~ spl0_693 ),
inference(forward_demodulation,[],[f16429,f9423]) ).
fof(f16429,plain,
( ~ subclass(subset_relation,domain_of(y))
| ~ spl0_550
| ~ spl0_693 ),
inference(resolution,[],[f14097,f8732]) ).
fof(f14097,plain,
( ! [X0] :
( member(regular(identity_relation),X0)
| ~ subclass(subset_relation,X0) )
| ~ spl0_693 ),
inference(avatar_component_clause,[],[f14096]) ).
fof(f16455,plain,
( spl0_761
| ~ spl0_112
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1988,f1943,f856,f16453]) ).
fof(f16453,plain,
( spl0_761
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f1988,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))))))),cross_product(universal_class,universal_class))
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class))))) )
| ~ spl0_112
| ~ spl0_215 ),
inference(resolution,[],[f1944,f857]) ).
fof(f16451,plain,
( spl0_760
| ~ spl0_111
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1979,f1943,f852,f16449]) ).
fof(f16449,plain,
( spl0_760
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1979,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class)),universal_class)))),X3) )
| ~ spl0_111
| ~ spl0_215 ),
inference(resolution,[],[f1944,f853]) ).
fof(f16447,plain,
( spl0_759
| ~ spl0_112
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1962,f1939,f856,f16445]) ).
fof(f16445,plain,
( spl0_759
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f1962,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class))
| y = intersection(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class))))) )
| ~ spl0_112
| ~ spl0_214 ),
inference(resolution,[],[f1940,f857]) ).
fof(f16443,plain,
( spl0_758
| ~ spl0_111
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1953,f1939,f852,f16441]) ).
fof(f16441,plain,
( spl0_758
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1953,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class))
| y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_111
| ~ spl0_214 ),
inference(resolution,[],[f1940,f853]) ).
fof(f16395,plain,
( spl0_757
| ~ spl0_94
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f879,f856,f725,f16393]) ).
fof(f16393,plain,
( spl0_757
<=> ! [X0,X3,X2,X1] :
( y = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f879,plain,
( ! [X2,X3,X0,X1] :
( y = intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))),regular(intersection(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_112 ),
inference(resolution,[],[f857,f726]) ).
fof(f16391,plain,
( spl0_756
| ~ spl0_94
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f865,f852,f725,f16389]) ).
fof(f16389,plain,
( spl0_756
<=> ! [X0,X3,X2,X1] :
( y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f865,plain,
( ! [X2,X3,X0,X1] :
( y = intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)),regular(intersection(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_111 ),
inference(resolution,[],[f853,f726]) ).
fof(f16242,plain,
( spl0_755
| ~ spl0_76
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2014,f1999,f625,f16240]) ).
fof(f16240,plain,
( spl0_755
<=> ! [X2,X0,X1] :
( ~ subclass(composition_function,compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f625,plain,
( spl0_76
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f2014,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| compose(X0,X1) = unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))) )
| ~ spl0_76
| ~ spl0_216 ),
inference(resolution,[],[f2000,f626]) ).
fof(f626,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
| compose(X0,X1) = X4 )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f16238,plain,
( spl0_754
| ~ spl0_55
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1763,f1746,f492,f16236]) ).
fof(f16236,plain,
( spl0_754
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,unordered_pair(X1,X2))
| ~ member(X3,universal_class)
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f1763,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,unordered_pair(X1,X2))
| ~ member(X3,universal_class)
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X1
| domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))) = X2 )
| ~ spl0_55
| ~ spl0_196 ),
inference(resolution,[],[f1747,f493]) ).
fof(f16234,plain,
( spl0_753
| ~ spl0_55
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1717,f1646,f492,f16232]) ).
fof(f16232,plain,
( spl0_753
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f1717,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X0
| unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))) = X1 )
| ~ spl0_55
| ~ spl0_192 ),
inference(resolution,[],[f1647,f493]) ).
fof(f16230,plain,
( spl0_752
| ~ spl0_56
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1677,f1642,f496,f16228]) ).
fof(f16228,plain,
( spl0_752
<=> ! [X0,X3,X2,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
| subclass(X0,intersection(X1,intersection(X2,X3)))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f1677,plain,
( ! [X2,X3,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X1)
| subclass(X0,intersection(X1,intersection(X2,X3)))
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X3)
| ~ member(not_subclass_element(X0,intersection(X1,intersection(X2,X3))),X2) )
| ~ spl0_56
| ~ spl0_191 ),
inference(resolution,[],[f1643,f497]) ).
fof(f16226,plain,
( spl0_751
| ~ spl0_145
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1632,f1625,f1229,f16224]) ).
fof(f16224,plain,
( spl0_751
<=> ! [X0] :
( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
| subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f1229,plain,
( spl0_145
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1632,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0),subset_relation)
| subclass(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),X0) )
| ~ spl0_145
| ~ spl0_189 ),
inference(resolution,[],[f1626,f1230]) ).
fof(f1230,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(complement(X0),X1),X0)
| subclass(complement(X0),X1) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1229]) ).
fof(f16190,plain,
( spl0_750
| ~ spl0_57
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1875,f1866,f500,f16188]) ).
fof(f16188,plain,
( spl0_750
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f1866,plain,
( spl0_209
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_57
| ~ spl0_209 ),
inference(superposition,[],[f1867,f501]) ).
fof(f1867,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1866]) ).
fof(f16186,plain,
( spl0_749
| ~ spl0_57
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1872,f1866,f500,f16184]) ).
fof(f16184,plain,
( spl0_749
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f1872,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_57
| ~ spl0_209 ),
inference(superposition,[],[f1867,f501]) ).
fof(f16167,plain,
( spl0_748
| ~ spl0_73
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2007,f1999,f609,f16165]) ).
fof(f16165,plain,
( spl0_748
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f609,plain,
( spl0_73
<=> ! [X0,X3,X2,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f2007,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(compose(X2,X3),compose(X2,X3)))),X1) )
| ~ spl0_73
| ~ spl0_216 ),
inference(resolution,[],[f2000,f610]) ).
fof(f610,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| member(X3,X1) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f16077,plain,
( spl0_746
| spl0_747
| ~ spl0_82
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1113,f1078,f665,f16075,f16072]) ).
fof(f16072,plain,
( spl0_746
<=> ! [X2,X3] : unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f1113,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| unordered_pair(X2,X3) = unordered_pair(unordered_pair(first(unordered_pair(X2,X3)),first(unordered_pair(X2,X3))),unordered_pair(first(unordered_pair(X2,X3)),unordered_pair(second(unordered_pair(X2,X3)),second(unordered_pair(X2,X3))))) )
| ~ spl0_82
| ~ spl0_137 ),
inference(resolution,[],[f1079,f666]) ).
fof(f16070,plain,
( ~ spl0_745
| ~ spl0_550
| ~ spl0_567
| ~ spl0_691 ),
inference(avatar_split_clause,[],[f15652,f13889,f9421,f8731,f16067]) ).
fof(f15652,plain,
( ~ subclass(element_relation,y)
| ~ spl0_550
| ~ spl0_567
| ~ spl0_691 ),
inference(forward_demodulation,[],[f15642,f9423]) ).
fof(f15642,plain,
( ~ subclass(element_relation,domain_of(y))
| ~ spl0_550
| ~ spl0_691 ),
inference(resolution,[],[f13890,f8732]) ).
fof(f16038,plain,
( spl0_744
| ~ spl0_139
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1870,f1866,f1089,f16036]) ).
fof(f16036,plain,
( spl0_744
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f1870,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),subset_relation) )
| ~ spl0_139
| ~ spl0_209 ),
inference(resolution,[],[f1867,f1090]) ).
fof(f16003,plain,
( spl0_743
| ~ spl0_100
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1216,f1199,f763,f16001]) ).
fof(f16001,plain,
( spl0_743
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f763,plain,
( spl0_100
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1216,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = y )
| ~ spl0_100
| ~ spl0_144 ),
inference(superposition,[],[f764,f1200]) ).
fof(f764,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f15938,plain,
( spl0_741
| ~ spl0_742
| ~ spl0_68
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2015,f1999,f583,f15935,f15932]) ).
fof(f15932,plain,
( spl0_741
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f15935,plain,
( spl0_742
<=> subclass(composition_function,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f583,plain,
( spl0_68
<=> ! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f2015,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,domain_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| domain_of(X0) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))) )
| ~ spl0_68
| ~ spl0_216 ),
inference(resolution,[],[f2000,f584]) ).
fof(f584,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation)
| domain_of(X0) = X1 )
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f15930,plain,
( spl0_740
| ~ spl0_90
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1709,f1646,f706,f15928]) ).
fof(f15928,plain,
( spl0_740
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,compose(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1709,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,compose(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_90
| ~ spl0_192 ),
inference(resolution,[],[f1647,f707]) ).
fof(f15926,plain,
( spl0_739
| ~ spl0_35
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1631,f1625,f365,f15924]) ).
fof(f15924,plain,
( spl0_739
<=> ! [X0] :
( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
| subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1631,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
| subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_35
| ~ spl0_189 ),
inference(resolution,[],[f1626,f366]) ).
fof(f15727,plain,
( spl0_737
| ~ spl0_738
| ~ spl0_65
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2010,f1999,f569,f15724,f15721]) ).
fof(f15721,plain,
( spl0_737
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f15724,plain,
( spl0_738
<=> subclass(composition_function,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f569,plain,
( spl0_65
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f2010,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X0,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))) )
| ~ spl0_65
| ~ spl0_216 ),
inference(resolution,[],[f2000,f570]) ).
fof(f570,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X0,X1) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f15719,plain,
( spl0_736
| ~ spl0_153
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1682,f1642,f1264,f15717]) ).
fof(f15717,plain,
( spl0_736
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f1682,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),X1)
| subclass(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class)))))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation) )
| ~ spl0_153
| ~ spl0_191 ),
inference(resolution,[],[f1643,f1265]) ).
fof(f15715,plain,
( ~ spl0_735
| ~ spl0_31
| spl0_727 ),
inference(avatar_split_clause,[],[f15661,f15657,f342,f15712]) ).
fof(f15712,plain,
( spl0_735
<=> function(composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f15657,plain,
( spl0_727
<=> subclass(composition_function,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f15661,plain,
( ~ function(composition_function)
| ~ spl0_31
| spl0_727 ),
inference(resolution,[],[f15659,f343]) ).
fof(f15659,plain,
( ~ subclass(composition_function,cross_product(universal_class,universal_class))
| spl0_727 ),
inference(avatar_component_clause,[],[f15657]) ).
fof(f15710,plain,
( spl0_734
| ~ spl0_152
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1680,f1642,f1260,f15708]) ).
fof(f15708,plain,
( spl0_734
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f1680,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),X1)
| subclass(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation)))))
| ~ member(not_subclass_element(X0,intersection(X1,complement(compose(element_relation,complement(identity_relation))))),singleton_relation) )
| ~ spl0_152
| ~ spl0_191 ),
inference(resolution,[],[f1643,f1261]) ).
fof(f15706,plain,
( spl0_733
| ~ spl0_161
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1477,f1424,f1351,f15704]) ).
fof(f15704,plain,
( spl0_733
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
| member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
| subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f1477,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),subset_relation)
| member(not_subclass_element(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1),identity_relation)
| subclass(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),X1) )
| ~ spl0_161
| ~ spl0_167 ),
inference(resolution,[],[f1425,f1352]) ).
fof(f15702,plain,
( spl0_732
| ~ spl0_160
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1467,f1424,f1347,f15700]) ).
fof(f15700,plain,
( spl0_732
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
| member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
| subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f1467,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),subset_relation)
| member(not_subclass_element(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1),identity_relation)
| subclass(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),X1) )
| ~ spl0_160
| ~ spl0_167 ),
inference(resolution,[],[f1425,f1348]) ).
fof(f15698,plain,
( spl0_731
| ~ spl0_161
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1452,f1420,f1351,f15696]) ).
fof(f15696,plain,
( spl0_731
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
| member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
| subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f1452,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),element_relation)
| member(not_subclass_element(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1),singleton_relation)
| subclass(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),X1) )
| ~ spl0_161
| ~ spl0_166 ),
inference(resolution,[],[f1421,f1352]) ).
fof(f15694,plain,
( spl0_730
| ~ spl0_160
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1442,f1420,f1347,f15692]) ).
fof(f15692,plain,
( spl0_730
<=> ! [X0,X1] :
( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
| member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
| subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f1442,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),element_relation)
| member(not_subclass_element(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1),singleton_relation)
| subclass(intersection(complement(compose(element_relation,complement(identity_relation))),X0),X1) )
| ~ spl0_160
| ~ spl0_166 ),
inference(resolution,[],[f1421,f1348]) ).
fof(f15690,plain,
( spl0_729
| ~ spl0_89
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1134,f1089,f701,f15688]) ).
fof(f15688,plain,
( spl0_729
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f701,plain,
( spl0_89
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1134,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1)) )
| ~ spl0_89
| ~ spl0_139 ),
inference(resolution,[],[f1090,f702]) ).
fof(f702,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f15665,plain,
( spl0_728
| ~ spl0_82
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1048,f1043,f665,f15663]) ).
fof(f15663,plain,
( spl0_728
<=> ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f1048,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))))))) )
| ~ spl0_82
| ~ spl0_134 ),
inference(resolution,[],[f1044,f666]) ).
fof(f15660,plain,
( spl0_726
| ~ spl0_727
| ~ spl0_180
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2008,f1999,f1566,f15657,f15654]) ).
fof(f15654,plain,
( spl0_726
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),compose(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f1566,plain,
( spl0_180
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f2008,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),universal_class)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_180
| ~ spl0_216 ),
inference(resolution,[],[f2000,f1567]) ).
fof(f1567,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1566]) ).
fof(f15500,plain,
( spl0_725
| ~ spl0_144
| ~ spl0_221 ),
inference(avatar_split_clause,[],[f2147,f2118,f1199,f15498]) ).
fof(f15498,plain,
( spl0_725
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2147,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))),rotate(X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),cross_product(universal_class,universal_class))
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_221 ),
inference(superposition,[],[f2119,f1200]) ).
fof(f15496,plain,
( spl0_724
| ~ spl0_116
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1911,f1889,f912,f15494]) ).
fof(f15494,plain,
( spl0_724
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
| ~ operation(X2)
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1911,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class))))
| ~ operation(X2)
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2))))),universal_class) )
| ~ spl0_116
| ~ spl0_212 ),
inference(resolution,[],[f1890,f913]) ).
fof(f15492,plain,
( spl0_723
| ~ spl0_99
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1215,f1199,f759,f15490]) ).
fof(f15490,plain,
( spl0_723
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f1215,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),flip(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),unordered_pair(X2,X2))),X3)
| cross_product(X0,X1) = y )
| ~ spl0_99
| ~ spl0_144 ),
inference(superposition,[],[f760,f1200]) ).
fof(f15441,plain,
( spl0_722
| ~ spl0_154
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1837,f1816,f1287,f15439]) ).
fof(f15439,plain,
( spl0_722
<=> ! [X0,X1] :
( member(not_subclass_element(X0,X1),subset_relation)
| ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1837,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,X1),subset_relation)
| ~ member(not_subclass_element(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(X0,X1) )
| ~ spl0_154
| ~ spl0_203 ),
inference(resolution,[],[f1817,f1288]) ).
fof(f15437,plain,
( spl0_721
| ~ spl0_51
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1679,f1642,f472,f15435]) ).
fof(f15435,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
| subclass(X0,intersection(X1,complement(X2)))
| member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
| ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1679,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),X1)
| subclass(X0,intersection(X1,complement(X2)))
| member(not_subclass_element(X0,intersection(X1,complement(X2))),X2)
| ~ member(not_subclass_element(X0,intersection(X1,complement(X2))),universal_class) )
| ~ spl0_51
| ~ spl0_191 ),
inference(resolution,[],[f1643,f473]) ).
fof(f15433,plain,
( spl0_720
| ~ spl0_2
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2680,f2450,f213,f15431]) ).
fof(f2680,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(X0)) )
| ~ spl0_2
| ~ spl0_248 ),
inference(duplicate_literal_removal,[],[f2651]) ).
fof(f2651,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,complement(X0))
| y = X0 )
| ~ spl0_2
| ~ spl0_248 ),
inference(resolution,[],[f2451,f214]) ).
fof(f15387,plain,
( spl0_719
| ~ spl0_7
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2193,f2186,f238,f15385]) ).
fof(f15385,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2)
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2193,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2)))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))),X2)
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_224 ),
inference(superposition,[],[f2187,f239]) ).
fof(f15383,plain,
( spl0_718
| ~ spl0_134
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1984,f1943,f1043,f15381]) ).
fof(f15381,plain,
( spl0_718
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1984,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| ~ member(X1,universal_class)
| y = X1 )
| ~ spl0_134
| ~ spl0_215 ),
inference(resolution,[],[f1944,f1044]) ).
fof(f15379,plain,
( spl0_717
| ~ spl0_134
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1958,f1939,f1043,f15377]) ).
fof(f15377,plain,
( spl0_717
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1958,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(X1,universal_class)
| y = X1 )
| ~ spl0_134
| ~ spl0_214 ),
inference(resolution,[],[f1940,f1044]) ).
fof(f15375,plain,
( spl0_716
| ~ spl0_94
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1052,f1043,f725,f15373]) ).
fof(f15373,plain,
( spl0_716
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X0,universal_class)
| y = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1052,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| ~ member(X0,universal_class)
| y = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_134 ),
inference(resolution,[],[f1044,f726]) ).
fof(f15326,plain,
( spl0_715
| ~ spl0_46
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f15322,f973,f424,f15324]) ).
fof(f15324,plain,
( spl0_715
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(domain_of(domain_of(flip(cross_product(y,universal_class)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f15322,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(domain_of(domain_of(flip(cross_product(y,universal_class)))),X0) )
| ~ spl0_46
| ~ spl0_123 ),
inference(resolution,[],[f975,f425]) ).
fof(f975,plain,
( member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f15309,plain,
( spl0_714
| ~ spl0_662
| ~ spl0_713 ),
inference(avatar_split_clause,[],[f15305,f15300,f13193,f15307]) ).
fof(f15307,plain,
( spl0_714
<=> ! [X0,X1] :
( y = domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f15300,plain,
( spl0_713
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f15305,plain,
( ! [X0,X1] :
( y = domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_662
| ~ spl0_713 ),
inference(forward_demodulation,[],[f15304,f13195]) ).
fof(f13195,plain,
( y = domain_of(domain_of(flip(cross_product(y,universal_class))))
| ~ spl0_662 ),
inference(avatar_component_clause,[],[f13193]) ).
fof(f15304,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_662
| ~ spl0_713 ),
inference(forward_demodulation,[],[f15303,f13195]) ).
fof(f15303,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(y,universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_662
| ~ spl0_713 ),
inference(forward_demodulation,[],[f15301,f13195]) ).
fof(f15301,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_713 ),
inference(avatar_component_clause,[],[f15300]) ).
fof(f15302,plain,
( spl0_713
| ~ spl0_7
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1873,f1866,f238,f15300]) ).
fof(f1873,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_209 ),
inference(superposition,[],[f1867,f239]) ).
fof(f15220,plain,
( spl0_712
| ~ spl0_76
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1900,f1889,f625,f15218]) ).
fof(f15218,plain,
( spl0_712
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose_class(X3))
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1900,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),compose_class(X3))
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = compose(X3,not_homomorphism1(X0,X1,X2)) )
| ~ spl0_76
| ~ spl0_212 ),
inference(resolution,[],[f1890,f626]) ).
fof(f15216,plain,
( ~ spl0_711
| spl0_186
| ~ spl0_187
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2669,f2450,f1605,f1601,f15213]) ).
fof(f15213,plain,
( spl0_711
<=> subclass(identity_relation,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f2669,plain,
( identity_relation = y
| ~ subclass(identity_relation,complement(subset_relation))
| ~ spl0_187
| ~ spl0_248 ),
inference(resolution,[],[f2451,f1607]) ).
fof(f15211,plain,
( spl0_710
| ~ spl0_90
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1098,f1078,f706,f15209]) ).
fof(f15209,plain,
( spl0_710
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,compose(X0,X1))
| member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f1098,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,compose(X0,X1))
| member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X1),universal_class)))),universal_class),X0),universal_class))))) )
| ~ spl0_90
| ~ spl0_137 ),
inference(resolution,[],[f1079,f707]) ).
fof(f15096,plain,
( spl0_709
| ~ spl0_46
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f1845,f1841,f424,f15094]) ).
fof(f15094,plain,
( spl0_709
<=> ! [X2,X0,X1] :
( ~ member(compose(X0,X1),universal_class)
| ~ member(X1,universal_class)
| ~ subclass(compose_class(X0),X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f1845,plain,
( ! [X2,X0,X1] :
( ~ member(compose(X0,X1),universal_class)
| ~ member(X1,universal_class)
| ~ subclass(compose_class(X0),X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),X2) )
| ~ spl0_46
| ~ spl0_204 ),
inference(resolution,[],[f1842,f425]) ).
fof(f15092,plain,
( ~ spl0_707
| spl0_708
| ~ spl0_137
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1836,f1816,f1078,f15090,f15086]) ).
fof(f15086,plain,
( spl0_707
<=> subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f15090,plain,
( spl0_708
<=> ! [X0,X1] :
( member(unordered_pair(X0,X1),subset_relation)
| ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f1836,plain,
( ! [X0,X1] :
( member(unordered_pair(X0,X1),subset_relation)
| ~ member(unordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ subclass(universal_class,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_137
| ~ spl0_203 ),
inference(resolution,[],[f1817,f1079]) ).
fof(f15084,plain,
( spl0_706
| ~ spl0_79
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1687,f1642,f642,f15082]) ).
fof(f15082,plain,
( spl0_706
<=> ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
| subclass(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f1687,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(not_subclass_element(X0,subset_relation),cross_product(universal_class,universal_class))
| subclass(X0,subset_relation) )
| ~ spl0_79
| ~ spl0_191 ),
inference(superposition,[],[f1643,f644]) ).
fof(f14969,plain,
( spl0_705
| ~ spl0_80
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1869,f1866,f647,f14967]) ).
fof(f14967,plain,
( spl0_705
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f1869,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))
| ~ member(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_209 ),
inference(resolution,[],[f1867,f648]) ).
fof(f14965,plain,
( spl0_704
| ~ spl0_96
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1214,f1199,f746,f14963]) ).
fof(f14963,plain,
( spl0_704
<=> ! [X0,X3,X2,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f1214,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))),unordered_pair(regular(cross_product(X0,X1)),unordered_pair(X2,X2))),rotate(X3))
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),unordered_pair(second(regular(cross_product(X0,X1))),unordered_pair(X2,X2))),unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))),X3)
| cross_product(X0,X1) = y )
| ~ spl0_96
| ~ spl0_144 ),
inference(superposition,[],[f747,f1200]) ).
fof(f14896,plain,
( spl0_703
| ~ spl0_68
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1901,f1889,f583,f14894]) ).
fof(f14894,plain,
( spl0_703
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f1901,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),domain_relation)
| ~ operation(X2)
| not_homomorphism2(X0,X1,X2) = domain_of(not_homomorphism1(X0,X1,X2)) )
| ~ spl0_68
| ~ spl0_212 ),
inference(resolution,[],[f1890,f584]) ).
fof(f14892,plain,
( spl0_702
| ~ spl0_142
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1668,f1638,f1181,f14890]) ).
fof(f14890,plain,
( spl0_702
<=> ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
| not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
| function(unordered_pair(X0,X1))
| ~ single_valued_class(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1668,plain,
( ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X1
| not_subclass_element(unordered_pair(X0,X1),cross_product(universal_class,universal_class)) = X0
| function(unordered_pair(X0,X1))
| ~ single_valued_class(unordered_pair(X0,X1)) )
| ~ spl0_142
| ~ spl0_190 ),
inference(resolution,[],[f1639,f1182]) ).
fof(f14888,plain,
( spl0_701
| ~ spl0_79
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1546,f1533,f642,f14886]) ).
fof(f14886,plain,
( spl0_701
<=> ! [X0,X1] :
( ~ subclass(subset_relation,X0)
| ~ member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f1533,plain,
( spl0_178
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(intersection(X2,X1),X3)
| member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1546,plain,
( ! [X0,X1] :
( ~ subclass(subset_relation,X0)
| ~ member(X1,cross_product(universal_class,universal_class))
| ~ member(X1,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| member(X1,X0) )
| ~ spl0_79
| ~ spl0_178 ),
inference(superposition,[],[f1534,f644]) ).
fof(f1534,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,X3) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f14833,plain,
( ~ spl0_700
| spl0_168
| ~ spl0_169
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2659,f2450,f1432,f1428,f14830]) ).
fof(f2659,plain,
( singleton_relation = y
| ~ subclass(singleton_relation,complement(element_relation))
| ~ spl0_169
| ~ spl0_248 ),
inference(resolution,[],[f2451,f1434]) ).
fof(f14729,plain,
( spl0_699
| ~ spl0_65
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1896,f1889,f569,f14727]) ).
fof(f14727,plain,
( spl0_699
<=> ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),element_relation)
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1896,plain,
( ! [X2,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),element_relation)
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),not_homomorphism2(X0,X1,X2)) )
| ~ spl0_65
| ~ spl0_212 ),
inference(resolution,[],[f1890,f570]) ).
fof(f14707,plain,
( spl0_698
| ~ spl0_20
| ~ spl0_85
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1705,f1646,f683,f296,f14705]) ).
fof(f14705,plain,
( spl0_698
<=> ! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1705,plain,
( ! [X0] :
( ~ subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation)
| ~ member(X0,domain_of(X0)) )
| ~ spl0_85
| ~ spl0_192 ),
inference(resolution,[],[f1647,f684]) ).
fof(f14695,plain,
( spl0_697
| ~ spl0_90
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2458,f1497,f706,f14693]) ).
fof(f14693,plain,
( spl0_697
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f2458,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_90
| ~ spl0_171 ),
inference(resolution,[],[f1498,f707]) ).
fof(f14691,plain,
( ~ spl0_696
| ~ spl0_29
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2513,f2454,f334,f14688]) ).
fof(f2513,plain,
( ~ member(regular(singleton_relation),compose(element_relation,complement(identity_relation)))
| ~ spl0_29
| ~ spl0_249 ),
inference(resolution,[],[f2456,f335]) ).
fof(f14331,plain,
( spl0_186
| ~ spl0_199
| spl0_695
| ~ spl0_50
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1162,f1139,f441,f14328,f1758,f1601]) ).
fof(f1758,plain,
( spl0_199
<=> member(identity_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f14328,plain,
( spl0_695
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1162,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(identity_relation,universal_class)
| identity_relation = y
| ~ spl0_50
| ~ spl0_140 ),
inference(superposition,[],[f1140,f443]) ).
fof(f14152,plain,
( spl0_694
| ~ spl0_186
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2530,f2527,f1601,f14150]) ).
fof(f14150,plain,
( spl0_694
<=> ! [X0] :
( identity_relation = intersection(X0,singleton_relation)
| member(regular(intersection(X0,singleton_relation)),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2530,plain,
( ! [X0] :
( identity_relation = intersection(X0,singleton_relation)
| member(regular(intersection(X0,singleton_relation)),element_relation) )
| ~ spl0_186
| ~ spl0_253 ),
inference(forward_demodulation,[],[f2528,f1603]) ).
fof(f1603,plain,
( identity_relation = y
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1601]) ).
fof(f14098,plain,
( spl0_693
| ~ spl0_46
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1937,f1605,f424,f14096]) ).
fof(f1937,plain,
( ! [X0] :
( ~ subclass(subset_relation,X0)
| member(regular(identity_relation),X0) )
| ~ spl0_46
| ~ spl0_187 ),
inference(resolution,[],[f1607,f425]) ).
fof(f13965,plain,
( spl0_692
| ~ spl0_109
| ~ spl0_166
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1459,f1428,f1420,f831,f13963]) ).
fof(f13963,plain,
( spl0_692
<=> ! [X0] :
( singleton_relation = X0
| ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1459,plain,
( ! [X0] :
( singleton_relation = X0
| ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_109
| ~ spl0_166
| ~ spl0_168 ),
inference(forward_demodulation,[],[f1448,f1430]) ).
fof(f1448,plain,
( ! [X0] :
( ~ member(regular(X0),element_relation)
| member(regular(X0),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| y = X0 )
| ~ spl0_109
| ~ spl0_166 ),
inference(resolution,[],[f1421,f832]) ).
fof(f13891,plain,
( spl0_691
| ~ spl0_46
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1564,f1432,f424,f13889]) ).
fof(f1564,plain,
( ! [X0] :
( ~ subclass(element_relation,X0)
| member(regular(singleton_relation),X0) )
| ~ spl0_46
| ~ spl0_169 ),
inference(resolution,[],[f1434,f425]) ).
fof(f13887,plain,
( spl0_690
| ~ spl0_139
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1676,f1642,f1089,f13885]) ).
fof(f13885,plain,
( spl0_690
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
| subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1676,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1)
| subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),subset_relation) )
| ~ spl0_139
| ~ spl0_191 ),
inference(resolution,[],[f1643,f1090]) ).
fof(f13883,plain,
( spl0_689
| ~ spl0_34
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1466,f1424,f361,f13881]) ).
fof(f13881,plain,
( spl0_689
<=> ! [X0] :
( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
| member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
| subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1466,plain,
( ! [X0] :
( ~ member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),subset_relation)
| member(not_subclass_element(domain_of(flip(cross_product(subset_relation,universal_class))),X0),identity_relation)
| subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X0) )
| ~ spl0_34
| ~ spl0_167 ),
inference(resolution,[],[f1425,f362]) ).
fof(f13879,plain,
( spl0_688
| ~ spl0_34
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1441,f1420,f361,f13877]) ).
fof(f13877,plain,
( spl0_688
<=> ! [X0] :
( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
| member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
| subclass(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1441,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),element_relation)
| member(not_subclass_element(complement(compose(element_relation,complement(identity_relation))),X0),singleton_relation)
| subclass(complement(compose(element_relation,complement(identity_relation))),X0) )
| ~ spl0_34
| ~ spl0_166 ),
inference(resolution,[],[f1421,f362]) ).
fof(f13875,plain,
( spl0_687
| ~ spl0_55
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1390,f1351,f492,f13873]) ).
fof(f13873,plain,
( spl0_687
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1390,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,unordered_pair(X1,X2)),X3)
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X1
| not_subclass_element(intersection(X0,unordered_pair(X1,X2)),X3) = X2 )
| ~ spl0_55
| ~ spl0_161 ),
inference(resolution,[],[f1352,f493]) ).
fof(f13871,plain,
( spl0_686
| ~ spl0_55
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1369,f1347,f492,f13869]) ).
fof(f13869,plain,
( spl0_686
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(unordered_pair(X0,X1),X2),X3)
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1369,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(unordered_pair(X0,X1),X2),X3)
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X0
| not_subclass_element(intersection(unordered_pair(X0,X1),X2),X3) = X1 )
| ~ spl0_55
| ~ spl0_160 ),
inference(resolution,[],[f1348,f493]) ).
fof(f13867,plain,
( spl0_685
| ~ spl0_85
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1130,f1089,f683,f13865]) ).
fof(f13865,plain,
( spl0_685
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f1130,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1) )
| ~ spl0_85
| ~ spl0_139 ),
inference(resolution,[],[f1090,f684]) ).
fof(f13863,plain,
( ~ spl0_5
| ~ spl0_683
| spl0_684
| ~ spl0_67
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1124,f1082,f577,f13860,f13856,f228]) ).
fof(f228,plain,
( spl0_5
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f13856,plain,
( spl0_683
<=> inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f13860,plain,
( spl0_684
<=> omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f577,plain,
( spl0_67
<=> ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1082,plain,
( spl0_138
<=> ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1124,plain,
( omega = domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class))))
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(omega,universal_class)),universal_class)))))
| ~ inductive(omega)
| ~ spl0_67
| ~ spl0_138 ),
inference(resolution,[],[f1083,f578]) ).
fof(f578,plain,
( ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f577]) ).
fof(f1083,plain,
( ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f13814,plain,
( spl0_682
| ~ spl0_73
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1893,f1889,f609,f13812]) ).
fof(f13812,plain,
( spl0_682
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1893,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism2(X0,X1,X2),X4) )
| ~ spl0_73
| ~ spl0_212 ),
inference(resolution,[],[f1890,f610]) ).
fof(f13810,plain,
( spl0_681
| ~ spl0_74
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1892,f1889,f613,f13808]) ).
fof(f13808,plain,
( spl0_681
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f613,plain,
( spl0_74
<=> ! [X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1892,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(X3,X4))
| ~ operation(X2)
| member(not_homomorphism1(X0,X1,X2),X3) )
| ~ spl0_74
| ~ spl0_212 ),
inference(resolution,[],[f1890,f614]) ).
fof(f614,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| member(X2,X0) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f13806,plain,
( spl0_680
| ~ spl0_48
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1666,f1638,f432,f13804]) ).
fof(f13804,plain,
( spl0_680
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| ~ subclass(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f1666,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| ~ subclass(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = X2 )
| ~ spl0_48
| ~ spl0_190 ),
inference(resolution,[],[f1639,f433]) ).
fof(f13802,plain,
( spl0_679
| ~ spl0_55
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1551,f1537,f492,f13800]) ).
fof(f13800,plain,
( spl0_679
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f1551,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| ~ member(X2,universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,X2))) = X1 )
| ~ spl0_55
| ~ spl0_179 ),
inference(resolution,[],[f1538,f493]) ).
fof(f13574,plain,
( spl0_678
| ~ spl0_31
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f1814,f1809,f342,f13572]) ).
fof(f13572,plain,
( spl0_678
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ function(cross_product(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f1814,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ function(cross_product(X1,X3)) )
| ~ spl0_31
| ~ spl0_202 ),
inference(resolution,[],[f1810,f343]) ).
fof(f13570,plain,
( spl0_677
| ~ spl0_46
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1795,f1754,f424,f13568]) ).
fof(f13568,plain,
( spl0_677
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ subclass(element_relation,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f1795,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| ~ subclass(element_relation,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2) )
| ~ spl0_46
| ~ spl0_198 ),
inference(resolution,[],[f1755,f425]) ).
fof(f13566,plain,
( spl0_676
| ~ spl0_46
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1780,f1750,f424,f13564]) ).
fof(f13564,plain,
( spl0_676
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1780,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X2) )
| ~ spl0_46
| ~ spl0_197 ),
inference(resolution,[],[f1751,f425]) ).
fof(f13562,plain,
( spl0_675
| ~ spl0_46
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1762,f1746,f424,f13560]) ).
fof(f1762,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,X1)
| ~ member(X2,universal_class)
| ~ subclass(X1,X3)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X3) )
| ~ spl0_46
| ~ spl0_196 ),
inference(resolution,[],[f1747,f425]) ).
fof(f13558,plain,
( spl0_674
| ~ spl0_138
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1667,f1638,f1082,f13556]) ).
fof(f13556,plain,
( spl0_674
<=> ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),omega) = X1
| not_subclass_element(unordered_pair(X0,X1),omega) = X0
| unordered_pair(X0,X1) = omega
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1667,plain,
( ! [X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),omega) = X1
| not_subclass_element(unordered_pair(X0,X1),omega) = X0
| unordered_pair(X0,X1) = omega
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_138
| ~ spl0_190 ),
inference(resolution,[],[f1639,f1083]) ).
fof(f13538,plain,
( spl0_673
| ~ spl0_7
| ~ spl0_224 ),
inference(avatar_split_clause,[],[f2196,f2186,f238,f13536]) ).
fof(f13536,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| subclass(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2)
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f2196,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2)))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2),not_subclass_element(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2)))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| subclass(domain_of(domain_of(flip(cross_product(y,universal_class)))),X2)
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_7
| ~ spl0_224 ),
inference(superposition,[],[f2187,f239]) ).
fof(f13534,plain,
( spl0_672
| ~ spl0_180
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1894,f1889,f1566,f13532]) ).
fof(f13532,plain,
( spl0_672
<=> ! [X4,X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
| ~ member(not_homomorphism2(X0,X1,X2),universal_class)
| y = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1894,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),cross_product(universal_class,universal_class))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),compose(X3,X4))
| ~ member(not_homomorphism2(X0,X1,X2),universal_class)
| y = intersection(cross_product(unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),universal_class),X4),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_180
| ~ spl0_212 ),
inference(resolution,[],[f1890,f1567]) ).
fof(f13530,plain,
( ~ spl0_671
| spl0_572
| ~ spl0_662 ),
inference(avatar_split_clause,[],[f13203,f13193,f9489,f13527]) ).
fof(f13203,plain,
( y != cross_product(y,universal_class)
| spl0_572
| ~ spl0_662 ),
inference(superposition,[],[f9490,f13195]) ).
fof(f13487,plain,
( spl0_670
| ~ spl0_113
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2034,f1999,f888,f13485]) ).
fof(f13485,plain,
( spl0_670
<=> ! [X2,X0,X1] :
( ~ subclass(composition_function,regular(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),y)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f2034,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,regular(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),y)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2)))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(compose(X1,X2),compose(X1,X2))))))),X0)
| y = X0 )
| ~ spl0_113
| ~ spl0_216 ),
inference(resolution,[],[f2000,f889]) ).
fof(f13300,plain,
( spl0_669
| ~ spl0_39
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1784,f1750,f381,f13298]) ).
fof(f13298,plain,
( spl0_669
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1784,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X0) )
| ~ spl0_39
| ~ spl0_197 ),
inference(resolution,[],[f1751,f382]) ).
fof(f13296,plain,
( spl0_668
| ~ spl0_40
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1783,f1750,f385,f13294]) ).
fof(f13294,plain,
( spl0_668
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1783,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),X1) )
| ~ spl0_40
| ~ spl0_197 ),
inference(resolution,[],[f1751,f386]) ).
fof(f13290,plain,
( ~ spl0_21
| spl0_123
| ~ spl0_662 ),
inference(avatar_split_clause,[],[f13200,f13193,f973,f301]) ).
fof(f13200,plain,
( ~ member(y,universal_class)
| spl0_123
| ~ spl0_662 ),
inference(superposition,[],[f974,f13195]) ).
fof(f13289,plain,
( spl0_667
| ~ spl0_39
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1766,f1746,f381,f13287]) ).
fof(f13287,plain,
( spl0_667
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f1766,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X1) )
| ~ spl0_39
| ~ spl0_196 ),
inference(resolution,[],[f1747,f382]) ).
fof(f13285,plain,
( spl0_666
| ~ spl0_40
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1765,f1746,f385,f13283]) ).
fof(f13283,plain,
( spl0_666
<=> ! [X0,X3,X2,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1765,plain,
( ! [X2,X3,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,intersection(X1,X2))
| ~ member(X3,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X3,universal_class),X0),universal_class)))),X2) )
| ~ spl0_40
| ~ spl0_196 ),
inference(resolution,[],[f1747,f386]) ).
fof(f13281,plain,
( spl0_665
| ~ spl0_46
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1716,f1646,f424,f13279]) ).
fof(f13279,plain,
( spl0_665
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f1716,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X2) )
| ~ spl0_46
| ~ spl0_192 ),
inference(resolution,[],[f1647,f425]) ).
fof(f13277,plain,
( spl0_664
| ~ spl0_56
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1268,f1229,f496,f13275]) ).
fof(f13275,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( subclass(complement(intersection(X0,X1)),X2)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f1268,plain,
( ! [X2,X0,X1] :
( subclass(complement(intersection(X0,X1)),X2)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X1)
| ~ member(not_subclass_element(complement(intersection(X0,X1)),X2),X0) )
| ~ spl0_56
| ~ spl0_145 ),
inference(resolution,[],[f1230,f497]) ).
fof(f13199,plain,
( spl0_662
| spl0_663
| ~ spl0_7
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f1876,f1866,f238,f13197,f13193]) ).
fof(f13197,plain,
( spl0_663
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,universal_class)))))))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f1876,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,universal_class)))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(y,universal_class))))),regular(domain_of(domain_of(flip(cross_product(y,universal_class)))))))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| y = domain_of(domain_of(flip(cross_product(y,universal_class))))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_7
| ~ spl0_209 ),
inference(superposition,[],[f1867,f239]) ).
fof(f13178,plain,
( spl0_661
| ~ spl0_116
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1053,f1043,f912,f13176]) ).
fof(f13176,plain,
( spl0_661
<=> ! [X0] :
( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
| ~ member(X0,universal_class)
| y = X0
| y = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f1053,plain,
( ! [X0] :
( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class))))
| ~ member(X0,universal_class)
| y = X0
| y = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))))),universal_class) )
| ~ spl0_116
| ~ spl0_134 ),
inference(resolution,[],[f1044,f913]) ).
fof(f13143,plain,
( spl0_660
| ~ spl0_2
| ~ spl0_154
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8974,f8731,f1287,f213,f13141]) ).
fof(f13141,plain,
( spl0_660
<=> ! [X0,X1] :
( ~ subclass(X0,y)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f8974,plain,
( ! [X0,X1] :
( ~ subclass(X0,y)
| subclass(X0,X1) )
| ~ spl0_2
| ~ spl0_154
| ~ spl0_550 ),
inference(forward_demodulation,[],[f8933,f8914]) ).
fof(f8933,plain,
( ! [X0,X1] :
( ~ subclass(X0,domain_of(y))
| subclass(X0,X1) )
| ~ spl0_154
| ~ spl0_550 ),
inference(resolution,[],[f8732,f1288]) ).
fof(f13073,plain,
( spl0_659
| ~ spl0_74
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2006,f1999,f613,f13071]) ).
fof(f13071,plain,
( spl0_659
<=> ! [X0,X3,X2,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2006,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(composition_function,cross_product(X0,X1))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class))
| member(X2,X0) )
| ~ spl0_74
| ~ spl0_216 ),
inference(resolution,[],[f2000,f614]) ).
fof(f13069,plain,
( spl0_658
| ~ spl0_29
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1785,f1750,f334,f13067]) ).
fof(f13067,plain,
( spl0_658
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1785,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0) )
| ~ spl0_29
| ~ spl0_197 ),
inference(resolution,[],[f1751,f335]) ).
fof(f13065,plain,
( spl0_657
| ~ spl0_29
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1767,f1746,f334,f13063]) ).
fof(f13063,plain,
( spl0_657
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,complement(X1))
| ~ member(X2,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1767,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,complement(X1))
| ~ member(X2,universal_class)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1) )
| ~ spl0_29
| ~ spl0_196 ),
inference(resolution,[],[f1747,f335]) ).
fof(f13061,plain,
( spl0_656
| ~ spl0_39
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1720,f1646,f381,f13059]) ).
fof(f13059,plain,
( spl0_656
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f1720,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X0) )
| ~ spl0_39
| ~ spl0_192 ),
inference(resolution,[],[f1647,f382]) ).
fof(f13057,plain,
( spl0_655
| ~ spl0_40
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1719,f1646,f385,f13055]) ).
fof(f13055,plain,
( spl0_655
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f1719,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(domain_of(X2),domain_of(X2)))),X1) )
| ~ spl0_40
| ~ spl0_192 ),
inference(resolution,[],[f1647,f386]) ).
fof(f13053,plain,
( spl0_654
| ~ spl0_46
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1630,f1625,f424,f13051]) ).
fof(f13051,plain,
( spl0_654
<=> ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f1630,plain,
( ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X1)
| member(X0,X1) )
| ~ spl0_46
| ~ spl0_189 ),
inference(resolution,[],[f1626,f425]) ).
fof(f13048,plain,
( spl0_653
| ~ spl0_2
| ~ spl0_548
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8955,f8731,f8590,f213,f13046]) ).
fof(f13046,plain,
( spl0_653
<=> ! [X0] : subclass(intersection(universal_class,X0),complement(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f8590,plain,
( spl0_548
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f8955,plain,
( ! [X0] : subclass(intersection(universal_class,X0),complement(y))
| ~ spl0_2
| ~ spl0_548
| ~ spl0_550 ),
inference(forward_demodulation,[],[f8920,f8914]) ).
fof(f8920,plain,
( ! [X0] : subclass(intersection(universal_class,X0),complement(domain_of(y)))
| ~ spl0_548
| ~ spl0_550 ),
inference(resolution,[],[f8732,f8591]) ).
fof(f8591,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_548 ),
inference(avatar_component_clause,[],[f8590]) ).
fof(f12915,plain,
( spl0_652
| ~ spl0_2
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2045,f2038,f213,f12913]) ).
fof(f12913,plain,
( spl0_652
<=> ! [X2,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))))))
| ~ member(X0,X2)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2038,plain,
( spl0_217
<=> ! [X0,X3,X2,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X1,X2)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f2045,plain,
( ! [X2,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1))))))))
| ~ member(X0,X2)
| y = X1 )
| ~ spl0_2
| ~ spl0_217 ),
inference(resolution,[],[f2039,f214]) ).
fof(f2039,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X1,X2)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X0,X3) )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2038]) ).
fof(f12911,plain,
( spl0_651
| ~ spl0_12
| ~ spl0_57
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1076,f1066,f500,f261,f12909]) ).
fof(f12909,plain,
( spl0_651
<=> ! [X0] :
( y = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
| ~ member(complement(domain_of(X0)),universal_class)
| y = complement(domain_of(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1066,plain,
( spl0_136
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1076,plain,
( ! [X0] :
( y = intersection(X0,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class))
| ~ member(complement(domain_of(X0)),universal_class)
| y = complement(domain_of(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class) )
| ~ spl0_12
| ~ spl0_57
| ~ spl0_136 ),
inference(forward_demodulation,[],[f1073,f501]) ).
fof(f1073,plain,
( ! [X0] :
( ~ member(complement(domain_of(X0)),universal_class)
| y = complement(domain_of(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),universal_class)
| y = intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(X0)),complement(domain_of(X0))),universal_class)),universal_class)))))))),universal_class),X0) )
| ~ spl0_12
| ~ spl0_136 ),
inference(resolution,[],[f1067,f262]) ).
fof(f1067,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = y )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f12672,plain,
( spl0_650
| ~ spl0_2
| ~ spl0_547
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8954,f8731,f8586,f213,f12670]) ).
fof(f12670,plain,
( spl0_650
<=> ! [X0] : subclass(intersection(X0,universal_class),complement(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f8586,plain,
( spl0_547
<=> ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f8954,plain,
( ! [X0] : subclass(intersection(X0,universal_class),complement(y))
| ~ spl0_2
| ~ spl0_547
| ~ spl0_550 ),
inference(forward_demodulation,[],[f8919,f8914]) ).
fof(f8919,plain,
( ! [X0] : subclass(intersection(X0,universal_class),complement(domain_of(y)))
| ~ spl0_547
| ~ spl0_550 ),
inference(resolution,[],[f8732,f8587]) ).
fof(f8587,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_547 ),
inference(avatar_component_clause,[],[f8586]) ).
fof(f12649,plain,
( spl0_648
| ~ spl0_649
| ~ spl0_87
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2003,f1999,f693,f12646,f12643]) ).
fof(f12643,plain,
( spl0_648
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f12646,plain,
( spl0_649
<=> subclass(composition_function,application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f693,plain,
( spl0_87
<=> ! [X4,X0,X1] :
( member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f2003,plain,
( ! [X0,X1] :
( ~ subclass(composition_function,application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(X1,domain_of(X0)) )
| ~ spl0_87
| ~ spl0_216 ),
inference(resolution,[],[f2000,f694]) ).
fof(f694,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
| member(X1,domain_of(X0)) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f12641,plain,
( spl0_647
| ~ spl0_29
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1721,f1646,f334,f12639]) ).
fof(f12639,plain,
( spl0_647
<=> ! [X0,X1] :
( ~ subclass(domain_relation,complement(X0))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f1721,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,complement(X0))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0) )
| ~ spl0_29
| ~ spl0_192 ),
inference(resolution,[],[f1647,f335]) ).
fof(f12637,plain,
( spl0_646
| ~ spl0_155
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1664,f1638,f1291,f12635]) ).
fof(f12635,plain,
( spl0_646
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X0,X2)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1291,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1664,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_155
| ~ spl0_190 ),
inference(resolution,[],[f1639,f1292]) ).
fof(f1292,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f12633,plain,
( spl0_645
| ~ spl0_156
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1663,f1638,f1295,f12631]) ).
fof(f12631,plain,
( spl0_645
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X1,X2)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1295,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1663,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_156
| ~ spl0_190 ),
inference(resolution,[],[f1639,f1296]) ).
fof(f1296,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f12629,plain,
( spl0_644
| ~ spl0_46
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1621,f1618,f424,f12627]) ).
fof(f12627,plain,
( spl0_644
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f1618,plain,
( spl0_188
<=> ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1621,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),X2) )
| ~ spl0_46
| ~ spl0_188 ),
inference(resolution,[],[f1619,f425]) ).
fof(f1619,plain,
( ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X1) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1618]) ).
fof(f12625,plain,
( spl0_643
| ~ spl0_154
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1479,f1424,f1287,f12623]) ).
fof(f12623,plain,
( spl0_643
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),subset_relation)
| member(not_subclass_element(X0,X1),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f1479,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),subset_relation)
| member(not_subclass_element(X0,X1),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,X1) )
| ~ spl0_154
| ~ spl0_167 ),
inference(resolution,[],[f1425,f1288]) ).
fof(f12621,plain,
( spl0_642
| ~ spl0_154
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1454,f1420,f1287,f12619]) ).
fof(f12619,plain,
( spl0_642
<=> ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1454,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),element_relation)
| member(not_subclass_element(X0,X1),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,X1) )
| ~ spl0_154
| ~ spl0_166 ),
inference(resolution,[],[f1421,f1288]) ).
fof(f12593,plain,
( spl0_641
| ~ spl0_160
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8909,f8731,f1347,f12591]) ).
fof(f12591,plain,
( spl0_641
<=> ! [X0,X1] : subclass(intersection(domain_of(y),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f8909,plain,
( ! [X0,X1] : subclass(intersection(domain_of(y),X0),X1)
| ~ spl0_160
| ~ spl0_550 ),
inference(resolution,[],[f8732,f1348]) ).
fof(f12139,plain,
( spl0_640
| ~ spl0_46
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f4108,f2322,f424,f12137]) ).
fof(f4108,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(subset_relation,X0) )
| ~ spl0_46
| ~ spl0_244 ),
inference(resolution,[],[f2324,f425]) ).
fof(f2324,plain,
( member(subset_relation,universal_class)
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2322]) ).
fof(f11829,plain,
( spl0_639
| ~ spl0_238
| ~ spl0_334 ),
inference(avatar_split_clause,[],[f4030,f4027,f2279,f11827]) ).
fof(f4030,plain,
( ! [X2,X0,X1] :
( unordered_pair(X0,X1) = subset_relation
| member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_238
| ~ spl0_334 ),
inference(forward_demodulation,[],[f4028,f2281]) ).
fof(f11752,plain,
( spl0_638
| ~ spl0_332
| ~ spl0_504 ),
inference(avatar_split_clause,[],[f11668,f7572,f3977,f11749]) ).
fof(f11749,plain,
( spl0_638
<=> member(regular(subset_relation),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f7572,plain,
( spl0_504
<=> y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f11668,plain,
( member(regular(subset_relation),y)
| ~ spl0_332
| ~ spl0_504 ),
inference(superposition,[],[f3979,f7574]) ).
fof(f7574,plain,
( y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_504 ),
inference(avatar_component_clause,[],[f7572]) ).
fof(f11661,plain,
( spl0_637
| ~ spl0_111
| spl0_505
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f11657,f11654,f7576,f852,f11659]) ).
fof(f11659,plain,
( spl0_637
<=> ! [X0] :
( member(not_subclass_element(subset_relation,X0),y)
| subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f7576,plain,
( spl0_505
<=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f11654,plain,
( spl0_636
<=> ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f11657,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),y)
| subclass(subset_relation,X0) )
| ~ spl0_111
| spl0_505
| ~ spl0_636 ),
inference(forward_demodulation,[],[f11655,f7589]) ).
fof(f7589,plain,
( y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_111
| spl0_505 ),
inference(resolution,[],[f7578,f853]) ).
fof(f7578,plain,
( ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
| spl0_505 ),
inference(avatar_component_clause,[],[f7576]) ).
fof(f11655,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) )
| ~ spl0_636 ),
inference(avatar_component_clause,[],[f11654]) ).
fof(f11656,plain,
( spl0_636
| ~ spl0_79
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1403,f1351,f642,f11654]) ).
fof(f1403,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subclass(subset_relation,X0) )
| ~ spl0_79
| ~ spl0_161 ),
inference(superposition,[],[f1352,f644]) ).
fof(f11558,plain,
( spl0_635
| ~ spl0_141
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1476,f1424,f1143,f11556]) ).
fof(f11556,plain,
( spl0_635
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f11554,plain,
( spl0_634
| ~ spl0_140
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1469,f1424,f1139,f11552]) ).
fof(f11552,plain,
( spl0_634
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),universal_class)),universal_class))))))),identity_relation)
| ~ member(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0),universal_class)
| y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f11550,plain,
( spl0_633
| ~ spl0_141
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1451,f1420,f1143,f11548]) ).
fof(f11548,plain,
( spl0_633
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),intersection(X0,complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(X0,complement(compose(element_relation,complement(identity_relation)))),universal_class)
| y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f11545,plain,
( spl0_632
| ~ spl0_458
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8910,f8731,f6488,f11542]) ).
fof(f11542,plain,
( spl0_632
<=> subclass(universal_class,complement(domain_of(y))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f6488,plain,
( spl0_458
<=> ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f8910,plain,
( subclass(universal_class,complement(domain_of(y)))
| ~ spl0_458
| ~ spl0_550 ),
inference(resolution,[],[f8732,f6489]) ).
fof(f6489,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl0_458 ),
inference(avatar_component_clause,[],[f6488]) ).
fof(f11540,plain,
( spl0_631
| ~ spl0_140
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1444,f1420,f1139,f11538]) ).
fof(f11538,plain,
( spl0_631
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(compose(element_relation,complement(identity_relation))),X0),intersection(complement(compose(element_relation,complement(identity_relation))),X0)),universal_class)),universal_class))))))),singleton_relation)
| ~ member(intersection(complement(compose(element_relation,complement(identity_relation))),X0),universal_class)
| y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f11523,plain,
( spl0_630
| ~ spl0_144
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1580,f1575,f1199,f11521]) ).
fof(f11521,plain,
( spl0_630
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1580,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)),X2))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_181 ),
inference(superposition,[],[f1576,f1200]) ).
fof(f11516,plain,
( ~ spl0_629
| ~ spl0_111
| spl0_505
| ~ spl0_612
| spl0_628 ),
inference(avatar_split_clause,[],[f11509,f11504,f11087,f7576,f852,f11513]) ).
fof(f11513,plain,
( spl0_629
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f11504,plain,
( spl0_628
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f11509,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))),subset_relation)
| ~ spl0_111
| spl0_505
| ~ spl0_612
| spl0_628 ),
inference(forward_demodulation,[],[f11508,f11089]) ).
fof(f11508,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(y),complement(y)),universal_class)),universal_class))))))),subset_relation)
| ~ spl0_111
| spl0_505
| spl0_628 ),
inference(forward_demodulation,[],[f11506,f7589]) ).
fof(f11506,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| spl0_628 ),
inference(avatar_component_clause,[],[f11504]) ).
fof(f11507,plain,
( spl0_429
| ~ spl0_627
| ~ spl0_628
| ~ spl0_136
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1633,f1625,f1066,f11504,f11500,f5772]) ).
fof(f5772,plain,
( spl0_429
<=> y = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f11500,plain,
( spl0_627
<=> member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1633,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),universal_class)),universal_class))))))),subset_relation)
| ~ member(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class)
| y = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_136
| ~ spl0_189 ),
inference(resolution,[],[f1626,f1067]) ).
fof(f11377,plain,
( spl0_626
| ~ spl0_56
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1839,f1816,f496,f11375]) ).
fof(f11375,plain,
( spl0_626
<=> ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1839,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
| ~ spl0_56
| ~ spl0_203 ),
inference(duplicate_literal_removal,[],[f1820]) ).
fof(f1820,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_56
| ~ spl0_203 ),
inference(resolution,[],[f1817,f497]) ).
fof(f11252,plain,
( spl0_624
| ~ spl0_625
| ~ spl0_130
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1728,f1646,f1005,f11249,f11246]) ).
fof(f11246,plain,
( spl0_624
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f11249,plain,
( spl0_625
<=> subclass(domain_relation,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f1728,plain,
( ! [X0] :
( ~ subclass(domain_relation,singleton_relation)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),element_relation) )
| ~ spl0_130
| ~ spl0_192 ),
inference(resolution,[],[f1647,f1006]) ).
fof(f11244,plain,
( spl0_622
| ~ spl0_623
| ~ spl0_131
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1726,f1646,f1009,f11241,f11238]) ).
fof(f11238,plain,
( spl0_622
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f11241,plain,
( spl0_623
<=> subclass(domain_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1726,plain,
( ! [X0] :
( ~ subclass(domain_relation,identity_relation)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),subset_relation) )
| ~ spl0_131
| ~ spl0_192 ),
inference(resolution,[],[f1647,f1010]) ).
fof(f11236,plain,
( spl0_621
| ~ spl0_51
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1269,f1229,f472,f11234]) ).
fof(f11234,plain,
( spl0_621
<=> ! [X0,X1] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f1269,plain,
( ! [X0,X1] :
( subclass(complement(complement(X0)),X1)
| member(not_subclass_element(complement(complement(X0)),X1),X0)
| ~ member(not_subclass_element(complement(complement(X0)),X1),universal_class) )
| ~ spl0_51
| ~ spl0_145 ),
inference(resolution,[],[f1230,f473]) ).
fof(f11232,plain,
( spl0_620
| ~ spl0_82
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1127,f1089,f665,f11230]) ).
fof(f11230,plain,
( spl0_620
<=> ! [X0] :
( ~ member(X0,subset_relation)
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1127,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 )
| ~ spl0_82
| ~ spl0_139 ),
inference(resolution,[],[f1090,f666]) ).
fof(f11218,plain,
( spl0_619
| ~ spl0_90
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1578,f1575,f706,f11216]) ).
fof(f11216,plain,
( spl0_619
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f1578,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class))),universal_class))))) )
| ~ spl0_90
| ~ spl0_181 ),
inference(resolution,[],[f1576,f707]) ).
fof(f11160,plain,
( spl0_618
| ~ spl0_55
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1311,f1287,f492,f11158]) ).
fof(f11158,plain,
( spl0_618
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = X1
| not_subclass_element(X0,X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1311,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| not_subclass_element(X0,X3) = X1
| not_subclass_element(X0,X3) = X2 )
| ~ spl0_55
| ~ spl0_154 ),
inference(resolution,[],[f1288,f493]) ).
fof(f11156,plain,
( spl0_617
| ~ spl0_145
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1281,f1264,f1229,f11154]) ).
fof(f11154,plain,
( spl0_617
<=> ! [X0] :
( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
| subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1281,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0),identity_relation)
| subclass(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),X0) )
| ~ spl0_145
| ~ spl0_153 ),
inference(resolution,[],[f1265,f1230]) ).
fof(f11152,plain,
( spl0_616
| ~ spl0_145
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1276,f1260,f1229,f11150]) ).
fof(f11150,plain,
( spl0_616
<=> ! [X0] :
( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
| subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1276,plain,
( ! [X0] :
( ~ member(not_subclass_element(complement(complement(compose(element_relation,complement(identity_relation)))),X0),singleton_relation)
| subclass(complement(complement(compose(element_relation,complement(identity_relation)))),X0) )
| ~ spl0_145
| ~ spl0_152 ),
inference(resolution,[],[f1261,f1230]) ).
fof(f11108,plain,
( spl0_615
| ~ spl0_113
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1914,f1889,f888,f11106]) ).
fof(f11106,plain,
( spl0_615
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),regular(X3))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),y)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
| y = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1914,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),regular(X3))
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),y)
| ~ member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
| y = X3 )
| ~ spl0_113
| ~ spl0_212 ),
inference(resolution,[],[f1890,f889]) ).
fof(f11104,plain,
( spl0_614
| ~ spl0_144
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1572,f1566,f1199,f11102]) ).
fof(f11102,plain,
( spl0_614
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),compose(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| y = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1572,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),compose(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| y = intersection(cross_product(unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_180 ),
inference(superposition,[],[f1567,f1200]) ).
fof(f11094,plain,
( spl0_613
| ~ spl0_144
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1502,f1491,f1199,f11092]) ).
fof(f11092,plain,
( spl0_613
<=> ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1502,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),compose(X2,regular(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class))))
| ~ member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class)))))
| ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_170 ),
inference(superposition,[],[f1492,f1200]) ).
fof(f11090,plain,
( spl0_612
| ~ spl0_129
| ~ spl0_591 ),
inference(avatar_split_clause,[],[f10868,f10596,f1001,f11087]) ).
fof(f1001,plain,
( spl0_129
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f10868,plain,
( universal_class = complement(y)
| ~ spl0_129
| ~ spl0_591 ),
inference(resolution,[],[f10598,f1002]) ).
fof(f1002,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f10961,plain,
( spl0_610
| ~ spl0_611
| ~ spl0_81
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1708,f1646,f661,f10958,f10955]) ).
fof(f10955,plain,
( spl0_610
<=> ! [X0] :
( ~ member(X0,universal_class)
| domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f10958,plain,
( spl0_611
<=> subclass(domain_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f1708,plain,
( ! [X0] :
( ~ subclass(domain_relation,successor_relation)
| ~ member(X0,universal_class)
| domain_of(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) )
| ~ spl0_81
| ~ spl0_192 ),
inference(resolution,[],[f1647,f662]) ).
fof(f10953,plain,
( spl0_609
| ~ spl0_50
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1689,f1642,f441,f10951]) ).
fof(f10951,plain,
( spl0_609
<=> ! [X0] :
( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1689,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,identity_relation),subset_relation)
| ~ member(not_subclass_element(X0,identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(X0,identity_relation) )
| ~ spl0_50
| ~ spl0_191 ),
inference(superposition,[],[f1643,f443]) ).
fof(f10949,plain,
( spl0_608
| ~ spl0_49
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1688,f1642,f436,f10947]) ).
fof(f10947,plain,
( spl0_608
<=> ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1688,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,singleton_relation),element_relation)
| ~ member(not_subclass_element(X0,singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| subclass(X0,singleton_relation) )
| ~ spl0_49
| ~ spl0_191 ),
inference(superposition,[],[f1643,f438]) ).
fof(f10945,plain,
( spl0_607
| ~ spl0_46
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1550,f1537,f424,f10943]) ).
fof(f1550,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X2) )
| ~ spl0_46
| ~ spl0_179 ),
inference(resolution,[],[f1538,f425]) ).
fof(f10939,plain,
( ~ spl0_605
| spl0_606
| ~ spl0_137
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1478,f1424,f1078,f10937,f10933]) ).
fof(f10933,plain,
( spl0_605
<=> subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f10937,plain,
( spl0_606
<=> ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),subset_relation)
| member(unordered_pair(X0,X1),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f1478,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),subset_relation)
| member(unordered_pair(X0,X1),identity_relation)
| ~ subclass(universal_class,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_137
| ~ spl0_167 ),
inference(resolution,[],[f1425,f1079]) ).
fof(f10930,plain,
( spl0_604
| ~ spl0_132
| ~ spl0_591 ),
inference(avatar_split_clause,[],[f10867,f10596,f1033,f10927]) ).
fof(f10927,plain,
( spl0_604
<=> member(y,complement(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f1033,plain,
( spl0_132
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(y,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f10867,plain,
( member(y,complement(y))
| ~ spl0_132
| ~ spl0_591 ),
inference(resolution,[],[f10598,f1034]) ).
fof(f1034,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(y,X0) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1033]) ).
fof(f10925,plain,
( ~ spl0_602
| spl0_603
| ~ spl0_137
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1453,f1420,f1078,f10923,f10919]) ).
fof(f10919,plain,
( spl0_602
<=> subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f10923,plain,
( spl0_603
<=> ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),element_relation)
| member(unordered_pair(X0,X1),singleton_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1453,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),element_relation)
| member(unordered_pair(X0,X1),singleton_relation)
| ~ subclass(universal_class,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_137
| ~ spl0_166 ),
inference(resolution,[],[f1421,f1079]) ).
fof(f10894,plain,
( spl0_366
| ~ spl0_599
| spl0_600
| ~ spl0_601
| ~ spl0_28
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1468,f1424,f330,f10891,f10887,f10883,f4488]) ).
fof(f10883,plain,
( spl0_599
<=> member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f10887,plain,
( spl0_600
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f10891,plain,
( spl0_601
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1468,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(flip(cross_product(subset_relation,universal_class))),domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)),universal_class))))))),identity_relation)
| ~ member(domain_of(flip(cross_product(subset_relation,universal_class))),universal_class)
| y = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_28
| ~ spl0_167 ),
inference(resolution,[],[f1425,f331]) ).
fof(f10865,plain,
( spl0_363
| ~ spl0_596
| spl0_597
| ~ spl0_598
| ~ spl0_28
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1443,f1420,f330,f10862,f10858,f10854,f4470]) ).
fof(f10854,plain,
( spl0_596
<=> member(complement(compose(element_relation,complement(identity_relation))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f10858,plain,
( spl0_597
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f10862,plain,
( spl0_598
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1443,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(compose(element_relation,complement(identity_relation))),complement(compose(element_relation,complement(identity_relation)))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(complement(compose(element_relation,complement(identity_relation))),universal_class)
| complement(compose(element_relation,complement(identity_relation))) = y
| ~ spl0_28
| ~ spl0_166 ),
inference(resolution,[],[f1421,f331]) ).
fof(f10852,plain,
( spl0_595
| ~ spl0_55
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1164,f1143,f492,f10850]) ).
fof(f10850,plain,
( spl0_595
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
| y = intersection(X0,unordered_pair(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1164,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,unordered_pair(X1,X2)),universal_class)
| y = intersection(X0,unordered_pair(X1,X2))
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,unordered_pair(X1,X2)),intersection(X0,unordered_pair(X1,X2))),universal_class)),universal_class))))))) = X2 )
| ~ spl0_55
| ~ spl0_141 ),
inference(resolution,[],[f1144,f493]) ).
fof(f10848,plain,
( spl0_594
| ~ spl0_55
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1147,f1139,f492,f10846]) ).
fof(f10846,plain,
( spl0_594
<=> ! [X2,X0,X1] :
( ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
| y = intersection(unordered_pair(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1147,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(unordered_pair(X0,X1),X2),universal_class)
| y = intersection(unordered_pair(X0,X1),X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(unordered_pair(X0,X1),X2),intersection(unordered_pair(X0,X1),X2)),universal_class)),universal_class))))))) = X1 )
| ~ spl0_55
| ~ spl0_140 ),
inference(resolution,[],[f1140,f493]) ).
fof(f10719,plain,
( spl0_593
| ~ spl0_21
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2709,f2038,f301,f10717]) ).
fof(f10717,plain,
( spl0_593
<=> ! [X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))))))
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2709,plain,
( ! [X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y)))))))
| ~ member(X0,X1) )
| ~ spl0_21
| ~ spl0_217 ),
inference(resolution,[],[f302,f2039]) ).
fof(f10715,plain,
( spl0_592
| ~ spl0_46
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1579,f1575,f424,f10713]) ).
fof(f10713,plain,
( spl0_592
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1579,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)
| ~ subclass(compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class)),X2),X3)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),X3) )
| ~ spl0_46
| ~ spl0_181 ),
inference(resolution,[],[f1576,f425]) ).
fof(f10599,plain,
( spl0_591
| ~ spl0_458
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f10259,f9669,f6488,f10596]) ).
fof(f10259,plain,
( subclass(universal_class,complement(y))
| ~ spl0_458
| ~ spl0_585 ),
inference(resolution,[],[f9670,f6489]) ).
fof(f10531,plain,
( spl0_590
| ~ spl0_531
| ~ spl0_572
| ~ spl0_589 ),
inference(avatar_split_clause,[],[f10527,f10523,f9489,f8328,f10529]) ).
fof(f10529,plain,
( spl0_590
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f10523,plain,
( spl0_589
<=> ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f10527,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_531
| ~ spl0_572
| ~ spl0_589 ),
inference(forward_demodulation,[],[f10526,f8329]) ).
fof(f10526,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(y,X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_572
| ~ spl0_589 ),
inference(forward_demodulation,[],[f10524,f9491]) ).
fof(f9491,plain,
( y = cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f9489]) ).
fof(f10524,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_589 ),
inference(avatar_component_clause,[],[f10523]) ).
fof(f10525,plain,
( spl0_589
| ~ spl0_90
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1500,f1491,f706,f10523]) ).
fof(f1500,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X2,X2),universal_class),regular(cross_product(unordered_pair(X2,X2),universal_class))),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_90
| ~ spl0_170 ),
inference(resolution,[],[f1492,f707]) ).
fof(f10521,plain,
( spl0_588
| ~ spl0_113
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1171,f1143,f888,f10519]) ).
fof(f10519,plain,
( spl0_588
<=> ! [X0,X1] :
( ~ member(intersection(X0,regular(X1)),universal_class)
| y = intersection(X0,regular(X1))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1171,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,regular(X1)),universal_class)
| y = intersection(X0,regular(X1))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,regular(X1)),intersection(X0,regular(X1))),universal_class)),universal_class))))))),X1)
| y = X1 )
| ~ spl0_113
| ~ spl0_141 ),
inference(resolution,[],[f1144,f889]) ).
fof(f10517,plain,
( spl0_587
| ~ spl0_113
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1154,f1139,f888,f10515]) ).
fof(f10515,plain,
( spl0_587
<=> ! [X0,X1] :
( ~ member(intersection(regular(X0),X1),universal_class)
| y = intersection(regular(X0),X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1154,plain,
( ! [X0,X1] :
( ~ member(intersection(regular(X0),X1),universal_class)
| y = intersection(regular(X0),X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(regular(X0),X1),intersection(regular(X0),X1)),universal_class)),universal_class))))))),X0)
| y = X0 )
| ~ spl0_113
| ~ spl0_140 ),
inference(resolution,[],[f1140,f889]) ).
fof(f9675,plain,
( spl0_586
| ~ spl0_160
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1692,f1642,f1347,f9673]) ).
fof(f9673,plain,
( spl0_586
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1692,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_160
| ~ spl0_191 ),
inference(duplicate_literal_removal,[],[f1673]) ).
fof(f1673,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X0)),X2)
| subclass(intersection(X0,X1),intersection(X2,X0))
| subclass(intersection(X0,X1),intersection(X2,X0)) )
| ~ spl0_160
| ~ spl0_191 ),
inference(resolution,[],[f1643,f1348]) ).
fof(f9671,plain,
( spl0_585
| ~ spl0_550
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f9592,f9421,f8731,f9669]) ).
fof(f9592,plain,
( ! [X0] : ~ member(X0,y)
| ~ spl0_550
| ~ spl0_567 ),
inference(superposition,[],[f8732,f9423]) ).
fof(f9667,plain,
( spl0_584
| ~ spl0_161
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1691,f1642,f1351,f9665]) ).
fof(f9665,plain,
( spl0_584
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f1691,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_161
| ~ spl0_191 ),
inference(duplicate_literal_removal,[],[f1674]) ).
fof(f1674,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(intersection(X0,X1),intersection(X2,X1)),X2)
| subclass(intersection(X0,X1),intersection(X2,X1))
| subclass(intersection(X0,X1),intersection(X2,X1)) )
| ~ spl0_161
| ~ spl0_191 ),
inference(resolution,[],[f1643,f1352]) ).
fof(f9663,plain,
( spl0_583
| ~ spl0_39
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1554,f1537,f381,f9661]) ).
fof(f9661,plain,
( spl0_583
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1554,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X0) )
| ~ spl0_39
| ~ spl0_179 ),
inference(resolution,[],[f1538,f382]) ).
fof(f9659,plain,
( spl0_582
| ~ spl0_40
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1553,f1537,f385,f9657]) ).
fof(f9657,plain,
( spl0_582
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1553,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X2))),X1) )
| ~ spl0_40
| ~ spl0_179 ),
inference(resolution,[],[f1538,f386]) ).
fof(f9655,plain,
( spl0_581
| ~ spl0_50
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1548,f1533,f441,f9653]) ).
fof(f9653,plain,
( spl0_581
<=> ! [X0,X1] :
( ~ subclass(identity_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1548,plain,
( ! [X0,X1] :
( ~ subclass(identity_relation,X0)
| ~ member(X1,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X1,subset_relation)
| member(X1,X0) )
| ~ spl0_50
| ~ spl0_178 ),
inference(superposition,[],[f1534,f443]) ).
fof(f9651,plain,
( spl0_580
| ~ spl0_49
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1547,f1533,f436,f9649]) ).
fof(f9649,plain,
( spl0_580
<=> ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,element_relation)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1547,plain,
( ! [X0,X1] :
( ~ subclass(singleton_relation,X0)
| ~ member(X1,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X1,element_relation)
| member(X1,X0) )
| ~ spl0_49
| ~ spl0_178 ),
inference(superposition,[],[f1534,f438]) ).
fof(f9647,plain,
( spl0_579
| ~ spl0_39
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1393,f1351,f381,f9645]) ).
fof(f9645,plain,
( spl0_579
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1393,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X1) )
| ~ spl0_39
| ~ spl0_161 ),
inference(resolution,[],[f1352,f382]) ).
fof(f9643,plain,
( spl0_578
| ~ spl0_40
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1392,f1351,f385,f9641]) ).
fof(f9641,plain,
( spl0_578
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1392,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,intersection(X1,X2)),X3)
| member(not_subclass_element(intersection(X0,intersection(X1,X2)),X3),X2) )
| ~ spl0_40
| ~ spl0_161 ),
inference(resolution,[],[f1352,f386]) ).
fof(f9639,plain,
( spl0_577
| ~ spl0_39
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1372,f1347,f381,f9637]) ).
fof(f9637,plain,
( spl0_577
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1372,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X0) )
| ~ spl0_39
| ~ spl0_160 ),
inference(resolution,[],[f1348,f382]) ).
fof(f9635,plain,
( spl0_576
| ~ spl0_40
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1371,f1347,f385,f9633]) ).
fof(f9633,plain,
( spl0_576
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1371,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(intersection(X0,X1),X2),X3)
| member(not_subclass_element(intersection(intersection(X0,X1),X2),X3),X1) )
| ~ spl0_40
| ~ spl0_160 ),
inference(resolution,[],[f1348,f386]) ).
fof(f9631,plain,
( spl0_575
| ~ spl0_35
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1280,f1264,f365,f9629]) ).
fof(f9629,plain,
( spl0_575
<=> ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1280,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_35
| ~ spl0_153 ),
inference(resolution,[],[f1265,f366]) ).
fof(f9591,plain,
( spl0_574
| ~ spl0_35
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1275,f1260,f365,f9589]) ).
fof(f9589,plain,
( spl0_574
<=> ! [X0] :
( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1275,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| subclass(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_35
| ~ spl0_152 ),
inference(resolution,[],[f1261,f366]) ).
fof(f9495,plain,
( spl0_572
| spl0_573
| ~ spl0_7
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1582,f1575,f238,f9493,f9489]) ).
fof(f9493,plain,
( spl0_573
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,domain_of(domain_of(flip(cross_product(y,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1582,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)),regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(X1,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_181 ),
inference(superposition,[],[f1576,f239]) ).
fof(f9487,plain,
( spl0_571
| ~ spl0_57
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1581,f1575,f500,f9485]) ).
fof(f9485,plain,
( spl0_571
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),X1))
| ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1581,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),X1))
| ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class) )
| ~ spl0_57
| ~ spl0_181 ),
inference(superposition,[],[f1576,f501]) ).
fof(f9480,plain,
( spl0_570
| ~ spl0_116
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1788,f1750,f912,f9478]) ).
fof(f9478,plain,
( spl0_570
<=> ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
| ~ member(X0,universal_class)
| y = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1788,plain,
( ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class))))
| ~ member(X0,universal_class)
| y = cross_product(unordered_pair(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class)))))),universal_class) )
| ~ spl0_116
| ~ spl0_197 ),
inference(resolution,[],[f1751,f913]) ).
fof(f9476,plain,
( spl0_568
| ~ spl0_569
| ~ spl0_7
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1344,f1337,f238,f9473,f9470]) ).
fof(f9470,plain,
( spl0_568
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f1337,plain,
( spl0_159
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1344,plain,
( ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(y,universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_7
| ~ spl0_159 ),
inference(superposition,[],[f1338,f239]) ).
fof(f1338,plain,
( ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,X2)) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f9424,plain,
( spl0_567
| ~ spl0_2
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8914,f8731,f213,f9421]) ).
fof(f9419,plain,
( spl0_566
| ~ spl0_56
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1071,f1066,f496,f9417]) ).
fof(f9417,plain,
( spl0_566
<=> ! [X0,X1] :
( ~ member(complement(intersection(X0,X1)),universal_class)
| complement(intersection(X0,X1)) = y
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1071,plain,
( ! [X0,X1] :
( ~ member(complement(intersection(X0,X1)),universal_class)
| complement(intersection(X0,X1)) = y
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(intersection(X0,X1)),complement(intersection(X0,X1))),universal_class)),universal_class))))))),X0) )
| ~ spl0_56
| ~ spl0_136 ),
inference(resolution,[],[f1067,f497]) ).
fof(f9414,plain,
( spl0_565
| ~ spl0_134
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1831,f1816,f1043,f9412]) ).
fof(f9412,plain,
( spl0_565
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1831,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,universal_class)
| y = X0 )
| ~ spl0_134
| ~ spl0_203 ),
inference(resolution,[],[f1817,f1044]) ).
fof(f9083,plain,
( spl0_564
| ~ spl0_154
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1690,f1642,f1287,f9081]) ).
fof(f9081,plain,
( spl0_564
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f1690,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) )
| ~ spl0_154
| ~ spl0_191 ),
inference(duplicate_literal_removal,[],[f1675]) ).
fof(f1675,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2)
| subclass(X0,intersection(X1,X2)) )
| ~ spl0_154
| ~ spl0_191 ),
inference(resolution,[],[f1643,f1288]) ).
fof(f9078,plain,
( spl0_563
| ~ spl0_34
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f8908,f8731,f361,f9076]) ).
fof(f9076,plain,
( spl0_563
<=> ! [X0] : subclass(domain_of(y),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f8908,plain,
( ! [X0] : subclass(domain_of(y),X0)
| ~ spl0_34
| ~ spl0_550 ),
inference(resolution,[],[f8732,f362]) ).
fof(f9074,plain,
( spl0_562
| ~ spl0_29
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1555,f1537,f334,f9072]) ).
fof(f9072,plain,
( spl0_562
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1555,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0) )
| ~ spl0_29
| ~ spl0_179 ),
inference(resolution,[],[f1538,f335]) ).
fof(f9070,plain,
( spl0_561
| ~ spl0_31
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1542,f1533,f342,f9068]) ).
fof(f9068,plain,
( spl0_561
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1542,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(intersection(X1,X2)) )
| ~ spl0_31
| ~ spl0_178 ),
inference(resolution,[],[f1534,f343]) ).
fof(f9066,plain,
( spl0_560
| ~ spl0_51
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1440,f1420,f472,f9064]) ).
fof(f9064,plain,
( spl0_560
<=> ! [X0] :
( ~ member(X0,element_relation)
| member(X0,singleton_relation)
| member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1440,plain,
( ! [X0] :
( ~ member(X0,element_relation)
| member(X0,singleton_relation)
| member(X0,compose(element_relation,complement(identity_relation)))
| ~ member(X0,universal_class) )
| ~ spl0_51
| ~ spl0_166 ),
inference(resolution,[],[f1421,f473]) ).
fof(f9062,plain,
( spl0_559
| ~ spl0_46
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1389,f1351,f424,f9060]) ).
fof(f9060,plain,
( spl0_559
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1389,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) )
| ~ spl0_46
| ~ spl0_161 ),
inference(resolution,[],[f1352,f425]) ).
fof(f9058,plain,
( spl0_558
| ~ spl0_46
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1368,f1347,f424,f9056]) ).
fof(f9056,plain,
( spl0_558
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X0,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f1368,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| ~ subclass(X0,X3)
| member(not_subclass_element(intersection(X0,X1),X2),X3) )
| ~ spl0_46
| ~ spl0_160 ),
inference(resolution,[],[f1348,f425]) ).
fof(f9054,plain,
( spl0_557
| ~ spl0_55
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1112,f1078,f492,f9052]) ).
fof(f9052,plain,
( spl0_557
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| unordered_pair(X2,X3) = X0
| unordered_pair(X2,X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f1112,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,unordered_pair(X0,X1))
| unordered_pair(X2,X3) = X0
| unordered_pair(X2,X3) = X1 )
| ~ spl0_55
| ~ spl0_137 ),
inference(resolution,[],[f1079,f493]) ).
fof(f9047,plain,
( spl0_556
| ~ spl0_116
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1724,f1646,f912,f9045]) ).
fof(f9045,plain,
( spl0_556
<=> ! [X0] :
( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
| ~ member(X0,universal_class)
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f1724,plain,
( ! [X0] :
( ~ subclass(domain_relation,domain_of(regular(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class))))
| ~ member(X0,universal_class)
| y = cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0))))),universal_class) )
| ~ spl0_116
| ~ spl0_192 ),
inference(resolution,[],[f1647,f913]) ).
fof(f8991,plain,
( spl0_555
| ~ spl0_46
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2462,f1497,f424,f8989]) ).
fof(f8989,plain,
( spl0_555
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2462,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X1),universal_class)))))
| singleton_relation = cross_product(unordered_pair(X2,X2),universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
| ~ spl0_46
| ~ spl0_171 ),
inference(resolution,[],[f1498,f425]) ).
fof(f8905,plain,
( spl0_554
| ~ spl0_46
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1501,f1491,f424,f8903]) ).
fof(f8903,plain,
( spl0_554
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f1501,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X2,X2),universal_class)
| ~ subclass(compose(X1,regular(cross_product(unordered_pair(X2,X2),universal_class))),X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X3) )
| ~ spl0_46
| ~ spl0_170 ),
inference(resolution,[],[f1492,f425]) ).
fof(f8870,plain,
( spl0_553
| ~ spl0_12
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1972,f1943,f261,f8868]) ).
fof(f8868,plain,
( spl0_553
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f1972,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))) )
| ~ spl0_12
| ~ spl0_215 ),
inference(resolution,[],[f1944,f262]) ).
fof(f8866,plain,
( spl0_552
| ~ spl0_12
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1946,f1939,f261,f8864]) ).
fof(f8864,plain,
( spl0_552
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f1946,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_12
| ~ spl0_214 ),
inference(resolution,[],[f1940,f262]) ).
fof(f8862,plain,
( spl0_551
| ~ spl0_116
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1770,f1746,f912,f8860]) ).
fof(f1770,plain,
( ! [X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class))))
| ~ member(X1,universal_class)
| y = cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(X1,universal_class),X0),universal_class))))),universal_class) )
| ~ spl0_116
| ~ spl0_196 ),
inference(resolution,[],[f1747,f913]) ).
fof(f8733,plain,
( spl0_550
| ~ spl0_115
| ~ spl0_531 ),
inference(avatar_split_clause,[],[f8578,f8328,f897,f8731]) ).
fof(f897,plain,
( spl0_115
<=> ! [X0,X1] :
( y != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f8578,plain,
( ! [X0] : ~ member(X0,domain_of(y))
| ~ spl0_115
| ~ spl0_531 ),
inference(trivial_inequality_removal,[],[f8550]) ).
fof(f8550,plain,
( ! [X0] :
( y != y
| ~ member(X0,domain_of(y)) )
| ~ spl0_115
| ~ spl0_531 ),
inference(superposition,[],[f898,f8329]) ).
fof(f898,plain,
( ! [X0,X1] :
( y != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f8596,plain,
( spl0_549
| ~ spl0_40
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1628,f1625,f385,f8594]) ).
fof(f8594,plain,
( spl0_549
<=> ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f1628,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))) )
| ~ spl0_40
| ~ spl0_189 ),
inference(resolution,[],[f1626,f386]) ).
fof(f8592,plain,
( spl0_548
| ~ spl0_160
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1615,f1593,f1347,f8590]) ).
fof(f1593,plain,
( spl0_184
<=> ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1615,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_160
| ~ spl0_184 ),
inference(duplicate_literal_removal,[],[f1610]) ).
fof(f1610,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1))
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl0_160
| ~ spl0_184 ),
inference(resolution,[],[f1594,f1348]) ).
fof(f1594,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1)) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1593]) ).
fof(f8588,plain,
( spl0_547
| ~ spl0_161
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1614,f1593,f1351,f8586]) ).
fof(f1614,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_161
| ~ spl0_184 ),
inference(duplicate_literal_removal,[],[f1611]) ).
fof(f1611,plain,
( ! [X0,X1] :
( member(not_subclass_element(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1))
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl0_161
| ~ spl0_184 ),
inference(resolution,[],[f1594,f1352]) ).
fof(f8503,plain,
( spl0_546
| ~ spl0_31
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1438,f1416,f342,f8501]) ).
fof(f8501,plain,
( spl0_546
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f1416,plain,
( spl0_165
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(complement(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1438,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ function(complement(X1)) )
| ~ spl0_31
| ~ spl0_165 ),
inference(resolution,[],[f1417,f343]) ).
fof(f1417,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X1),X2)
| ~ member(X0,universal_class)
| member(X0,X1)
| member(X0,X2) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f8499,plain,
( spl0_545
| ~ spl0_29
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1394,f1351,f334,f8497]) ).
fof(f8497,plain,
( spl0_545
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f1394,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(not_subclass_element(intersection(X0,complement(X1)),X2),X1) )
| ~ spl0_29
| ~ spl0_161 ),
inference(resolution,[],[f1352,f335]) ).
fof(f8495,plain,
( spl0_544
| ~ spl0_29
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1373,f1347,f334,f8493]) ).
fof(f8493,plain,
( spl0_544
<=> ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f1373,plain,
( ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(not_subclass_element(intersection(complement(X0),X1),X2),X0) )
| ~ spl0_29
| ~ spl0_160 ),
inference(resolution,[],[f1348,f335]) ).
fof(f8491,plain,
( spl0_543
| ~ spl0_46
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1310,f1287,f424,f8489]) ).
fof(f8489,plain,
( spl0_543
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(X0,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f1310,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| ~ subclass(X1,X3)
| member(not_subclass_element(X0,X2),X3) )
| ~ spl0_46
| ~ spl0_154 ),
inference(resolution,[],[f1288,f425]) ).
fof(f8487,plain,
( spl0_542
| ~ spl0_139
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1267,f1229,f1089,f8485]) ).
fof(f8485,plain,
( spl0_542
<=> ! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f1267,plain,
( ! [X0] :
( subclass(complement(cross_product(universal_class,universal_class)),X0)
| ~ member(not_subclass_element(complement(cross_product(universal_class,universal_class)),X0),subset_relation) )
| ~ spl0_139
| ~ spl0_145 ),
inference(resolution,[],[f1230,f1090]) ).
fof(f8483,plain,
( spl0_541
| ~ spl0_73
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1132,f1089,f609,f8481]) ).
fof(f8481,plain,
( spl0_541
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f1132,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X1,universal_class) )
| ~ spl0_73
| ~ spl0_139 ),
inference(resolution,[],[f1090,f610]) ).
fof(f8479,plain,
( spl0_540
| ~ spl0_74
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1131,f1089,f613,f8477]) ).
fof(f8477,plain,
( spl0_540
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f1131,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation)
| member(X0,universal_class) )
| ~ spl0_74
| ~ spl0_139 ),
inference(resolution,[],[f1090,f614]) ).
fof(f8424,plain,
( spl0_539
| ~ spl0_344
| ~ spl0_507 ),
inference(avatar_split_clause,[],[f8107,f7603,f4190,f8422]) ).
fof(f7603,plain,
( spl0_507
<=> ! [X0] :
( y = X0
| ~ subclass(X0,y) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f8107,plain,
( ! [X0] : y = intersection(X0,y)
| ~ spl0_344
| ~ spl0_507 ),
inference(resolution,[],[f7604,f4191]) ).
fof(f7604,plain,
( ! [X0] :
( ~ subclass(X0,y)
| y = X0 )
| ~ spl0_507 ),
inference(avatar_component_clause,[],[f7603]) ).
fof(f8398,plain,
( spl0_538
| ~ spl0_109
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1987,f1943,f831,f8396]) ).
fof(f8396,plain,
( spl0_538
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f1987,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class)),universal_class)))))
| y = X1 )
| ~ spl0_109
| ~ spl0_215 ),
inference(resolution,[],[f1944,f832]) ).
fof(f8394,plain,
( spl0_537
| ~ spl0_109
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f1961,f1939,f831,f8392]) ).
fof(f8392,plain,
( spl0_537
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f1961,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(X1),regular(X1)))),cross_product(universal_class,universal_class))
| ~ subclass(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| y = X1 )
| ~ spl0_109
| ~ spl0_214 ),
inference(resolution,[],[f1940,f832]) ).
fof(f8390,plain,
( spl0_536
| ~ spl0_51
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1072,f1066,f472,f8388]) ).
fof(f8388,plain,
( spl0_536
<=> ! [X0] :
( ~ member(complement(complement(X0)),universal_class)
| y = complement(complement(X0))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f1072,plain,
( ! [X0] :
( ~ member(complement(complement(X0)),universal_class)
| y = complement(complement(X0))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),X0)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(X0)),complement(complement(X0))),universal_class)),universal_class))))))),universal_class) )
| ~ spl0_51
| ~ spl0_136 ),
inference(resolution,[],[f1067,f473]) ).
fof(f8386,plain,
( spl0_535
| ~ spl0_94
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f848,f831,f725,f8384]) ).
fof(f8384,plain,
( spl0_535
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| y = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f848,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))))
| y = X0
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(regular(X0),regular(X0)))),cross_product(universal_class,universal_class)) )
| ~ spl0_94
| ~ spl0_109 ),
inference(resolution,[],[f832,f726]) ).
fof(f8352,plain,
( spl0_534
| ~ spl0_7
| ~ spl0_215 ),
inference(avatar_split_clause,[],[f1994,f1943,f238,f8350]) ).
fof(f8350,plain,
( spl0_534
<=> ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f1994,plain,
( ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_215 ),
inference(superposition,[],[f1944,f239]) ).
fof(f8343,plain,
( spl0_533
| ~ spl0_112
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1835,f1816,f856,f8341]) ).
fof(f8341,plain,
( spl0_533
<=> ! [X0] :
( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
| y = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f1835,plain,
( ! [X0] :
( member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| ~ member(regular(intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class))
| y = intersection(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_112
| ~ spl0_203 ),
inference(resolution,[],[f1817,f857]) ).
fof(f8334,plain,
( spl0_532
| ~ spl0_111
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1826,f1816,f852,f8332]) ).
fof(f8332,plain,
( spl0_532
<=> ! [X0] :
( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
| ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
| y = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f1826,plain,
( ! [X0] :
( member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),subset_relation)
| ~ member(regular(intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0)),cross_product(universal_class,universal_class))
| y = intersection(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))),X0) )
| ~ spl0_111
| ~ spl0_203 ),
inference(resolution,[],[f1817,f853]) ).
fof(f8330,plain,
( spl0_531
| ~ spl0_343
| ~ spl0_507 ),
inference(avatar_split_clause,[],[f8106,f7603,f4186,f8328]) ).
fof(f8106,plain,
( ! [X0] : y = intersection(y,X0)
| ~ spl0_343
| ~ spl0_507 ),
inference(resolution,[],[f7604,f4187]) ).
fof(f8326,plain,
( spl0_530
| ~ spl0_139
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1570,f1566,f1089,f8324]) ).
fof(f8324,plain,
( spl0_530
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f1570,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),subset_relation) )
| ~ spl0_139
| ~ spl0_180 ),
inference(resolution,[],[f1567,f1090]) ).
fof(f8314,plain,
( spl0_528
| ~ spl0_529
| ~ spl0_107
| ~ spl0_216 ),
inference(avatar_split_clause,[],[f2036,f1999,f814,f8311,f8308]) ).
fof(f8308,plain,
( spl0_528
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = X2
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f8311,plain,
( spl0_529
<=> subclass(composition_function,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f814,plain,
( spl0_107
<=> ! [X0,X1] :
( ~ member(X1,y)
| member(X1,X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f2036,plain,
( ! [X2,X0,X1] :
( ~ subclass(composition_function,y)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2)
| y = X2 )
| ~ spl0_107
| ~ spl0_216 ),
inference(resolution,[],[f2000,f815]) ).
fof(f815,plain,
( ! [X0,X1] :
( ~ member(X1,y)
| member(X1,X0)
| y = X0 )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f8306,plain,
( spl0_527
| ~ spl0_7
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1341,f1337,f238,f8304]) ).
fof(f8304,plain,
( spl0_527
<=> ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f1341,plain,
( ! [X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X1),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_159 ),
inference(superposition,[],[f1338,f239]) ).
fof(f8102,plain,
( spl0_526
| ~ spl0_144
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1669,f1638,f1199,f8100]) ).
fof(f8100,plain,
( spl0_526
<=> ! [X2,X0,X1] :
( subclass(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f1669,plain,
( ! [X2,X0,X1] :
( subclass(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = not_subclass_element(regular(cross_product(X0,X1)),X2)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_190 ),
inference(superposition,[],[f1639,f1200]) ).
fof(f8098,plain,
( spl0_525
| ~ spl0_92
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1213,f1199,f715,f8096]) ).
fof(f8096,plain,
( spl0_525
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f715,plain,
( spl0_92
<=> ! [X4,X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1213,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| second(regular(cross_product(X0,X1))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X2),universal_class)))))))
| cross_product(X0,X1) = y )
| ~ spl0_92
| ~ spl0_144 ),
inference(superposition,[],[f716,f1200]) ).
fof(f716,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4 )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f8094,plain,
( spl0_524
| ~ spl0_28
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f902,f888,f330,f8092]) ).
fof(f8092,plain,
( spl0_524
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
| y = X0
| ~ member(regular(X0),universal_class)
| regular(X0) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f902,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)),universal_class))))))),X0)
| y = X0
| ~ member(regular(X0),universal_class)
| regular(X0) = y )
| ~ spl0_28
| ~ spl0_113 ),
inference(resolution,[],[f889,f331]) ).
fof(f8090,plain,
( spl0_523
| ~ spl0_82
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f875,f856,f665,f8088]) ).
fof(f875,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,cross_product(X1,X2))
| regular(intersection(X0,cross_product(X1,X2))) = unordered_pair(unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),first(regular(intersection(X0,cross_product(X1,X2))))),unordered_pair(first(regular(intersection(X0,cross_product(X1,X2)))),unordered_pair(second(regular(intersection(X0,cross_product(X1,X2)))),second(regular(intersection(X0,cross_product(X1,X2))))))) )
| ~ spl0_82
| ~ spl0_112 ),
inference(resolution,[],[f857,f666]) ).
fof(f8086,plain,
( spl0_522
| ~ spl0_82
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f861,f852,f665,f8084]) ).
fof(f861,plain,
( ! [X2,X0,X1] :
( y = intersection(cross_product(X0,X1),X2)
| regular(intersection(cross_product(X0,X1),X2)) = unordered_pair(unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),first(regular(intersection(cross_product(X0,X1),X2)))),unordered_pair(first(regular(intersection(cross_product(X0,X1),X2))),unordered_pair(second(regular(intersection(cross_product(X0,X1),X2))),second(regular(intersection(cross_product(X0,X1),X2)))))) )
| ~ spl0_82
| ~ spl0_111 ),
inference(resolution,[],[f853,f666]) ).
fof(f7939,plain,
( spl0_521
| ~ spl0_76
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1710,f1646,f625,f7937]) ).
fof(f7937,plain,
( spl0_521
<=> ! [X0,X1] :
( ~ subclass(domain_relation,compose_class(X0))
| ~ member(X1,universal_class)
| compose(X0,X1) = domain_of(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f1710,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,compose_class(X0))
| ~ member(X1,universal_class)
| compose(X0,X1) = domain_of(X1) )
| ~ spl0_76
| ~ spl0_192 ),
inference(resolution,[],[f1647,f626]) ).
fof(f7935,plain,
( spl0_520
| ~ spl0_154
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1613,f1593,f1287,f7933]) ).
fof(f1613,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) )
| ~ spl0_154
| ~ spl0_184 ),
inference(duplicate_literal_removal,[],[f1612]) ).
fof(f1612,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,complement(X1)) )
| ~ spl0_154
| ~ spl0_184 ),
inference(resolution,[],[f1594,f1288]) ).
fof(f7931,plain,
( spl0_519
| ~ spl0_39
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1314,f1287,f381,f7929]) ).
fof(f7929,plain,
( spl0_519
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f1314,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X1) )
| ~ spl0_39
| ~ spl0_154 ),
inference(resolution,[],[f1288,f382]) ).
fof(f7927,plain,
( spl0_518
| ~ spl0_40
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1313,f1287,f385,f7925]) ).
fof(f7925,plain,
( spl0_518
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f1313,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(not_subclass_element(X0,X3),X2) )
| ~ spl0_40
| ~ spl0_154 ),
inference(resolution,[],[f1288,f386]) ).
fof(f7923,plain,
( spl0_517
| ~ spl0_46
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1279,f1264,f424,f7921]) ).
fof(f7921,plain,
( spl0_517
<=> ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f1279,plain,
( ! [X0,X1] :
( ~ member(X0,identity_relation)
| ~ subclass(domain_of(flip(cross_product(subset_relation,universal_class))),X1)
| member(X0,X1) )
| ~ spl0_46
| ~ spl0_153 ),
inference(resolution,[],[f1265,f425]) ).
fof(f7919,plain,
( spl0_516
| ~ spl0_46
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1274,f1260,f424,f7917]) ).
fof(f7917,plain,
( spl0_516
<=> ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f1274,plain,
( ! [X0,X1] :
( ~ member(X0,singleton_relation)
| ~ subclass(complement(compose(element_relation,complement(identity_relation))),X1)
| member(X0,X1) )
| ~ spl0_46
| ~ spl0_152 ),
inference(resolution,[],[f1261,f425]) ).
fof(f7915,plain,
( spl0_514
| ~ spl0_515
| ~ spl0_81
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1097,f1078,f661,f7912,f7909]) ).
fof(f7909,plain,
( spl0_514
<=> ! [X0,X1] : complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f7912,plain,
( spl0_515
<=> subclass(universal_class,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f1097,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,successor_relation)
| complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1 )
| ~ spl0_81
| ~ spl0_137 ),
inference(resolution,[],[f1079,f662]) ).
fof(f7795,plain,
( spl0_513
| ~ spl0_40
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f6421,f4236,f385,f7793]) ).
fof(f7793,plain,
( spl0_513
<=> ! [X0,X1] :
( ~ member(X1,y)
| member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f4236,plain,
( spl0_346
<=> ! [X0] : y = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f6421,plain,
( ! [X0,X1] :
( ~ member(X1,y)
| member(X1,X0) )
| ~ spl0_40
| ~ spl0_346 ),
inference(superposition,[],[f386,f4237]) ).
fof(f4237,plain,
( ! [X0] : y = intersection(complement(X0),X0)
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f4236]) ).
fof(f7627,plain,
( spl0_512
| ~ spl0_16
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1507,f1504,f278,f7625]) ).
fof(f7625,plain,
( spl0_512
<=> ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f1504,plain,
( spl0_172
<=> ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| ~ member(unordered_pair(X0,X1),universal_class)
| unordered_pair(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1507,plain,
( ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_16
| ~ spl0_172 ),
inference(resolution,[],[f1505,f279]) ).
fof(f1505,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(X0,X1),universal_class)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f7623,plain,
( spl0_511
| ~ spl0_134
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1475,f1424,f1043,f7621]) ).
fof(f7621,plain,
( spl0_511
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),identity_relation)
| ~ subclass(X0,domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ member(X0,universal_class)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f7619,plain,
( spl0_510
| ~ spl0_134
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1450,f1420,f1043,f7617]) ).
fof(f7617,plain,
( spl0_510
<=> ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),singleton_relation)
| ~ subclass(X0,complement(compose(element_relation,complement(identity_relation))))
| ~ member(X0,universal_class)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f7615,plain,
( spl0_509
| ~ spl0_118
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1225,f1199,f925,f7613]) ).
fof(f7613,plain,
( spl0_509
<=> ! [X0,X1] :
( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
| y = regular(cross_product(X0,X1))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f925,plain,
( spl0_118
<=> ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1225,plain,
( ! [X0,X1] :
( unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = regular(regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = regular(regular(cross_product(X0,X1)))
| y = regular(cross_product(X0,X1))
| cross_product(X0,X1) = y )
| ~ spl0_118
| ~ spl0_144 ),
inference(superposition,[],[f926,f1200]) ).
fof(f926,plain,
( ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f7611,plain,
( spl0_508
| ~ spl0_113
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1055,f1043,f888,f7609]) ).
fof(f7609,plain,
( spl0_508
<=> ! [X0,X1] :
( ~ subclass(X0,regular(X1))
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f1055,plain,
( ! [X0,X1] :
( ~ subclass(X0,regular(X1))
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| y = X1 )
| ~ spl0_113
| ~ spl0_134 ),
inference(resolution,[],[f1044,f889]) ).
fof(f7605,plain,
( spl0_507
| ~ spl0_48
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4987,f3142,f432,f7603]) ).
fof(f3142,plain,
( spl0_288
<=> ! [X0] :
( y = X0
| subclass(y,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f4987,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,y) )
| ~ spl0_48
| ~ spl0_288 ),
inference(duplicate_literal_removal,[],[f4975]) ).
fof(f4975,plain,
( ! [X0] :
( y = X0
| ~ subclass(X0,y)
| y = X0 )
| ~ spl0_48
| ~ spl0_288 ),
inference(resolution,[],[f3143,f433]) ).
fof(f3143,plain,
( ! [X0] :
( subclass(y,X0)
| y = X0 )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3142]) ).
fof(f7583,plain,
( spl0_504
| ~ spl0_505
| spl0_506
| ~ spl0_2
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1825,f1816,f213,f7580,f7576,f7572]) ).
fof(f7580,plain,
( spl0_506
<=> member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f1825,plain,
( member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),subset_relation)
| ~ member(regular(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),cross_product(universal_class,universal_class))
| y = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))
| ~ spl0_2
| ~ spl0_203 ),
inference(resolution,[],[f1817,f214]) ).
fof(f7569,plain,
( ~ spl0_502
| spl0_503
| ~ spl0_137
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1571,f1566,f1078,f7567,f7563]) ).
fof(f7563,plain,
( spl0_502
<=> subclass(universal_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f7567,plain,
( spl0_503
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f1571,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ subclass(universal_class,cross_product(universal_class,universal_class)) )
| ~ spl0_137
| ~ spl0_180 ),
inference(resolution,[],[f1567,f1079]) ).
fof(f7561,plain,
( spl0_501
| ~ spl0_144
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1332,f1295,f1199,f7559]) ).
fof(f7559,plain,
( spl0_501
<=> ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f1332,plain,
( ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_156 ),
inference(superposition,[],[f1296,f1200]) ).
fof(f7557,plain,
( spl0_500
| ~ spl0_55
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1047,f1043,f492,f7555]) ).
fof(f7555,plain,
( spl0_500
<=> ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f1047,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X1
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))) = X2 )
| ~ spl0_55
| ~ spl0_134 ),
inference(resolution,[],[f1044,f493]) ).
fof(f7550,plain,
( spl0_499
| ~ spl0_29
| ~ spl0_236 ),
inference(avatar_split_clause,[],[f2999,f2269,f334,f7548]) ).
fof(f7548,plain,
( spl0_499
<=> ! [X0] :
( ~ member(X0,y)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2999,plain,
( ! [X0] :
( ~ member(X0,y)
| ~ member(X0,universal_class) )
| ~ spl0_29
| ~ spl0_236 ),
inference(superposition,[],[f335,f2271]) ).
fof(f7285,plain,
( spl0_498
| ~ spl0_10
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1736,f1650,f251,f7283]) ).
fof(f7283,plain,
( spl0_498
<=> ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f1650,plain,
( spl0_193
<=> ! [X0,X1] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1736,plain,
( ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,flip(cross_product(domain_of(X0),universal_class))) )
| ~ spl0_10
| ~ spl0_193 ),
inference(resolution,[],[f1651,f252]) ).
fof(f1651,plain,
( ! [X0,X1] :
( ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1)))
| ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,X1) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1650]) ).
fof(f7281,plain,
( spl0_497
| ~ spl0_63
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f1735,f1650,f555,f7279]) ).
fof(f7279,plain,
( spl0_497
<=> ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f555,plain,
( spl0_63
<=> ! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1735,plain,
( ! [X0] :
( ~ function(domain_of(X0))
| compatible(domain_of(X0),X0,domain_of(X0))
| ~ operation(domain_of(X0)) )
| ~ spl0_63
| ~ spl0_193 ),
inference(resolution,[],[f1651,f556]) ).
fof(f556,plain,
( ! [X8] :
( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| ~ operation(X8) )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f7277,plain,
( spl0_496
| ~ spl0_73
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1703,f1646,f609,f7275]) ).
fof(f7275,plain,
( spl0_496
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f1703,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(domain_of(X2),X1) )
| ~ spl0_73
| ~ spl0_192 ),
inference(resolution,[],[f1647,f610]) ).
fof(f7273,plain,
( spl0_495
| ~ spl0_34
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1693,f1642,f361,f7271]) ).
fof(f1693,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_34
| ~ spl0_191 ),
inference(duplicate_literal_removal,[],[f1672]) ).
fof(f1672,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0)) )
| ~ spl0_34
| ~ spl0_191 ),
inference(resolution,[],[f1643,f362]) ).
fof(f7269,plain,
( spl0_494
| ~ spl0_130
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1398,f1351,f1005,f7267]) ).
fof(f7267,plain,
( spl0_494
<=> ! [X0,X1] :
( subclass(intersection(X0,singleton_relation),X1)
| member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f1398,plain,
( ! [X0,X1] :
( subclass(intersection(X0,singleton_relation),X1)
| member(not_subclass_element(intersection(X0,singleton_relation),X1),element_relation) )
| ~ spl0_130
| ~ spl0_161 ),
inference(resolution,[],[f1352,f1006]) ).
fof(f7265,plain,
( spl0_493
| ~ spl0_131
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1396,f1351,f1009,f7263]) ).
fof(f7263,plain,
( spl0_493
<=> ! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f1396,plain,
( ! [X0,X1] :
( subclass(intersection(X0,identity_relation),X1)
| member(not_subclass_element(intersection(X0,identity_relation),X1),subset_relation) )
| ~ spl0_131
| ~ spl0_161 ),
inference(resolution,[],[f1352,f1010]) ).
fof(f7261,plain,
( spl0_492
| ~ spl0_50
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1384,f1347,f441,f7259]) ).
fof(f7259,plain,
( spl0_492
<=> ! [X0] :
( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f1384,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),domain_of(flip(cross_product(subset_relation,universal_class))))
| subclass(identity_relation,X0) )
| ~ spl0_50
| ~ spl0_160 ),
inference(superposition,[],[f1348,f443]) ).
fof(f7257,plain,
( spl0_491
| ~ spl0_236
| ~ spl0_369 ),
inference(avatar_split_clause,[],[f7117,f4788,f2269,f7254]) ).
fof(f7254,plain,
( spl0_491
<=> y = intersection(universal_class,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f4788,plain,
( spl0_369
<=> ! [X0] : y = intersection(X0,complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f7117,plain,
( y = intersection(universal_class,y)
| ~ spl0_236
| ~ spl0_369 ),
inference(superposition,[],[f4789,f2271]) ).
fof(f4789,plain,
( ! [X0] : y = intersection(X0,complement(X0))
| ~ spl0_369 ),
inference(avatar_component_clause,[],[f4788]) ).
fof(f7252,plain,
( spl0_490
| ~ spl0_49
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1383,f1347,f436,f7250]) ).
fof(f7250,plain,
( spl0_490
<=> ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f1383,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),complement(compose(element_relation,complement(identity_relation))))
| subclass(singleton_relation,X0) )
| ~ spl0_49
| ~ spl0_160 ),
inference(superposition,[],[f1348,f438]) ).
fof(f7248,plain,
( spl0_489
| ~ spl0_130
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1377,f1347,f1005,f7246]) ).
fof(f7246,plain,
( spl0_489
<=> ! [X0,X1] :
( subclass(intersection(singleton_relation,X0),X1)
| member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f1377,plain,
( ! [X0,X1] :
( subclass(intersection(singleton_relation,X0),X1)
| member(not_subclass_element(intersection(singleton_relation,X0),X1),element_relation) )
| ~ spl0_130
| ~ spl0_160 ),
inference(resolution,[],[f1348,f1006]) ).
fof(f7244,plain,
( spl0_488
| ~ spl0_131
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1375,f1347,f1009,f7242]) ).
fof(f7242,plain,
( spl0_488
<=> ! [X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f1375,plain,
( ! [X0,X1] :
( subclass(intersection(identity_relation,X0),X1)
| member(not_subclass_element(intersection(identity_relation,X0),X1),subset_relation) )
| ~ spl0_131
| ~ spl0_160 ),
inference(resolution,[],[f1348,f1010]) ).
fof(f7240,plain,
( spl0_487
| ~ spl0_31
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1331,f1295,f342,f7238]) ).
fof(f7238,plain,
( spl0_487
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f1331,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) )
| ~ spl0_31
| ~ spl0_156 ),
inference(resolution,[],[f1296,f343]) ).
fof(f7236,plain,
( spl0_486
| ~ spl0_31
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1327,f1291,f342,f7234]) ).
fof(f7234,plain,
( spl0_486
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f1327,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) )
| ~ spl0_31
| ~ spl0_155 ),
inference(resolution,[],[f1292,f343]) ).
fof(f7232,plain,
( spl0_485
| ~ spl0_29
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1315,f1287,f334,f7230]) ).
fof(f1315,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(not_subclass_element(X0,X2),X1) )
| ~ spl0_29
| ~ spl0_154 ),
inference(resolution,[],[f1288,f335]) ).
fof(f7228,plain,
( spl0_484
| ~ spl0_35
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1129,f1089,f365,f7226]) ).
fof(f7226,plain,
( spl0_484
<=> ! [X0] :
( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f1129,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,cross_product(universal_class,universal_class)),subset_relation)
| subclass(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_35
| ~ spl0_139 ),
inference(resolution,[],[f1090,f366]) ).
fof(f7116,plain,
( spl0_483
| ~ spl0_57
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1343,f1337,f500,f7114]) ).
fof(f7114,plain,
( spl0_483
<=> ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f1343,plain,
( ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) )
| ~ spl0_57
| ~ spl0_159 ),
inference(superposition,[],[f1338,f501]) ).
fof(f7112,plain,
( spl0_482
| ~ spl0_57
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1340,f1337,f500,f7110]) ).
fof(f7110,plain,
( spl0_482
<=> ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f1340,plain,
( ! [X2,X0,X1] :
( ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X2),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X2,X1)) )
| ~ spl0_57
| ~ spl0_159 ),
inference(superposition,[],[f1338,f501]) ).
fof(f7108,plain,
( spl0_481
| ~ spl0_90
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1212,f1199,f706,f7106]) ).
fof(f7106,plain,
( spl0_481
<=> ! [X0,X3,X2,X1] :
( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
| member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f1212,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),compose(X2,X3))
| member(second(regular(cross_product(X0,X1))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))))
| cross_product(X0,X1) = y )
| ~ spl0_90
| ~ spl0_144 ),
inference(superposition,[],[f707,f1200]) ).
fof(f7089,plain,
( spl0_480
| ~ spl0_80
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1573,f1566,f647,f7087]) ).
fof(f7087,plain,
( spl0_480
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f1573,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_180 ),
inference(duplicate_literal_removal,[],[f1569]) ).
fof(f1569,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class))))
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_180 ),
inference(resolution,[],[f1567,f648]) ).
fof(f7074,plain,
( spl0_479
| ~ spl0_38
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1222,f1199,f377,f7072]) ).
fof(f7072,plain,
( spl0_479
<=> ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f1222,plain,
( ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_38
| ~ spl0_144 ),
inference(superposition,[],[f378,f1200]) ).
fof(f7028,plain,
( spl0_478
| ~ spl0_107
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f1916,f1889,f814,f7026]) ).
fof(f7026,plain,
( spl0_478
<=> ! [X0,X3,X2,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),y)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
| y = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f1916,plain,
( ! [X2,X3,X0,X1] :
( ~ compatible(X0,X1,X2)
| homomorphism(X0,X1,X2)
| ~ operation(X1)
| ~ subclass(domain_of(X1),y)
| ~ operation(X2)
| member(unordered_pair(unordered_pair(not_homomorphism1(X0,X1,X2),not_homomorphism1(X0,X1,X2)),unordered_pair(not_homomorphism1(X0,X1,X2),unordered_pair(not_homomorphism2(X0,X1,X2),not_homomorphism2(X0,X1,X2)))),X3)
| y = X3 )
| ~ spl0_107
| ~ spl0_212 ),
inference(resolution,[],[f1890,f815]) ).
fof(f6984,plain,
( spl0_321
| ~ spl0_476
| ~ spl0_477
| ~ spl0_136
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1283,f1264,f1066,f6981,f6977,f3623]) ).
fof(f6977,plain,
( spl0_476
<=> member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f6981,plain,
( spl0_477
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f1283,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),complement(domain_of(flip(cross_product(subset_relation,universal_class))))),universal_class)),universal_class))))))),identity_relation)
| ~ member(complement(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| y = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_136
| ~ spl0_153 ),
inference(resolution,[],[f1265,f1067]) ).
fof(f6973,plain,
( spl0_319
| ~ spl0_474
| ~ spl0_475
| ~ spl0_136
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1277,f1260,f1066,f6970,f6966,f3612]) ).
fof(f6966,plain,
( spl0_474
<=> member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f6970,plain,
( spl0_475
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f1277,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(complement(compose(element_relation,complement(identity_relation)))),complement(complement(compose(element_relation,complement(identity_relation))))),universal_class)),universal_class))))))),singleton_relation)
| ~ member(complement(complement(compose(element_relation,complement(identity_relation)))),universal_class)
| y = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_136
| ~ spl0_152 ),
inference(resolution,[],[f1261,f1067]) ).
fof(f6879,plain,
( spl0_473
| ~ spl0_74
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1702,f1646,f613,f6877]) ).
fof(f6877,plain,
( spl0_473
<=> ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f1702,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_relation,cross_product(X0,X1))
| ~ member(X2,universal_class)
| member(X2,X0) )
| ~ spl0_74
| ~ spl0_192 ),
inference(resolution,[],[f1647,f614]) ).
fof(f6875,plain,
( spl0_472
| ~ spl0_130
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1320,f1287,f1005,f6873]) ).
fof(f6873,plain,
( spl0_472
<=> ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f1320,plain,
( ! [X0,X1] :
( ~ subclass(X0,singleton_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),element_relation) )
| ~ spl0_130
| ~ spl0_154 ),
inference(resolution,[],[f1288,f1006]) ).
fof(f6871,plain,
( spl0_471
| ~ spl0_131
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1318,f1287,f1009,f6869]) ).
fof(f6869,plain,
( spl0_471
<=> ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f1318,plain,
( ! [X0,X1] :
( ~ subclass(X0,identity_relation)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),subset_relation) )
| ~ spl0_131
| ~ spl0_154 ),
inference(resolution,[],[f1288,f1010]) ).
fof(f6867,plain,
( spl0_470
| ~ spl0_46
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1128,f1089,f424,f6865]) ).
fof(f6865,plain,
( spl0_470
<=> ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f1128,plain,
( ! [X0,X1] :
( ~ member(X0,subset_relation)
| ~ subclass(cross_product(universal_class,universal_class),X1)
| member(X0,X1) )
| ~ spl0_46
| ~ spl0_139 ),
inference(resolution,[],[f1090,f425]) ).
fof(f6863,plain,
( spl0_469
| ~ spl0_46
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1111,f1078,f424,f6861]) ).
fof(f6861,plain,
( spl0_469
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f1111,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) )
| ~ spl0_46
| ~ spl0_137 ),
inference(resolution,[],[f1079,f425]) ).
fof(f6820,plain,
( spl0_468
| ~ spl0_55
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1223,f1199,f492,f6818]) ).
fof(f6818,plain,
( spl0_468
<=> ! [X2,X0,X1] :
( ~ member(X2,regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f1223,plain,
( ! [X2,X0,X1] :
( ~ member(X2,regular(cross_product(X0,X1)))
| unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))) = X2
| unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))) = X2
| cross_product(X0,X1) = y )
| ~ spl0_55
| ~ spl0_144 ),
inference(superposition,[],[f493,f1200]) ).
fof(f6816,plain,
( spl0_467
| ~ spl0_110
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1224,f1199,f835,f6814]) ).
fof(f6814,plain,
( spl0_467
<=> ! [X0,X1] :
( ~ inductive(regular(cross_product(X0,X1)))
| y = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
| y = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f835,plain,
( spl0_110
<=> ! [X0,X1] :
( y = X0
| y = X1
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1224,plain,
( ! [X0,X1] :
( ~ inductive(regular(cross_product(X0,X1)))
| y = unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1)))))
| y = unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y )
| ~ spl0_110
| ~ spl0_144 ),
inference(superposition,[],[f836,f1200]) ).
fof(f836,plain,
( ! [X0,X1] :
( ~ inductive(unordered_pair(X0,X1))
| y = X1
| y = X0 )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f6584,plain,
( spl0_466
| ~ spl0_12
| ~ spl0_57
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1694,f1642,f500,f261,f6582]) ).
fof(f6582,plain,
( spl0_466
<=> ! [X2,X0,X1] :
( y = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
| subclass(X0,intersection(X1,domain_of(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f1694,plain,
( ! [X2,X0,X1] :
( y = intersection(X2,cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
| subclass(X0,intersection(X1,domain_of(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class) )
| ~ spl0_12
| ~ spl0_57
| ~ spl0_191 ),
inference(forward_demodulation,[],[f1681,f501]) ).
fof(f1681,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),X1)
| subclass(X0,intersection(X1,domain_of(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,domain_of(X2))),universal_class)
| y = intersection(cross_product(unordered_pair(not_subclass_element(X0,intersection(X1,domain_of(X2))),not_subclass_element(X0,intersection(X1,domain_of(X2)))),universal_class),X2) )
| ~ spl0_12
| ~ spl0_191 ),
inference(resolution,[],[f1643,f262]) ).
fof(f6580,plain,
( spl0_465
| ~ spl0_39
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1167,f1143,f381,f6578]) ).
fof(f6578,plain,
( spl0_465
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| y = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f1167,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| y = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X1) )
| ~ spl0_39
| ~ spl0_141 ),
inference(resolution,[],[f1144,f382]) ).
fof(f6576,plain,
( spl0_464
| ~ spl0_40
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1166,f1143,f385,f6574]) ).
fof(f6574,plain,
( spl0_464
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| y = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f1166,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,intersection(X1,X2)),universal_class)
| y = intersection(X0,intersection(X1,X2))
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,intersection(X1,X2)),intersection(X0,intersection(X1,X2))),universal_class)),universal_class))))))),X2) )
| ~ spl0_40
| ~ spl0_141 ),
inference(resolution,[],[f1144,f386]) ).
fof(f6572,plain,
( spl0_463
| ~ spl0_39
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1150,f1139,f381,f6570]) ).
fof(f6570,plain,
( spl0_463
<=> ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| y = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f1150,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| y = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X0) )
| ~ spl0_39
| ~ spl0_140 ),
inference(resolution,[],[f1140,f382]) ).
fof(f6568,plain,
( spl0_462
| ~ spl0_40
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1149,f1139,f385,f6566]) ).
fof(f6566,plain,
( spl0_462
<=> ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| y = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f1149,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(intersection(X0,X1),X2),universal_class)
| y = intersection(intersection(X0,X1),X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(intersection(X0,X1),X2),intersection(intersection(X0,X1),X2)),universal_class)),universal_class))))))),X1) )
| ~ spl0_40
| ~ spl0_140 ),
inference(resolution,[],[f1140,f386]) ).
fof(f6535,plain,
( spl0_461
| ~ spl0_236
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f6415,f4236,f2269,f6532]) ).
fof(f6532,plain,
( spl0_461
<=> y = intersection(y,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f6415,plain,
( y = intersection(y,universal_class)
| ~ spl0_236
| ~ spl0_346 ),
inference(superposition,[],[f4237,f2271]) ).
fof(f6498,plain,
( spl0_459
| ~ spl0_460
| ~ spl0_65
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1706,f1646,f569,f6495,f6492]) ).
fof(f6492,plain,
( spl0_459
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(X0,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f6495,plain,
( spl0_460
<=> subclass(domain_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f1706,plain,
( ! [X0] :
( ~ subclass(domain_relation,element_relation)
| ~ member(X0,universal_class)
| member(X0,domain_of(X0)) )
| ~ spl0_65
| ~ spl0_192 ),
inference(resolution,[],[f1647,f570]) ).
fof(f6490,plain,
( spl0_458
| ~ spl0_34
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1616,f1593,f361,f6488]) ).
fof(f1616,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl0_34
| ~ spl0_184 ),
inference(duplicate_literal_removal,[],[f1609]) ).
fof(f1609,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0))
| subclass(universal_class,complement(X0)) )
| ~ spl0_34
| ~ spl0_184 ),
inference(resolution,[],[f1594,f362]) ).
fof(f6486,plain,
( spl0_457
| ~ spl0_79
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1382,f1347,f642,f6484]) ).
fof(f6484,plain,
( spl0_457
<=> ! [X0] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(subset_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f1382,plain,
( ! [X0] :
( member(not_subclass_element(subset_relation,X0),cross_product(universal_class,universal_class))
| subclass(subset_relation,X0) )
| ~ spl0_79
| ~ spl0_160 ),
inference(superposition,[],[f1348,f644]) ).
fof(f6482,plain,
( spl0_456
| ~ spl0_39
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1115,f1078,f381,f6480]) ).
fof(f6480,plain,
( spl0_456
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f1115,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) )
| ~ spl0_39
| ~ spl0_137 ),
inference(resolution,[],[f1079,f382]) ).
fof(f6478,plain,
( spl0_455
| ~ spl0_40
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1114,f1078,f385,f6476]) ).
fof(f6476,plain,
( spl0_455
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1114,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) )
| ~ spl0_40
| ~ spl0_137 ),
inference(resolution,[],[f1079,f386]) ).
fof(f6414,plain,
( spl0_454
| ~ spl0_116
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1558,f1537,f912,f6412]) ).
fof(f6412,plain,
( spl0_454
<=> ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
| ~ member(X0,universal_class)
| y = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f1558,plain,
( ! [X0] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class))))
| ~ member(X0,universal_class)
| y = cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,X0))),domain_of(intersection(element_relation,cross_product(universal_class,X0)))),universal_class) )
| ~ spl0_116
| ~ spl0_179 ),
inference(resolution,[],[f1538,f913]) ).
fof(f6390,plain,
( spl0_453
| ~ spl0_113
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1791,f1750,f888,f6388]) ).
fof(f6388,plain,
( spl0_453
<=> ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),y)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f1791,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),y)
| ~ member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X1),universal_class)),universal_class))))),X0)
| y = X0 )
| ~ spl0_113
| ~ spl0_197 ),
inference(resolution,[],[f1751,f889]) ).
fof(f6302,plain,
( spl0_452
| ~ spl0_144
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1328,f1291,f1199,f6300]) ).
fof(f6300,plain,
( spl0_452
<=> ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f1328,plain,
( ! [X2,X0,X1] :
( ~ subclass(regular(cross_product(X0,X1)),X2)
| member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),X2)
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_155 ),
inference(superposition,[],[f1292,f1200]) ).
fof(f6298,plain,
( spl0_451
| ~ spl0_81
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1208,f1199,f661,f6296]) ).
fof(f6296,plain,
( spl0_451
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),successor_relation)
| second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f1208,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),successor_relation)
| second(regular(cross_product(X0,X1))) = complement(intersection(complement(first(regular(cross_product(X0,X1)))),complement(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))))))
| cross_product(X0,X1) = y )
| ~ spl0_81
| ~ spl0_144 ),
inference(superposition,[],[f662,f1200]) ).
fof(f6294,plain,
( spl0_450
| ~ spl0_29
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1168,f1143,f334,f6292]) ).
fof(f6292,plain,
( spl0_450
<=> ! [X0,X1] :
( ~ member(intersection(X0,complement(X1)),universal_class)
| y = intersection(X0,complement(X1))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f1168,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,complement(X1)),universal_class)
| y = intersection(X0,complement(X1))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,complement(X1)),intersection(X0,complement(X1))),universal_class)),universal_class))))))),X1) )
| ~ spl0_29
| ~ spl0_141 ),
inference(resolution,[],[f1144,f335]) ).
fof(f6290,plain,
( spl0_449
| ~ spl0_29
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1151,f1139,f334,f6288]) ).
fof(f6288,plain,
( spl0_449
<=> ! [X0,X1] :
( ~ member(intersection(complement(X0),X1),universal_class)
| y = intersection(complement(X0),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f1151,plain,
( ! [X0,X1] :
( ~ member(intersection(complement(X0),X1),universal_class)
| y = intersection(complement(X0),X1)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(complement(X0),X1),intersection(complement(X0),X1)),universal_class)),universal_class))))))),X0) )
| ~ spl0_29
| ~ spl0_140 ),
inference(resolution,[],[f1140,f335]) ).
fof(f6283,plain,
( spl0_276
| ~ spl0_447
| ~ spl0_448
| ~ spl0_136
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1135,f1089,f1066,f6280,f6276,f2842]) ).
fof(f6276,plain,
( spl0_447
<=> member(complement(cross_product(universal_class,universal_class)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f6280,plain,
( spl0_448
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f1135,plain,
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(cross_product(universal_class,universal_class)),complement(cross_product(universal_class,universal_class))),universal_class)),universal_class))))))),subset_relation)
| ~ member(complement(cross_product(universal_class,universal_class)),universal_class)
| y = complement(cross_product(universal_class,universal_class))
| ~ spl0_136
| ~ spl0_139 ),
inference(resolution,[],[f1090,f1067]) ).
fof(f6117,plain,
( spl0_446
| ~ spl0_8
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1540,f1533,f242,f6115]) ).
fof(f1540,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,universal_class) )
| ~ spl0_8
| ~ spl0_178 ),
inference(resolution,[],[f1534,f243]) ).
fof(f6113,plain,
( spl0_445
| ~ spl0_29
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1273,f1260,f334,f6111]) ).
fof(f1273,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| ~ member(X0,compose(element_relation,complement(identity_relation))) )
| ~ spl0_29
| ~ spl0_152 ),
inference(resolution,[],[f1261,f335]) ).
fof(f6109,plain,
( spl0_444
| ~ spl0_29
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1116,f1078,f334,f6107]) ).
fof(f6107,plain,
( spl0_444
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f1116,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) )
| ~ spl0_29
| ~ spl0_137 ),
inference(resolution,[],[f1079,f335]) ).
fof(f6105,plain,
( spl0_443
| ~ spl0_76
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1099,f1078,f625,f6103]) ).
fof(f6103,plain,
( spl0_443
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,compose_class(X0))
| compose(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f1099,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,compose_class(X0))
| compose(X0,X1) = X2 )
| ~ spl0_76
| ~ spl0_137 ),
inference(resolution,[],[f1079,f626]) ).
fof(f5887,plain,
( ~ spl0_441
| spl0_442
| ~ spl0_142
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f5829,f5764,f1181,f5884,f5880]) ).
fof(f5829,plain,
( function(y)
| ~ single_valued_class(y)
| ~ spl0_142
| ~ spl0_427 ),
inference(resolution,[],[f5765,f1182]) ).
fof(f5878,plain,
( spl0_440
| ~ spl0_144
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f1796,f1754,f1199,f5876]) ).
fof(f1796,plain,
( ! [X0,X1] :
( member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| ~ member(second(regular(cross_product(X0,X1))),universal_class)
| ~ member(first(regular(cross_product(X0,X1))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_144
| ~ spl0_198 ),
inference(superposition,[],[f1755,f1200]) ).
fof(f5874,plain,
( spl0_439
| ~ spl0_113
| ~ spl0_196 ),
inference(avatar_split_clause,[],[f1773,f1746,f888,f5872]) ).
fof(f1773,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ subclass(universal_class,regular(X1))
| ~ member(X2,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),y)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X2,universal_class),X0),universal_class)))),X1)
| y = X1 )
| ~ spl0_113
| ~ spl0_196 ),
inference(resolution,[],[f1747,f889]) ).
fof(f5870,plain,
( spl0_438
| ~ spl0_113
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1727,f1646,f888,f5868]) ).
fof(f5868,plain,
( spl0_438
<=> ! [X0,X1] :
( ~ subclass(domain_relation,regular(X0))
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),y)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f1727,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,regular(X0))
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),y)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(X1),domain_of(X1)))),X0)
| y = X0 )
| ~ spl0_113
| ~ spl0_192 ),
inference(resolution,[],[f1647,f889]) ).
fof(f5866,plain,
( spl0_437
| ~ spl0_107
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1173,f1143,f814,f5864]) ).
fof(f5864,plain,
( spl0_437
<=> ! [X0,X1] :
( ~ member(intersection(X0,y),universal_class)
| y = intersection(X0,y)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,y),intersection(X0,y)),universal_class)),universal_class))))))),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f1173,plain,
( ! [X0,X1] :
( ~ member(intersection(X0,y),universal_class)
| y = intersection(X0,y)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,y),intersection(X0,y)),universal_class)),universal_class))))))),X1)
| y = X1 )
| ~ spl0_107
| ~ spl0_141 ),
inference(resolution,[],[f1144,f815]) ).
fof(f5862,plain,
( spl0_436
| ~ spl0_46
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1163,f1143,f424,f5860]) ).
fof(f5860,plain,
( spl0_436
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f1163,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
| ~ spl0_46
| ~ spl0_141 ),
inference(resolution,[],[f1144,f425]) ).
fof(f5858,plain,
( spl0_435
| ~ spl0_107
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1156,f1139,f814,f5856]) ).
fof(f5856,plain,
( spl0_435
<=> ! [X0,X1] :
( ~ member(intersection(y,X0),universal_class)
| y = intersection(y,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(y,X0),intersection(y,X0)),universal_class)),universal_class))))))),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f1156,plain,
( ! [X0,X1] :
( ~ member(intersection(y,X0),universal_class)
| y = intersection(y,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(y,X0),intersection(y,X0)),universal_class)),universal_class))))))),X1)
| y = X1 )
| ~ spl0_107
| ~ spl0_140 ),
inference(resolution,[],[f1140,f815]) ).
fof(f5854,plain,
( spl0_434
| ~ spl0_46
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1146,f1139,f424,f5852]) ).
fof(f5852,plain,
( spl0_434
<=> ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f1146,plain,
( ! [X2,X0,X1] :
( ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y
| ~ subclass(X0,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X2) )
| ~ spl0_46
| ~ spl0_140 ),
inference(resolution,[],[f1140,f425]) ).
fof(f5850,plain,
( spl0_433
| ~ spl0_108
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1074,f1066,f826,f5848]) ).
fof(f5848,plain,
( spl0_433
<=> ! [X0] :
( ~ member(complement(regular(X0)),universal_class)
| y = complement(regular(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),y)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f826,plain,
( spl0_108
<=> ! [X0,X1] :
( ~ member(X1,y)
| member(X1,regular(X0))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1074,plain,
( ! [X0] :
( ~ member(complement(regular(X0)),universal_class)
| y = complement(regular(X0))
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(regular(X0)),complement(regular(X0))),universal_class)),universal_class))))))),y)
| y = X0 )
| ~ spl0_108
| ~ spl0_136 ),
inference(resolution,[],[f1067,f827]) ).
fof(f827,plain,
( ! [X0,X1] :
( member(X1,regular(X0))
| ~ member(X1,y)
| y = X0 )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f5845,plain,
( spl0_432
| ~ spl0_88
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1211,f1199,f697,f5843]) ).
fof(f5843,plain,
( spl0_432
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f697,plain,
( spl0_88
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1211,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),composition_function)
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y )
| ~ spl0_88
| ~ spl0_144 ),
inference(superposition,[],[f698,f1200]) ).
fof(f698,plain,
( ! [X0,X1,X4] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function)
| compose(X0,X1) = X4 )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f5817,plain,
( spl0_431
| ~ spl0_36
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1221,f1199,f369,f5815]) ).
fof(f5815,plain,
( spl0_431
<=> ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f1221,plain,
( ! [X0,X1] :
( member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),regular(cross_product(X0,X1)))
| ~ member(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_36
| ~ spl0_144 ),
inference(superposition,[],[f370,f1200]) ).
fof(f5779,plain,
( spl0_429
| ~ spl0_430
| ~ spl0_106
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1634,f1625,f810,f5776,f5772]) ).
fof(f5776,plain,
( spl0_430
<=> member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f1634,plain,
( ~ member(regular(complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),subset_relation)
| y = complement(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_106
| ~ spl0_189 ),
inference(resolution,[],[f1626,f811]) ).
fof(f5770,plain,
( spl0_428
| ~ spl0_130
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1172,f1143,f1005,f5768]) ).
fof(f5768,plain,
( spl0_428
<=> ! [X0] :
( ~ member(intersection(X0,singleton_relation),universal_class)
| y = intersection(X0,singleton_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f1172,plain,
( ! [X0] :
( ~ member(intersection(X0,singleton_relation),universal_class)
| y = intersection(X0,singleton_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,singleton_relation),intersection(X0,singleton_relation)),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_130
| ~ spl0_141 ),
inference(resolution,[],[f1144,f1006]) ).
fof(f5766,plain,
( spl0_427
| ~ spl0_8
| ~ spl0_236
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f5750,f5696,f2269,f242,f5764]) ).
fof(f5696,plain,
( spl0_423
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f5750,plain,
( ! [X0] : subclass(y,X0)
| ~ spl0_8
| ~ spl0_236
| ~ spl0_423 ),
inference(forward_demodulation,[],[f5746,f2271]) ).
fof(f5746,plain,
( ! [X0] : subclass(complement(universal_class),X0)
| ~ spl0_8
| ~ spl0_423 ),
inference(resolution,[],[f5697,f243]) ).
fof(f5697,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) )
| ~ spl0_423 ),
inference(avatar_component_clause,[],[f5696]) ).
fof(f5762,plain,
( spl0_426
| ~ spl0_131
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f1170,f1143,f1009,f5760]) ).
fof(f5760,plain,
( spl0_426
<=> ! [X0] :
( ~ member(intersection(X0,identity_relation),universal_class)
| y = intersection(X0,identity_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f1170,plain,
( ! [X0] :
( ~ member(intersection(X0,identity_relation),universal_class)
| y = intersection(X0,identity_relation)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,identity_relation),intersection(X0,identity_relation)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_131
| ~ spl0_141 ),
inference(resolution,[],[f1144,f1010]) ).
fof(f5758,plain,
( spl0_425
| ~ spl0_130
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1155,f1139,f1005,f5756]) ).
fof(f5756,plain,
( spl0_425
<=> ! [X0] :
( ~ member(intersection(singleton_relation,X0),universal_class)
| y = intersection(singleton_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f1155,plain,
( ! [X0] :
( ~ member(intersection(singleton_relation,X0),universal_class)
| y = intersection(singleton_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(singleton_relation,X0),intersection(singleton_relation,X0)),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_130
| ~ spl0_140 ),
inference(resolution,[],[f1140,f1006]) ).
fof(f5754,plain,
( spl0_424
| ~ spl0_131
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1153,f1139,f1009,f5752]) ).
fof(f5752,plain,
( spl0_424
<=> ! [X0] :
( ~ member(intersection(identity_relation,X0),universal_class)
| y = intersection(identity_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f1153,plain,
( ! [X0] :
( ~ member(intersection(identity_relation,X0),universal_class)
| y = intersection(identity_relation,X0)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(identity_relation,X0),intersection(identity_relation,X0)),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_131
| ~ spl0_140 ),
inference(resolution,[],[f1140,f1010]) ).
fof(f5698,plain,
( spl0_423
| ~ spl0_145
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1322,f1287,f1229,f5696]) ).
fof(f1322,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) )
| ~ spl0_145
| ~ spl0_154 ),
inference(duplicate_literal_removal,[],[f1309]) ).
fof(f1309,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1)
| subclass(complement(X0),X1) )
| ~ spl0_145
| ~ spl0_154 ),
inference(resolution,[],[f1288,f1230]) ).
fof(f5694,plain,
( spl0_422
| ~ spl0_30
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1190,f1181,f338,f5692]) ).
fof(f5692,plain,
( spl0_422
<=> ! [X0,X1] :
( function(compose(X0,X1))
| ~ single_valued_class(compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f1190,plain,
( ! [X0,X1] :
( function(compose(X0,X1))
| ~ single_valued_class(compose(X0,X1)) )
| ~ spl0_30
| ~ spl0_142 ),
inference(resolution,[],[f1182,f339]) ).
fof(f5690,plain,
( ~ spl0_420
| spl0_421
| ~ spl0_10
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1185,f1181,f251,f5687,f5683]) ).
fof(f5683,plain,
( spl0_420
<=> single_valued_class(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f5687,plain,
( spl0_421
<=> function(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f1185,plain,
( function(cross_product(universal_class,universal_class))
| ~ single_valued_class(cross_product(universal_class,universal_class))
| ~ spl0_10
| ~ spl0_142 ),
inference(resolution,[],[f1182,f252]) ).
fof(f5681,plain,
( spl0_418
| ~ spl0_419
| ~ spl0_130
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1121,f1078,f1005,f5678,f5675]) ).
fof(f5675,plain,
( spl0_418
<=> ! [X0,X1] : member(unordered_pair(X0,X1),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f5678,plain,
( spl0_419
<=> subclass(universal_class,singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f1121,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,singleton_relation)
| member(unordered_pair(X0,X1),element_relation) )
| ~ spl0_130
| ~ spl0_137 ),
inference(resolution,[],[f1079,f1006]) ).
fof(f5673,plain,
( spl0_416
| ~ spl0_417
| ~ spl0_88
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1103,f1078,f697,f5670,f5667]) ).
fof(f5667,plain,
( spl0_416
<=> ! [X2,X0,X1] : compose(X0,X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f5670,plain,
( spl0_417
<=> subclass(universal_class,composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f1103,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,composition_function)
| compose(X0,X1) = X2 )
| ~ spl0_88
| ~ spl0_137 ),
inference(resolution,[],[f1079,f698]) ).
fof(f5665,plain,
( spl0_415
| ~ spl0_73
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1093,f1078,f609,f5663]) ).
fof(f5663,plain,
( spl0_415
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f1093,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) )
| ~ spl0_73
| ~ spl0_137 ),
inference(resolution,[],[f1079,f610]) ).
fof(f5658,plain,
( spl0_414
| ~ spl0_74
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1092,f1078,f613,f5656]) ).
fof(f5656,plain,
( spl0_414
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f1092,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) )
| ~ spl0_74
| ~ spl0_137 ),
inference(resolution,[],[f1079,f614]) ).
fof(f5654,plain,
( spl0_413
| ~ spl0_34
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1025,f1009,f361,f5652]) ).
fof(f5652,plain,
( spl0_413
<=> ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f1025,plain,
( ! [X0] :
( member(not_subclass_element(identity_relation,X0),subset_relation)
| subclass(identity_relation,X0) )
| ~ spl0_34
| ~ spl0_131 ),
inference(resolution,[],[f1010,f362]) ).
fof(f5650,plain,
( spl0_412
| ~ spl0_34
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1018,f1005,f361,f5648]) ).
fof(f1018,plain,
( ! [X0] :
( member(not_subclass_element(singleton_relation,X0),element_relation)
| subclass(singleton_relation,X0) )
| ~ spl0_34
| ~ spl0_130 ),
inference(resolution,[],[f1006,f362]) ).
fof(f5646,plain,
( spl0_411
| ~ spl0_45
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f923,f919,f405,f5644]) ).
fof(f5644,plain,
( spl0_411
<=> ! [X0] :
( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f919,plain,
( spl0_117
<=> ! [X0] :
( single_valued_class(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f923,plain,
( ! [X0] :
( single_valued_class(domain_of(flip(cross_product(X0,universal_class))))
| ~ one_to_one(X0) )
| ~ spl0_45
| ~ spl0_117 ),
inference(resolution,[],[f920,f406]) ).
fof(f920,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f5601,plain,
( spl0_410
| ~ spl0_46
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1046,f1043,f424,f5599]) ).
fof(f5599,plain,
( spl0_410
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| y = X0
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f1046,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| y = X0
| ~ subclass(X1,X2)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
| ~ spl0_46
| ~ spl0_134 ),
inference(resolution,[],[f1044,f425]) ).
fof(f5560,plain,
( spl0_409
| ~ spl0_295
| ~ spl0_343 ),
inference(avatar_split_clause,[],[f5224,f4186,f3222,f5557]) ).
fof(f5557,plain,
( spl0_409
<=> subclass(y,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f3222,plain,
( spl0_295
<=> y = intersection(complement(subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f5224,plain,
( subclass(y,complement(subset_relation))
| ~ spl0_295
| ~ spl0_343 ),
inference(superposition,[],[f4187,f3224]) ).
fof(f3224,plain,
( y = intersection(complement(subset_relation),identity_relation)
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3222]) ).
fof(f5537,plain,
( spl0_408
| ~ spl0_87
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1210,f1199,f693,f5535]) ).
fof(f5535,plain,
( spl0_408
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| member(first(regular(cross_product(X0,X1))),domain_of(X2))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f1210,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(regular(cross_product(X0,X1)),regular(cross_product(X0,X1))))),application_function)
| member(first(regular(cross_product(X0,X1))),domain_of(X2))
| cross_product(X0,X1) = y )
| ~ spl0_87
| ~ spl0_144 ),
inference(superposition,[],[f694,f1200]) ).
fof(f5533,plain,
( spl0_407
| ~ spl0_85
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1209,f1199,f683,f5531]) ).
fof(f5531,plain,
( spl0_407
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f1209,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(universal_class,universal_class))
| member(regular(cross_product(X0,X1)),element_relation)
| ~ member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y )
| ~ spl0_85
| ~ spl0_144 ),
inference(superposition,[],[f684,f1200]) ).
fof(f5529,plain,
( spl0_406
| ~ spl0_39
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1050,f1043,f381,f5527]) ).
fof(f5527,plain,
( spl0_406
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f1050,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
| ~ spl0_39
| ~ spl0_134 ),
inference(resolution,[],[f1044,f382]) ).
fof(f5525,plain,
( spl0_405
| ~ spl0_40
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1049,f1043,f385,f5523]) ).
fof(f5523,plain,
( spl0_405
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f1049,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X2) )
| ~ spl0_40
| ~ spl0_134 ),
inference(resolution,[],[f1044,f386]) ).
fof(f5521,plain,
( spl0_404
| ~ spl0_82
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f844,f831,f665,f5519]) ).
fof(f5519,plain,
( spl0_404
<=> ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| y = X0
| regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f844,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,cross_product(X1,X2))
| y = X0
| regular(X0) = unordered_pair(unordered_pair(first(regular(X0)),first(regular(X0))),unordered_pair(first(regular(X0)),unordered_pair(second(regular(X0)),second(regular(X0))))) )
| ~ spl0_82
| ~ spl0_109 ),
inference(resolution,[],[f832,f666]) ).
fof(f5378,plain,
( spl0_403
| ~ spl0_112
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1474,f1424,f856,f5376]) ).
fof(f5376,plain,
( spl0_403
<=> ! [X0] :
( ~ member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),subset_relation)
| member(regular(intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| y = intersection(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f5374,plain,
( spl0_402
| ~ spl0_111
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1471,f1424,f852,f5372]) ).
fof(f5372,plain,
( spl0_402
<=> ! [X0] :
( ~ member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),subset_relation)
| member(regular(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0)),identity_relation)
| y = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f5370,plain,
( spl0_401
| ~ spl0_112
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1449,f1420,f856,f5368]) ).
fof(f5368,plain,
( spl0_401
<=> ! [X0] :
( ~ member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),element_relation)
| member(regular(intersection(X0,complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| y = intersection(X0,complement(compose(element_relation,complement(identity_relation)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f5366,plain,
( spl0_400
| ~ spl0_111
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1446,f1420,f852,f5364]) ).
fof(f5364,plain,
( spl0_400
<=> ! [X0] :
( ~ member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),element_relation)
| member(regular(intersection(complement(compose(element_relation,complement(identity_relation))),X0)),singleton_relation)
| y = intersection(complement(compose(element_relation,complement(identity_relation))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f5362,plain,
( spl0_399
| ~ spl0_12
| ~ spl0_57
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1272,f1229,f500,f261,f5360]) ).
fof(f5360,plain,
( spl0_399
<=> ! [X0,X1] :
( y = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
| subclass(complement(domain_of(X0)),X1)
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f1272,plain,
( ! [X0,X1] :
( y = intersection(X0,cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class))
| subclass(complement(domain_of(X0)),X1)
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class) )
| ~ spl0_12
| ~ spl0_57
| ~ spl0_145 ),
inference(forward_demodulation,[],[f1270,f501]) ).
fof(f1270,plain,
( ! [X0,X1] :
( subclass(complement(domain_of(X0)),X1)
| ~ member(not_subclass_element(complement(domain_of(X0)),X1),universal_class)
| y = intersection(cross_product(unordered_pair(not_subclass_element(complement(domain_of(X0)),X1),not_subclass_element(complement(domain_of(X0)),X1)),universal_class),X0) )
| ~ spl0_12
| ~ spl0_145 ),
inference(resolution,[],[f1230,f262]) ).
fof(f5358,plain,
( spl0_398
| ~ spl0_29
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1051,f1043,f334,f5356]) ).
fof(f5356,plain,
( spl0_398
<=> ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| ~ member(X0,universal_class)
| y = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f1051,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| ~ member(X0,universal_class)
| y = X0
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
| ~ spl0_29
| ~ spl0_134 ),
inference(resolution,[],[f1044,f335]) ).
fof(f5354,plain,
( spl0_396
| ~ spl0_397
| ~ spl0_87
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1102,f1078,f693,f5351,f5348]) ).
fof(f5348,plain,
( spl0_396
<=> ! [X0,X1] : member(X0,domain_of(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f5351,plain,
( spl0_397
<=> subclass(universal_class,application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f1102,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,application_function)
| member(X0,domain_of(X1)) )
| ~ spl0_87
| ~ spl0_137 ),
inference(resolution,[],[f1079,f694]) ).
fof(f5346,plain,
( spl0_395
| ~ spl0_295
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f5225,f4190,f3222,f5343]) ).
fof(f5343,plain,
( spl0_395
<=> subclass(y,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f5225,plain,
( subclass(y,identity_relation)
| ~ spl0_295
| ~ spl0_344 ),
inference(superposition,[],[f4191,f3224]) ).
fof(f5341,plain,
( spl0_393
| ~ spl0_394
| ~ spl0_68
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1100,f1078,f583,f5338,f5335]) ).
fof(f5335,plain,
( spl0_393
<=> ! [X0,X1] : domain_of(X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f5338,plain,
( spl0_394
<=> subclass(universal_class,domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f1100,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,domain_relation)
| domain_of(X0) = X1 )
| ~ spl0_68
| ~ spl0_137 ),
inference(resolution,[],[f1079,f584]) ).
fof(f5312,plain,
( spl0_392
| ~ spl0_109
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f1834,f1816,f831,f5310]) ).
fof(f5310,plain,
( spl0_392
<=> ! [X0] :
( member(regular(X0),subset_relation)
| ~ member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f1834,plain,
( ! [X0] :
( member(regular(X0),subset_relation)
| ~ member(regular(X0),cross_product(universal_class,universal_class))
| ~ subclass(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| y = X0 )
| ~ spl0_109
| ~ spl0_203 ),
inference(resolution,[],[f1817,f832]) ).
fof(f5308,plain,
( spl0_391
| ~ spl0_130
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1056,f1043,f1005,f5306]) ).
fof(f5306,plain,
( spl0_391
<=> ! [X0] :
( ~ subclass(X0,singleton_relation)
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f1056,plain,
( ! [X0] :
( ~ subclass(X0,singleton_relation)
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),element_relation) )
| ~ spl0_130
| ~ spl0_134 ),
inference(resolution,[],[f1044,f1006]) ).
fof(f5304,plain,
( spl0_390
| ~ spl0_131
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1054,f1043,f1009,f5302]) ).
fof(f5302,plain,
( spl0_390
<=> ! [X0] :
( ~ subclass(X0,identity_relation)
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f1054,plain,
( ! [X0] :
( ~ subclass(X0,identity_relation)
| ~ member(X0,universal_class)
| y = X0
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),subset_relation) )
| ~ spl0_131
| ~ spl0_134 ),
inference(resolution,[],[f1044,f1010]) ).
fof(f5279,plain,
( spl0_389
| ~ spl0_136
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1549,f1537,f1066,f5277]) ).
fof(f5277,plain,
( spl0_389
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class)
| ~ member(complement(X0),universal_class)
| complement(X0) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f1549,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| ~ member(domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class)))),universal_class)
| ~ member(complement(X0),universal_class)
| complement(X0) = y )
| ~ spl0_136
| ~ spl0_179 ),
inference(resolution,[],[f1538,f1067]) ).
fof(f5275,plain,
( spl0_388
| ~ spl0_116
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1317,f1287,f912,f5273]) ).
fof(f5273,plain,
( spl0_388
<=> ! [X0,X1] :
( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
| subclass(X0,X1)
| y = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f1317,plain,
( ! [X0,X1] :
( ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class))))
| subclass(X0,X1)
| y = cross_product(unordered_pair(not_subclass_element(X0,X1),not_subclass_element(X0,X1)),universal_class) )
| ~ spl0_116
| ~ spl0_154 ),
inference(resolution,[],[f1288,f913]) ).
fof(f5271,plain,
( spl0_387
| ~ spl0_80
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1207,f1199,f647,f5269]) ).
fof(f5269,plain,
( spl0_387
<=> ! [X0,X3,X2,X1] :
( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),X3)
| ~ member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f1207,plain,
( ! [X2,X3,X0,X1] :
( member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| ~ member(second(regular(cross_product(X0,X1))),X3)
| ~ member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = y )
| ~ spl0_80
| ~ spl0_144 ),
inference(superposition,[],[f648,f1200]) ).
fof(f5264,plain,
( spl0_238
| ~ spl0_244
| spl0_386
| ~ spl0_79
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1160,f1139,f642,f5261,f2322,f2279]) ).
fof(f5261,plain,
( spl0_386
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f1160,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(subset_relation,subset_relation),universal_class)),universal_class))))))),cross_product(universal_class,universal_class))
| ~ member(subset_relation,universal_class)
| subset_relation = y
| ~ spl0_79
| ~ spl0_140 ),
inference(superposition,[],[f1140,f644]) ).
fof(f5233,plain,
( spl0_385
| ~ spl0_113
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f1561,f1537,f888,f5231]) ).
fof(f5231,plain,
( spl0_385
<=> ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f1561,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,regular(X0))
| ~ member(X1,universal_class)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),y)
| ~ member(domain_of(intersection(element_relation,cross_product(universal_class,X1))),X0)
| y = X0 )
| ~ spl0_113
| ~ spl0_179 ),
inference(resolution,[],[f1538,f889]) ).
fof(f5229,plain,
( spl0_384
| ~ spl0_12
| ~ spl0_57
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f820,f810,f500,f261,f5227]) ).
fof(f5227,plain,
( spl0_384
<=> ! [X0] :
( y = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
| y = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f820,plain,
( ! [X0] :
( y = intersection(X0,cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class))
| y = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class) )
| ~ spl0_12
| ~ spl0_57
| ~ spl0_106 ),
inference(forward_demodulation,[],[f819,f501]) ).
fof(f819,plain,
( ! [X0] :
( y = complement(domain_of(X0))
| ~ member(regular(complement(domain_of(X0))),universal_class)
| y = intersection(cross_product(unordered_pair(regular(complement(domain_of(X0))),regular(complement(domain_of(X0)))),universal_class),X0) )
| ~ spl0_12
| ~ spl0_106 ),
inference(resolution,[],[f811,f262]) ).
fof(f5033,plain,
( spl0_383
| ~ spl0_108
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1683,f1642,f826,f5031]) ).
fof(f5031,plain,
( spl0_383
<=> ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
| subclass(X0,intersection(X1,regular(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),y)
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f1683,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),X1)
| subclass(X0,intersection(X1,regular(X2)))
| ~ member(not_subclass_element(X0,intersection(X1,regular(X2))),y)
| y = X2 )
| ~ spl0_108
| ~ spl0_191 ),
inference(resolution,[],[f1643,f827]) ).
fof(f5029,plain,
( spl0_382
| ~ spl0_133
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1406,f1351,f1037,f5027]) ).
fof(f5027,plain,
( spl0_382
<=> ! [X0,X1] :
( subclass(intersection(X0,universal_class),domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f1037,plain,
( spl0_133
<=> ! [X0,X1] :
( y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
| subclass(X0,domain_of(X1))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1406,plain,
( ! [X0,X1] :
( subclass(intersection(X0,universal_class),domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) )
| ~ spl0_133
| ~ spl0_161 ),
inference(duplicate_literal_removal,[],[f1388]) ).
fof(f1388,plain,
( ! [X0,X1] :
( subclass(intersection(X0,universal_class),domain_of(X1))
| subclass(intersection(X0,universal_class),domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(X0,universal_class),domain_of(X1)),not_subclass_element(intersection(X0,universal_class),domain_of(X1))),universal_class)) )
| ~ spl0_133
| ~ spl0_161 ),
inference(resolution,[],[f1352,f1038]) ).
fof(f1038,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| subclass(X0,domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1037]) ).
fof(f5025,plain,
( spl0_381
| ~ spl0_113
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1397,f1351,f888,f5023]) ).
fof(f1397,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,regular(X1)),X2)
| member(not_subclass_element(intersection(X0,regular(X1)),X2),y)
| ~ member(not_subclass_element(intersection(X0,regular(X1)),X2),X1)
| y = X1 )
| ~ spl0_113
| ~ spl0_161 ),
inference(resolution,[],[f1352,f889]) ).
fof(f5021,plain,
( spl0_380
| ~ spl0_133
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1385,f1347,f1037,f5019]) ).
fof(f5019,plain,
( spl0_380
<=> ! [X0,X1] :
( subclass(intersection(universal_class,X0),domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f1385,plain,
( ! [X0,X1] :
( subclass(intersection(universal_class,X0),domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) )
| ~ spl0_133
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1367]) ).
fof(f1367,plain,
( ! [X0,X1] :
( subclass(intersection(universal_class,X0),domain_of(X1))
| subclass(intersection(universal_class,X0),domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(intersection(universal_class,X0),domain_of(X1)),not_subclass_element(intersection(universal_class,X0),domain_of(X1))),universal_class)) )
| ~ spl0_133
| ~ spl0_160 ),
inference(resolution,[],[f1348,f1038]) ).
fof(f5017,plain,
( spl0_379
| ~ spl0_113
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1376,f1347,f888,f5015]) ).
fof(f1376,plain,
( ! [X2,X0,X1] :
( subclass(intersection(regular(X0),X1),X2)
| member(not_subclass_element(intersection(regular(X0),X1),X2),y)
| ~ member(not_subclass_element(intersection(regular(X0),X1),X2),X0)
| y = X0 )
| ~ spl0_113
| ~ spl0_160 ),
inference(resolution,[],[f1348,f889]) ).
fof(f5013,plain,
( spl0_378
| ~ spl0_76
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1206,f1199,f625,f5011]) ).
fof(f5011,plain,
( spl0_378
<=> ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f1206,plain,
( ! [X2,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),compose_class(X2))
| second(regular(cross_product(X0,X1))) = compose(X2,first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y )
| ~ spl0_76
| ~ spl0_144 ),
inference(superposition,[],[f626,f1200]) ).
fof(f5007,plain,
( spl0_186
| ~ spl0_199
| spl0_377
| ~ spl0_28
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1026,f1009,f330,f5004,f1758,f1601]) ).
fof(f5004,plain,
( spl0_377
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f1026,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),subset_relation)
| ~ member(identity_relation,universal_class)
| identity_relation = y
| ~ spl0_28
| ~ spl0_131 ),
inference(resolution,[],[f1010,f331]) ).
fof(f5000,plain,
( spl0_168
| ~ spl0_375
| spl0_376
| ~ spl0_28
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1019,f1005,f330,f4997,f4993,f1428]) ).
fof(f4997,plain,
( spl0_376
<=> member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f1019,plain,
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(singleton_relation,singleton_relation),universal_class)),universal_class))))))),element_relation)
| ~ member(singleton_relation,universal_class)
| singleton_relation = y
| ~ spl0_28
| ~ spl0_130 ),
inference(resolution,[],[f1006,f331]) ).
fof(f4991,plain,
( spl0_374
| ~ spl0_67
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f957,f953,f577,f4989]) ).
fof(f4989,plain,
( spl0_374
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f957,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(intersection(successor_relation,cross_product(X1,universal_class)),universal_class))))
| ~ inductive(X1) )
| ~ spl0_67
| ~ spl0_119 ),
inference(resolution,[],[f954,f578]) ).
fof(f4972,plain,
( spl0_373
| ~ spl0_26
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1191,f1181,f322,f4970]) ).
fof(f4970,plain,
( spl0_373
<=> ! [X0] :
( function(compose_class(X0))
| ~ single_valued_class(compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f1191,plain,
( ! [X0] :
( function(compose_class(X0))
| ~ single_valued_class(compose_class(X0)) )
| ~ spl0_26
| ~ spl0_142 ),
inference(resolution,[],[f1182,f323]) ).
fof(f4968,plain,
( spl0_371
| ~ spl0_372
| ~ spl0_65
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1095,f1078,f569,f4965,f4962]) ).
fof(f4962,plain,
( spl0_371
<=> ! [X0,X1] : member(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f4965,plain,
( spl0_372
<=> subclass(universal_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f1095,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,element_relation)
| member(X0,X1) )
| ~ spl0_65
| ~ spl0_137 ),
inference(resolution,[],[f1079,f570]) ).
fof(f4957,plain,
( spl0_370
| ~ spl0_116
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1118,f1078,f912,f4955]) ).
fof(f4955,plain,
( spl0_370
<=> ! [X0,X1] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class))))
| y = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f1118,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,domain_of(regular(cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class))))
| y = cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class) )
| ~ spl0_116
| ~ spl0_137 ),
inference(resolution,[],[f1079,f913]) ).
fof(f4790,plain,
( spl0_369
| ~ spl0_111
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2969,f2838,f852,f4788]) ).
fof(f2969,plain,
( ! [X0] : y = intersection(X0,complement(X0))
| ~ spl0_111
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f2947]) ).
fof(f2947,plain,
( ! [X0] :
( y = intersection(X0,complement(X0))
| y = intersection(X0,complement(X0)) )
| ~ spl0_111
| ~ spl0_275 ),
inference(resolution,[],[f2839,f853]) ).
fof(f4499,plain,
( spl0_366
| spl0_367
| ~ spl0_368
| ~ spl0_2
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1470,f1424,f213,f4496,f4492,f4488]) ).
fof(f1470,plain,
( ~ member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),subset_relation)
| member(regular(domain_of(flip(cross_product(subset_relation,universal_class)))),identity_relation)
| y = domain_of(flip(cross_product(subset_relation,universal_class)))
| ~ spl0_2
| ~ spl0_167 ),
inference(resolution,[],[f1425,f214]) ).
fof(f4481,plain,
( spl0_363
| spl0_364
| ~ spl0_365
| ~ spl0_2
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1445,f1420,f213,f4478,f4474,f4470]) ).
fof(f1445,plain,
( ~ member(regular(complement(compose(element_relation,complement(identity_relation)))),element_relation)
| member(regular(complement(compose(element_relation,complement(identity_relation)))),singleton_relation)
| complement(compose(element_relation,complement(identity_relation))) = y
| ~ spl0_2
| ~ spl0_166 ),
inference(resolution,[],[f1421,f214]) ).
fof(f4468,plain,
( spl0_362
| ~ spl0_252
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2966,f2838,f2522,f4465]) ).
fof(f2966,plain,
( y = intersection(singleton_relation,complement(element_relation))
| ~ spl0_252
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f2951]) ).
fof(f2951,plain,
( y = intersection(singleton_relation,complement(element_relation))
| y = intersection(singleton_relation,complement(element_relation))
| ~ spl0_252
| ~ spl0_275 ),
inference(resolution,[],[f2839,f2523]) ).
fof(f4463,plain,
( spl0_361
| ~ spl0_68
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1203,f1199,f583,f4461]) ).
fof(f4461,plain,
( spl0_361
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),domain_relation)
| second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f1203,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),domain_relation)
| second(regular(cross_product(X0,X1))) = domain_of(first(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y )
| ~ spl0_68
| ~ spl0_144 ),
inference(superposition,[],[f584,f1200]) ).
fof(f4459,plain,
( spl0_360
| ~ spl0_63
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f956,f953,f555,f4457]) ).
fof(f4457,plain,
( spl0_360
<=> ! [X0,X1] :
( member(X0,domain_of(domain_of(X1)))
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
| ~ operation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f956,plain,
( ! [X0,X1] :
( member(X0,domain_of(domain_of(X1)))
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),domain_of(flip(cross_product(X1,universal_class))))
| ~ operation(X1) )
| ~ spl0_63
| ~ spl0_119 ),
inference(resolution,[],[f954,f556]) ).
fof(f4455,plain,
( spl0_359
| ~ spl0_109
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f917,f912,f831,f4453]) ).
fof(f4453,plain,
( spl0_359
<=> ! [X0] :
( y = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f917,plain,
( ! [X0] :
( y = cross_product(unordered_pair(regular(X0),regular(X0)),universal_class)
| ~ subclass(X0,domain_of(regular(cross_product(unordered_pair(regular(X0),regular(X0)),universal_class))))
| y = X0 )
| ~ spl0_109
| ~ spl0_116 ),
inference(resolution,[],[f913,f832]) ).
fof(f4451,plain,
( spl0_358
| ~ spl0_112
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f907,f888,f856,f4449]) ).
fof(f907,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,regular(X1))),y)
| ~ member(regular(intersection(X0,regular(X1))),X1)
| y = X1
| y = intersection(X0,regular(X1)) )
| ~ spl0_112
| ~ spl0_113 ),
inference(resolution,[],[f889,f857]) ).
fof(f4447,plain,
( spl0_357
| ~ spl0_111
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f904,f888,f852,f4445]) ).
fof(f904,plain,
( ! [X0,X1] :
( member(regular(intersection(regular(X0),X1)),y)
| ~ member(regular(intersection(regular(X0),X1)),X0)
| y = X0
| y = intersection(regular(X0),X1) )
| ~ spl0_111
| ~ spl0_113 ),
inference(resolution,[],[f889,f853]) ).
fof(f4443,plain,
( spl0_356
| ~ spl0_55
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f874,f856,f492,f4441]) ).
fof(f4441,plain,
( spl0_356
<=> ! [X2,X0,X1] :
( y = intersection(X0,unordered_pair(X1,X2))
| regular(intersection(X0,unordered_pair(X1,X2))) = X1
| regular(intersection(X0,unordered_pair(X1,X2))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f874,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,unordered_pair(X1,X2))
| regular(intersection(X0,unordered_pair(X1,X2))) = X1
| regular(intersection(X0,unordered_pair(X1,X2))) = X2 )
| ~ spl0_55
| ~ spl0_112 ),
inference(resolution,[],[f857,f493]) ).
fof(f4439,plain,
( spl0_355
| ~ spl0_55
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f860,f852,f492,f4437]) ).
fof(f4437,plain,
( spl0_355
<=> ! [X2,X0,X1] :
( y = intersection(unordered_pair(X0,X1),X2)
| regular(intersection(unordered_pair(X0,X1),X2)) = X0
| regular(intersection(unordered_pair(X0,X1),X2)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f860,plain,
( ! [X2,X0,X1] :
( y = intersection(unordered_pair(X0,X1),X2)
| regular(intersection(unordered_pair(X0,X1),X2)) = X0
| regular(intersection(unordered_pair(X0,X1),X2)) = X1 )
| ~ spl0_55
| ~ spl0_111 ),
inference(resolution,[],[f853,f493]) ).
fof(f4360,plain,
( spl0_354
| ~ spl0_254
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2964,f2838,f2532,f4357]) ).
fof(f4357,plain,
( spl0_354
<=> y = intersection(identity_relation,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2964,plain,
( y = intersection(identity_relation,complement(subset_relation))
| ~ spl0_254
| ~ spl0_275 ),
inference(duplicate_literal_removal,[],[f2960]) ).
fof(f2960,plain,
( y = intersection(identity_relation,complement(subset_relation))
| y = intersection(identity_relation,complement(subset_relation))
| ~ spl0_254
| ~ spl0_275 ),
inference(resolution,[],[f2839,f2533]) ).
fof(f4305,plain,
( spl0_352
| ~ spl0_353
| ~ spl0_107
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1729,f1646,f814,f4302,f4299]) ).
fof(f4299,plain,
( spl0_352
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| y = X1
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f4302,plain,
( spl0_353
<=> subclass(domain_relation,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f1729,plain,
( ! [X0,X1] :
( ~ subclass(domain_relation,y)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1)
| y = X1 )
| ~ spl0_107
| ~ spl0_192 ),
inference(resolution,[],[f1647,f815]) ).
fof(f4297,plain,
( spl0_351
| ~ spl0_133
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1323,f1287,f1037,f4295]) ).
fof(f4295,plain,
( spl0_351
<=> ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f1323,plain,
( ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
| ~ spl0_133
| ~ spl0_154 ),
inference(duplicate_literal_removal,[],[f1308]) ).
fof(f1308,plain,
( ! [X0,X1] :
( ~ subclass(X0,universal_class)
| subclass(X0,domain_of(X1))
| subclass(X0,domain_of(X1))
| y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class)) )
| ~ spl0_133
| ~ spl0_154 ),
inference(resolution,[],[f1288,f1038]) ).
fof(f4293,plain,
( spl0_350
| ~ spl0_65
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1202,f1199,f569,f4291]) ).
fof(f4291,plain,
( spl0_350
<=> ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),element_relation)
| member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f1202,plain,
( ! [X0,X1] :
( ~ member(regular(cross_product(X0,X1)),element_relation)
| member(first(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))
| cross_product(X0,X1) = y )
| ~ spl0_65
| ~ spl0_144 ),
inference(superposition,[],[f570,f1200]) ).
fof(f4289,plain,
( spl0_349
| ~ spl0_113
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f951,f925,f888,f4287]) ).
fof(f951,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,y)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_113
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f930]) ).
fof(f930,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,y)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_113
| ~ spl0_118 ),
inference(superposition,[],[f889,f926]) ).
fof(f4285,plain,
( spl0_348
| ~ spl0_113
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f946,f925,f888,f4283]) ).
fof(f946,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,y)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_113
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f935]) ).
fof(f935,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,y)
| ~ member(X2,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y )
| ~ spl0_113
| ~ spl0_118 ),
inference(superposition,[],[f889,f926]) ).
fof(f4242,plain,
( spl0_347
| ~ spl0_105
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1665,f1638,f789,f4240]) ).
fof(f4240,plain,
( spl0_347
<=> ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(y,X2)
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f789,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| member(y,X1)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1665,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X1
| not_subclass_element(unordered_pair(X0,X1),X2) = X0
| member(y,X2)
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_105
| ~ spl0_190 ),
inference(resolution,[],[f1639,f790]) ).
fof(f790,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(y,X1)
| ~ inductive(X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f4238,plain,
( spl0_346
| ~ spl0_112
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2943,f2834,f856,f4236]) ).
fof(f2943,plain,
( ! [X0] : y = intersection(complement(X0),X0)
| ~ spl0_112
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2919]) ).
fof(f2919,plain,
( ! [X0] :
( y = intersection(complement(X0),X0)
| y = intersection(complement(X0),X0) )
| ~ spl0_112
| ~ spl0_274 ),
inference(resolution,[],[f2835,f857]) ).
fof(f4234,plain,
( spl0_345
| ~ spl0_12
| ~ spl0_57
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1480,f1424,f500,f261,f4232]) ).
fof(f4232,plain,
( spl0_345
<=> ! [X0] :
( y = intersection(flip(cross_product(subset_relation,universal_class)),cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,subset_relation)
| member(X0,identity_relation)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f4192,plain,
( spl0_344
| ~ spl0_35
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1407,f1351,f365,f4190]) ).
fof(f1407,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl0_35
| ~ spl0_161 ),
inference(duplicate_literal_removal,[],[f1387]) ).
fof(f1387,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) )
| ~ spl0_35
| ~ spl0_161 ),
inference(resolution,[],[f1352,f366]) ).
fof(f4188,plain,
( spl0_343
| ~ spl0_35
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1386,f1347,f365,f4186]) ).
fof(f1386,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl0_35
| ~ spl0_160 ),
inference(duplicate_literal_removal,[],[f1366]) ).
fof(f1366,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) )
| ~ spl0_35
| ~ spl0_160 ),
inference(resolution,[],[f1348,f366]) ).
fof(f4106,plain,
( spl0_342
| ~ spl0_113
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1319,f1287,f888,f4104]) ).
fof(f1319,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,regular(X1))
| subclass(X0,X2)
| member(not_subclass_element(X0,X2),y)
| ~ member(not_subclass_element(X0,X2),X1)
| y = X1 )
| ~ spl0_113
| ~ spl0_154 ),
inference(resolution,[],[f1288,f889]) ).
fof(f4102,plain,
( spl0_341
| ~ spl0_74
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1205,f1199,f613,f4100]) ).
fof(f1205,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(first(regular(cross_product(X0,X1))),X2)
| cross_product(X0,X1) = y )
| ~ spl0_74
| ~ spl0_144 ),
inference(superposition,[],[f614,f1200]) ).
fof(f4098,plain,
( spl0_340
| ~ spl0_73
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1204,f1199,f609,f4096]) ).
fof(f1204,plain,
( ! [X2,X3,X0,X1] :
( ~ member(regular(cross_product(X0,X1)),cross_product(X2,X3))
| member(second(regular(cross_product(X0,X1))),X3)
| cross_product(X0,X1) = y )
| ~ spl0_73
| ~ spl0_144 ),
inference(superposition,[],[f610,f1200]) ).
fof(f4094,plain,
( spl0_339
| ~ spl0_31
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f960,f953,f342,f4092]) ).
fof(f960,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| y = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
| ~ function(domain_of(X1)) )
| ~ spl0_31
| ~ spl0_119 ),
inference(resolution,[],[f954,f343]) ).
fof(f4090,plain,
( spl0_338
| ~ spl0_56
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f817,f810,f496,f4088]) ).
fof(f4088,plain,
( spl0_338
<=> ! [X0,X1] :
( complement(intersection(X0,X1)) = y
| ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f817,plain,
( ! [X0,X1] :
( complement(intersection(X0,X1)) = y
| ~ member(regular(complement(intersection(X0,X1))),X1)
| ~ member(regular(complement(intersection(X0,X1))),X0) )
| ~ spl0_56
| ~ spl0_106 ),
inference(resolution,[],[f811,f497]) ).
fof(f4044,plain,
( spl0_337
| ~ spl0_238
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4025,f4021,f2279,f4042]) ).
fof(f4042,plain,
( spl0_337
<=> ! [X0,X1] :
( subset_relation = X0
| member(not_subclass_element(regular(X0),X1),subset_relation)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| subclass(regular(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f4025,plain,
( ! [X0,X1] :
( subset_relation = X0
| member(not_subclass_element(regular(X0),X1),subset_relation)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| subclass(regular(X0),X1) )
| ~ spl0_238
| ~ spl0_333 ),
inference(forward_demodulation,[],[f4024,f2281]) ).
fof(f4024,plain,
( ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),subset_relation)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| y = X0
| subclass(regular(X0),X1) )
| ~ spl0_238
| ~ spl0_333 ),
inference(forward_demodulation,[],[f4022,f2281]) ).
fof(f4039,plain,
( spl0_336
| ~ spl0_34
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1041,f1037,f361,f4037]) ).
fof(f4037,plain,
( spl0_336
<=> ! [X0] :
( subclass(universal_class,domain_of(X0))
| y = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f1041,plain,
( ! [X0] :
( subclass(universal_class,domain_of(X0))
| y = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class)) )
| ~ spl0_34
| ~ spl0_133 ),
inference(duplicate_literal_removal,[],[f1040]) ).
fof(f1040,plain,
( ! [X0] :
( subclass(universal_class,domain_of(X0))
| y = intersection(X0,cross_product(unordered_pair(not_subclass_element(universal_class,domain_of(X0)),not_subclass_element(universal_class,domain_of(X0))),universal_class))
| subclass(universal_class,domain_of(X0)) )
| ~ spl0_34
| ~ spl0_133 ),
inference(resolution,[],[f1038,f362]) ).
fof(f4034,plain,
( spl0_335
| ~ spl0_109
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f950,f925,f831,f4032]) ).
fof(f950,plain,
( ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_109
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f931]) ).
fof(f931,plain,
( ! [X2,X0,X1] :
( member(X1,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_109
| ~ spl0_118 ),
inference(superposition,[],[f832,f926]) ).
fof(f4029,plain,
( spl0_334
| ~ spl0_109
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f945,f925,f831,f4027]) ).
fof(f945,plain,
( ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_109
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f936]) ).
fof(f936,plain,
( ! [X2,X0,X1] :
( member(X0,X2)
| ~ subclass(unordered_pair(X0,X1),X2)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y )
| ~ spl0_109
| ~ spl0_118 ),
inference(superposition,[],[f832,f926]) ).
fof(f4023,plain,
( spl0_333
| ~ spl0_34
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f901,f888,f361,f4021]) ).
fof(f901,plain,
( ! [X0,X1] :
( member(not_subclass_element(regular(X0),X1),y)
| ~ member(not_subclass_element(regular(X0),X1),X0)
| y = X0
| subclass(regular(X0),X1) )
| ~ spl0_34
| ~ spl0_113 ),
inference(resolution,[],[f889,f362]) ).
fof(f3980,plain,
( spl0_238
| spl0_332
| ~ spl0_79
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f884,f856,f642,f3977,f2279]) ).
fof(f884,plain,
( member(regular(subset_relation),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| subset_relation = y
| ~ spl0_79
| ~ spl0_112 ),
inference(superposition,[],[f857,f644]) ).
fof(f3828,plain,
( spl0_331
| ~ spl0_109
| ~ spl0_167 ),
inference(avatar_split_clause,[],[f1473,f1424,f831,f3826]) ).
fof(f3824,plain,
( spl0_330
| ~ spl0_109
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1448,f1420,f831,f3822]) ).
fof(f3820,plain,
( spl0_329
| ~ spl0_7
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f948,f925,f238,f3818]) ).
fof(f3818,plain,
( spl0_329
<=> ! [X0,X1] :
( y = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f948,plain,
( ! [X0,X1] :
( y = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_7
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f933]) ).
fof(f933,plain,
( ! [X0,X1] :
( y = intersection(unordered_pair(X0,X1),X1)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_7
| ~ spl0_118 ),
inference(superposition,[],[f239,f926]) ).
fof(f3816,plain,
( spl0_328
| ~ spl0_7
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f943,f925,f238,f3814]) ).
fof(f3814,plain,
( spl0_328
<=> ! [X0,X1] :
( y = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f943,plain,
( ! [X0,X1] :
( y = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_7
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f938]) ).
fof(f938,plain,
( ! [X0,X1] :
( y = intersection(unordered_pair(X0,X1),X0)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y )
| ~ spl0_7
| ~ spl0_118 ),
inference(superposition,[],[f239,f926]) ).
fof(f3812,plain,
( spl0_327
| ~ spl0_109
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f906,f888,f831,f3810]) ).
fof(f906,plain,
( ! [X0,X1] :
( member(regular(X0),y)
| ~ member(regular(X0),X1)
| y = X1
| ~ subclass(X0,regular(X1))
| y = X0 )
| ~ spl0_109
| ~ spl0_113 ),
inference(resolution,[],[f889,f832]) ).
fof(f3807,plain,
( spl0_326
| ~ spl0_241
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f3712,f3490,f2306,f3804]) ).
fof(f3712,plain,
( member(second(y),universal_class)
| ~ spl0_241
| ~ spl0_306 ),
inference(resolution,[],[f3491,f2308]) ).
fof(f2308,plain,
( member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2306]) ).
fof(f3709,plain,
( spl0_325
| ~ spl0_74
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f3445,f965,f613,f3707]) ).
fof(f3707,plain,
( spl0_325
<=> ! [X0,X1] :
( ~ member(y,cross_product(X0,X1))
| member(first(y),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f965,plain,
( spl0_121
<=> y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f3445,plain,
( ! [X0,X1] :
( ~ member(y,cross_product(X0,X1))
| member(first(y),X0) )
| ~ spl0_74
| ~ spl0_121 ),
inference(superposition,[],[f614,f967]) ).
fof(f967,plain,
( y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y))))
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f3701,plain,
( spl0_324
| spl0_124
| ~ spl0_30
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f802,f789,f338,f978,f3699]) ).
fof(f3699,plain,
( spl0_324
<=> ! [X0,X1] : ~ inductive(compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f802,plain,
( ! [X0,X1] :
( member(y,cross_product(universal_class,universal_class))
| ~ inductive(compose(X0,X1)) )
| ~ spl0_30
| ~ spl0_105 ),
inference(resolution,[],[f790,f339]) ).
fof(f3697,plain,
( spl0_124
| ~ spl0_10
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2256,f2235,f251,f978]) ).
fof(f2235,plain,
( spl0_231
<=> ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(y,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2256,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ spl0_10
| ~ spl0_231 ),
inference(resolution,[],[f2236,f252]) ).
fof(f2236,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(y,X0) )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2235]) ).
fof(f3636,plain,
( spl0_323
| ~ spl0_7
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1684,f1642,f238,f3634]) ).
fof(f1684,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X1,y),regular(X0))
| ~ member(not_subclass_element(X1,y),X0)
| subclass(X1,y)
| y = X0 )
| ~ spl0_7
| ~ spl0_191 ),
inference(superposition,[],[f1643,f239]) ).
fof(f3630,plain,
( spl0_321
| ~ spl0_322
| ~ spl0_106
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1284,f1264,f810,f3627,f3623]) ).
fof(f1284,plain,
( ~ member(regular(complement(domain_of(flip(cross_product(subset_relation,universal_class))))),identity_relation)
| y = complement(domain_of(flip(cross_product(subset_relation,universal_class))))
| ~ spl0_106
| ~ spl0_153 ),
inference(resolution,[],[f1265,f811]) ).
fof(f3619,plain,
( spl0_319
| ~ spl0_320
| ~ spl0_106
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1278,f1260,f810,f3616,f3612]) ).
fof(f1278,plain,
( ~ member(regular(complement(complement(compose(element_relation,complement(identity_relation))))),singleton_relation)
| y = complement(complement(compose(element_relation,complement(identity_relation))))
| ~ spl0_106
| ~ spl0_152 ),
inference(resolution,[],[f1261,f811]) ).
fof(f3610,plain,
( spl0_318
| ~ spl0_113
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1120,f1078,f888,f3608]) ).
fof(f1120,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,regular(X0))
| member(unordered_pair(X1,X2),y)
| ~ member(unordered_pair(X1,X2),X0)
| y = X0 )
| ~ spl0_113
| ~ spl0_137 ),
inference(resolution,[],[f1079,f889]) ).
fof(f3606,plain,
( spl0_317
| ~ spl0_108
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f949,f925,f826,f3604]) ).
fof(f3604,plain,
( spl0_317
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,y)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f949,plain,
( ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,y)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_108
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f932]) ).
fof(f932,plain,
( ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,y)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_108
| ~ spl0_118 ),
inference(superposition,[],[f827,f926]) ).
fof(f3602,plain,
( spl0_316
| ~ spl0_108
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f944,f925,f826,f3600]) ).
fof(f3600,plain,
( spl0_316
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,y)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f944,plain,
( ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,y)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_108
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f937]) ).
fof(f937,plain,
( ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,y)
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y )
| ~ spl0_108
| ~ spl0_118 ),
inference(superposition,[],[f827,f926]) ).
fof(f3598,plain,
( spl0_315
| ~ spl0_2
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f903,f888,f213,f3596]) ).
fof(f903,plain,
( ! [X0] :
( member(regular(regular(X0)),y)
| ~ member(regular(regular(X0)),X0)
| y = X0
| regular(X0) = y )
| ~ spl0_2
| ~ spl0_113 ),
inference(resolution,[],[f889,f214]) ).
fof(f3594,plain,
( spl0_314
| ~ spl0_51
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f818,f810,f472,f3592]) ).
fof(f818,plain,
( ! [X0] :
( y = complement(complement(X0))
| member(regular(complement(complement(X0))),X0)
| ~ member(regular(complement(complement(X0))),universal_class) )
| ~ spl0_51
| ~ spl0_106 ),
inference(resolution,[],[f811,f473]) ).
fof(f3590,plain,
( ~ spl0_312
| spl0_313
| ~ spl0_20
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1192,f1181,f296,f3587,f3583]) ).
fof(f3583,plain,
( spl0_312
<=> single_valued_class(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f3587,plain,
( spl0_313
<=> function(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f1192,plain,
( function(domain_relation)
| ~ single_valued_class(domain_relation)
| ~ spl0_20
| ~ spl0_142 ),
inference(resolution,[],[f1182,f298]) ).
fof(f3581,plain,
( ~ spl0_311
| ~ spl0_6
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f3493,f2248,f233,f3578]) ).
fof(f3578,plain,
( spl0_311
<=> inductive(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f3493,plain,
( ~ inductive(choice)
| ~ spl0_6
| ~ spl0_233 ),
inference(resolution,[],[f2249,f235]) ).
fof(f3576,plain,
( ~ spl0_309
| spl0_310
| ~ spl0_18
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1188,f1181,f287,f3573,f3569]) ).
fof(f3569,plain,
( spl0_309
<=> single_valued_class(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f3573,plain,
( spl0_310
<=> function(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f1188,plain,
( function(successor_relation)
| ~ single_valued_class(successor_relation)
| ~ spl0_18
| ~ spl0_142 ),
inference(resolution,[],[f1182,f289]) ).
fof(f3567,plain,
( ~ spl0_307
| spl0_308
| ~ spl0_17
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1186,f1181,f282,f3564,f3560]) ).
fof(f3560,plain,
( spl0_307
<=> single_valued_class(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f3564,plain,
( spl0_308
<=> function(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f1186,plain,
( function(element_relation)
| ~ single_valued_class(element_relation)
| ~ spl0_17
| ~ spl0_142 ),
inference(resolution,[],[f1182,f284]) ).
fof(f3492,plain,
( spl0_306
| ~ spl0_73
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f3444,f965,f609,f3490]) ).
fof(f3444,plain,
( ! [X0,X1] :
( ~ member(y,cross_product(X0,X1))
| member(second(y),X1) )
| ~ spl0_73
| ~ spl0_121 ),
inference(superposition,[],[f610,f967]) ).
fof(f3487,plain,
( spl0_304
| ~ spl0_305
| ~ spl0_68
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f3443,f965,f583,f3484,f3480]) ).
fof(f3443,plain,
( ~ member(y,domain_relation)
| second(y) = domain_of(first(y))
| ~ spl0_68
| ~ spl0_121 ),
inference(superposition,[],[f584,f967]) ).
fof(f3441,plain,
( spl0_121
| ~ spl0_82
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f2227,f978,f665,f965]) ).
fof(f2227,plain,
( y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y))))
| ~ spl0_82
| ~ spl0_124 ),
inference(resolution,[],[f979,f666]) ).
fof(f979,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f978]) ).
fof(f3440,plain,
( spl0_303
| ~ spl0_7
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1543,f1533,f238,f3438]) ).
fof(f3438,plain,
( spl0_303
<=> ! [X2,X0,X1] :
( ~ subclass(y,X1)
| ~ member(X2,X0)
| ~ member(X2,regular(X0))
| member(X2,X1)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f1543,plain,
( ! [X2,X0,X1] :
( ~ subclass(y,X1)
| ~ member(X2,X0)
| ~ member(X2,regular(X0))
| member(X2,X1)
| y = X0 )
| ~ spl0_7
| ~ spl0_178 ),
inference(superposition,[],[f1534,f239]) ).
fof(f3436,plain,
( spl0_302
| ~ spl0_2
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f947,f925,f213,f3434]) ).
fof(f947,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0 )
| ~ spl0_2
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f934]) ).
fof(f934,plain,
( ! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_2
| ~ spl0_118 ),
inference(superposition,[],[f214,f926]) ).
fof(f3432,plain,
( spl0_301
| ~ spl0_2
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f942,f925,f213,f3430]) ).
fof(f942,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1 )
| ~ spl0_2
| ~ spl0_118 ),
inference(duplicate_literal_removal,[],[f939]) ).
fof(f939,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| unordered_pair(X0,X1) = y
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y )
| ~ spl0_2
| ~ spl0_118 ),
inference(superposition,[],[f214,f926]) ).
fof(f3428,plain,
( spl0_300
| ~ spl0_55
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f843,f831,f492,f3426]) ).
fof(f843,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| y = X0
| regular(X0) = X1
| regular(X0) = X2 )
| ~ spl0_55
| ~ spl0_109 ),
inference(resolution,[],[f832,f493]) ).
fof(f3424,plain,
( spl0_299
| ~ spl0_253
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2940,f2834,f2527,f3421]) ).
fof(f3421,plain,
( spl0_299
<=> y = intersection(complement(element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2940,plain,
( y = intersection(complement(element_relation),singleton_relation)
| ~ spl0_253
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2923]) ).
fof(f2923,plain,
( y = intersection(complement(element_relation),singleton_relation)
| y = intersection(complement(element_relation),singleton_relation)
| ~ spl0_253
| ~ spl0_274 ),
inference(resolution,[],[f2835,f2528]) ).
fof(f3237,plain,
( spl0_298
| ~ spl0_107
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1399,f1351,f814,f3235]) ).
fof(f1399,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,y),X1)
| member(not_subclass_element(intersection(X0,y),X1),X2)
| y = X2 )
| ~ spl0_107
| ~ spl0_161 ),
inference(resolution,[],[f1352,f815]) ).
fof(f3233,plain,
( spl0_297
| ~ spl0_107
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1378,f1347,f814,f3231]) ).
fof(f1378,plain,
( ! [X2,X0,X1] :
( subclass(intersection(y,X0),X1)
| member(not_subclass_element(intersection(y,X0),X1),X2)
| y = X2 )
| ~ spl0_107
| ~ spl0_160 ),
inference(resolution,[],[f1348,f815]) ).
fof(f3229,plain,
( spl0_296
| ~ spl0_108
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1271,f1229,f826,f3227]) ).
fof(f3227,plain,
( spl0_296
<=> ! [X0,X1] :
( subclass(complement(regular(X0)),X1)
| ~ member(not_subclass_element(complement(regular(X0)),X1),y)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f1271,plain,
( ! [X0,X1] :
( subclass(complement(regular(X0)),X1)
| ~ member(not_subclass_element(complement(regular(X0)),X1),y)
| y = X0 )
| ~ spl0_108
| ~ spl0_145 ),
inference(resolution,[],[f1230,f827]) ).
fof(f3225,plain,
( spl0_295
| ~ spl0_255
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2938,f2834,f2537,f3222]) ).
fof(f2938,plain,
( y = intersection(complement(subset_relation),identity_relation)
| ~ spl0_255
| ~ spl0_274 ),
inference(duplicate_literal_removal,[],[f2932]) ).
fof(f2932,plain,
( y = intersection(complement(subset_relation),identity_relation)
| y = intersection(complement(subset_relation),identity_relation)
| ~ spl0_255
| ~ spl0_274 ),
inference(resolution,[],[f2835,f2538]) ).
fof(f3220,plain,
( ~ spl0_293
| spl0_294
| ~ spl0_1
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f916,f912,f209,f3217,f3213]) ).
fof(f916,plain,
( y = cross_product(unordered_pair(y,y),universal_class)
| ~ inductive(domain_of(regular(cross_product(unordered_pair(y,y),universal_class))))
| ~ spl0_1
| ~ spl0_116 ),
inference(resolution,[],[f913,f210]) ).
fof(f3211,plain,
( spl0_292
| ~ spl0_39
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f877,f856,f381,f3209]) ).
fof(f877,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X1) )
| ~ spl0_39
| ~ spl0_112 ),
inference(resolution,[],[f857,f382]) ).
fof(f3207,plain,
( spl0_291
| ~ spl0_40
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f876,f856,f385,f3205]) ).
fof(f876,plain,
( ! [X2,X0,X1] :
( y = intersection(X0,intersection(X1,X2))
| member(regular(intersection(X0,intersection(X1,X2))),X2) )
| ~ spl0_40
| ~ spl0_112 ),
inference(resolution,[],[f857,f386]) ).
fof(f3203,plain,
( spl0_290
| ~ spl0_39
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f863,f852,f381,f3201]) ).
fof(f863,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X0) )
| ~ spl0_39
| ~ spl0_111 ),
inference(resolution,[],[f853,f382]) ).
fof(f3199,plain,
( spl0_289
| ~ spl0_40
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f862,f852,f385,f3197]) ).
fof(f862,plain,
( ! [X2,X0,X1] :
( y = intersection(intersection(X0,X1),X2)
| member(regular(intersection(intersection(X0,X1),X2)),X1) )
| ~ spl0_40
| ~ spl0_111 ),
inference(resolution,[],[f853,f386]) ).
fof(f3144,plain,
( spl0_288
| ~ spl0_35
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2591,f2446,f365,f3142]) ).
fof(f2446,plain,
( spl0_247
<=> ! [X0,X1] :
( member(not_subclass_element(y,X0),X1)
| y = X1
| subclass(y,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2591,plain,
( ! [X0] :
( y = X0
| subclass(y,X0) )
| ~ spl0_35
| ~ spl0_247 ),
inference(duplicate_literal_removal,[],[f2565]) ).
fof(f2565,plain,
( ! [X0] :
( y = X0
| subclass(y,X0)
| subclass(y,X0) )
| ~ spl0_35
| ~ spl0_247 ),
inference(resolution,[],[f2447,f366]) ).
fof(f2447,plain,
( ! [X0,X1] :
( member(not_subclass_element(y,X0),X1)
| y = X1
| subclass(y,X0) )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2446]) ).
fof(f3025,plain,
( spl0_287
| ~ spl0_107
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1321,f1287,f814,f3023]) ).
fof(f3023,plain,
( spl0_287
<=> ! [X2,X0,X1] :
( ~ subclass(X0,y)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f1321,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,y)
| subclass(X0,X1)
| member(not_subclass_element(X0,X1),X2)
| y = X2 )
| ~ spl0_107
| ~ spl0_154 ),
inference(resolution,[],[f1288,f815]) ).
fof(f3021,plain,
( spl0_286
| ~ spl0_137
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1227,f1199,f1078,f3019]) ).
fof(f1227,plain,
( ! [X2,X0,X1] :
( member(regular(cross_product(X0,X1)),X2)
| ~ subclass(universal_class,X2)
| cross_product(X0,X1) = y )
| ~ spl0_137
| ~ spl0_144 ),
inference(superposition,[],[f1079,f1200]) ).
fof(f3017,plain,
( spl0_285
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f941,f925,f3015]) ).
fof(f3015,plain,
( spl0_285
<=> ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f941,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y )
| ~ spl0_118 ),
inference(equality_factoring,[],[f926]) ).
fof(f2998,plain,
( spl0_284
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f940,f925,f2996]) ).
fof(f940,plain,
( ! [X0,X1] :
( X0 != X1
| regular(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = y )
| ~ spl0_118 ),
inference(equality_factoring,[],[f926]) ).
fof(f2994,plain,
( spl0_283
| ~ spl0_107
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f880,f856,f814,f2992]) ).
fof(f2992,plain,
( spl0_283
<=> ! [X0,X1] :
( y = intersection(X0,y)
| member(regular(intersection(X0,y)),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f880,plain,
( ! [X0,X1] :
( y = intersection(X0,y)
| member(regular(intersection(X0,y)),X1)
| y = X1 )
| ~ spl0_107
| ~ spl0_112 ),
inference(resolution,[],[f857,f815]) ).
fof(f2990,plain,
( spl0_282
| ~ spl0_46
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f873,f856,f424,f2988]) ).
fof(f873,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(X1,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_46
| ~ spl0_112 ),
inference(resolution,[],[f857,f425]) ).
fof(f2986,plain,
( spl0_281
| ~ spl0_107
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f866,f852,f814,f2984]) ).
fof(f2984,plain,
( spl0_281
<=> ! [X0,X1] :
( y = intersection(y,X0)
| member(regular(intersection(y,X0)),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f866,plain,
( ! [X0,X1] :
( y = intersection(y,X0)
| member(regular(intersection(y,X0)),X1)
| y = X1 )
| ~ spl0_107
| ~ spl0_111 ),
inference(resolution,[],[f853,f815]) ).
fof(f2982,plain,
( spl0_280
| ~ spl0_46
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f859,f852,f424,f2980]) ).
fof(f859,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = y
| ~ subclass(X0,X2)
| member(regular(intersection(X0,X1)),X2) )
| ~ spl0_46
| ~ spl0_111 ),
inference(resolution,[],[f853,f425]) ).
fof(f2978,plain,
( spl0_279
| ~ spl0_106
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f840,f826,f810,f2976]) ).
fof(f2976,plain,
( spl0_279
<=> ! [X0] :
( ~ member(regular(complement(regular(X0))),y)
| y = X0
| y = complement(regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f840,plain,
( ! [X0] :
( ~ member(regular(complement(regular(X0))),y)
| y = X0
| y = complement(regular(X0)) )
| ~ spl0_106
| ~ spl0_108 ),
inference(resolution,[],[f827,f811]) ).
fof(f2974,plain,
( spl0_278
| ~ spl0_63
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f796,f789,f555,f2972]) ).
fof(f2972,plain,
( spl0_278
<=> ! [X0] :
( member(y,domain_of(domain_of(X0)))
| ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| ~ operation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f796,plain,
( ! [X0] :
( member(y,domain_of(domain_of(X0)))
| ~ inductive(domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| ~ operation(X0) )
| ~ spl0_63
| ~ spl0_105 ),
inference(resolution,[],[f790,f556]) ).
fof(f2945,plain,
( spl0_97
| ~ spl0_131
| ~ spl0_268 ),
inference(avatar_split_clause,[],[f2814,f2805,f1009,f750]) ).
fof(f2814,plain,
( member(y,subset_relation)
| ~ spl0_131
| ~ spl0_268 ),
inference(resolution,[],[f2807,f1010]) ).
fof(f2807,plain,
( member(y,identity_relation)
| ~ spl0_268 ),
inference(avatar_component_clause,[],[f2805]) ).
fof(f2849,plain,
( spl0_276
| ~ spl0_277
| ~ spl0_106
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1136,f1089,f810,f2846,f2842]) ).
fof(f1136,plain,
( ~ member(regular(complement(cross_product(universal_class,universal_class))),subset_relation)
| y = complement(cross_product(universal_class,universal_class))
| ~ spl0_106
| ~ spl0_139 ),
inference(resolution,[],[f1090,f811]) ).
fof(f2840,plain,
( spl0_275
| ~ spl0_29
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f878,f856,f334,f2838]) ).
fof(f878,plain,
( ! [X0,X1] :
( y = intersection(X0,complement(X1))
| ~ member(regular(intersection(X0,complement(X1))),X1) )
| ~ spl0_29
| ~ spl0_112 ),
inference(resolution,[],[f857,f335]) ).
fof(f2836,plain,
( spl0_274
| ~ spl0_29
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f864,f852,f334,f2834]) ).
fof(f864,plain,
( ! [X0,X1] :
( y = intersection(complement(X0),X1)
| ~ member(regular(intersection(complement(X0),X1)),X0) )
| ~ spl0_29
| ~ spl0_111 ),
inference(resolution,[],[f853,f335]) ).
fof(f2832,plain,
( spl0_273
| ~ spl0_107
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f849,f831,f814,f2830]) ).
fof(f2830,plain,
( spl0_273
<=> ! [X0,X1] :
( ~ subclass(X0,y)
| y = X0
| member(regular(X0),X1)
| y = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f849,plain,
( ! [X0,X1] :
( ~ subclass(X0,y)
| y = X0
| member(regular(X0),X1)
| y = X1 )
| ~ spl0_107
| ~ spl0_109 ),
inference(resolution,[],[f832,f815]) ).
fof(f2828,plain,
( spl0_272
| ~ spl0_46
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f842,f831,f424,f2826]) ).
fof(f842,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| y = X0
| ~ subclass(X1,X2)
| member(regular(X0),X2) )
| ~ spl0_46
| ~ spl0_109 ),
inference(resolution,[],[f832,f425]) ).
fof(f2824,plain,
( spl0_271
| ~ spl0_35
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f839,f826,f365,f2822]) ).
fof(f839,plain,
( ! [X0,X1] :
( ~ member(not_subclass_element(X0,regular(X1)),y)
| y = X1
| subclass(X0,regular(X1)) )
| ~ spl0_35
| ~ spl0_108 ),
inference(resolution,[],[f827,f366]) ).
fof(f2820,plain,
( spl0_270
| ~ spl0_46
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f838,f826,f424,f2818]) ).
fof(f2818,plain,
( spl0_270
<=> ! [X2,X0,X1] :
( ~ member(X0,y)
| y = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f838,plain,
( ! [X2,X0,X1] :
( ~ member(X0,y)
| y = X1
| ~ subclass(regular(X1),X2)
| member(X0,X2) )
| ~ spl0_46
| ~ spl0_108 ),
inference(resolution,[],[f827,f425]) ).
fof(f2813,plain,
( spl0_269
| spl0_268
| ~ spl0_58
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f804,f789,f504,f2805,f2811]) ).
fof(f2811,plain,
( spl0_269
<=> ! [X0] :
( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ single_valued_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f504,plain,
( spl0_58
<=> ! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f804,plain,
( ! [X0] :
( member(y,identity_relation)
| ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ single_valued_class(X0) )
| ~ spl0_58
| ~ spl0_105 ),
inference(resolution,[],[f790,f505]) ).
fof(f505,plain,
( ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ single_valued_class(X0) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f2808,plain,
( spl0_267
| spl0_268
| ~ spl0_59
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f803,f789,f508,f2805,f2802]) ).
fof(f2802,plain,
( spl0_267
<=> ! [X0] :
( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f508,plain,
( spl0_59
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f803,plain,
( ! [X0] :
( member(y,identity_relation)
| ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) )
| ~ spl0_59
| ~ spl0_105 ),
inference(resolution,[],[f790,f509]) ).
fof(f509,plain,
( ! [X8] :
( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
| ~ function(X8) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f2766,plain,
( spl0_266
| ~ spl0_7
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1400,f1351,f238,f2764]) ).
fof(f2764,plain,
( spl0_266
<=> ! [X0,X1] :
( member(not_subclass_element(y,X1),regular(X0))
| subclass(y,X1)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1400,plain,
( ! [X0,X1] :
( member(not_subclass_element(y,X1),regular(X0))
| subclass(y,X1)
| y = X0 )
| ~ spl0_7
| ~ spl0_161 ),
inference(superposition,[],[f1352,f239]) ).
fof(f2757,plain,
( spl0_264
| spl0_265
| ~ spl0_1
| ~ spl0_113 ),
inference(avatar_split_clause,[],[f905,f888,f209,f2754,f2751]) ).
fof(f2751,plain,
( spl0_264
<=> ! [X0] :
( ~ member(y,X0)
| ~ inductive(regular(X0))
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2754,plain,
( spl0_265
<=> member(y,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f905,plain,
( ! [X0] :
( member(y,y)
| ~ member(y,X0)
| y = X0
| ~ inductive(regular(X0)) )
| ~ spl0_1
| ~ spl0_113 ),
inference(resolution,[],[f889,f210]) ).
fof(f2749,plain,
( spl0_263
| ~ spl0_39
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f846,f831,f381,f2747]) ).
fof(f846,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = X0
| member(regular(X0),X1) )
| ~ spl0_39
| ~ spl0_109 ),
inference(resolution,[],[f832,f382]) ).
fof(f2745,plain,
( spl0_262
| ~ spl0_40
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f845,f831,f385,f2743]) ).
fof(f845,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| y = X0
| member(regular(X0),X2) )
| ~ spl0_40
| ~ spl0_109 ),
inference(resolution,[],[f832,f386]) ).
fof(f2708,plain,
( spl0_261
| ~ spl0_186
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2525,f2522,f1601,f2706]) ).
fof(f2525,plain,
( ! [X0] :
( identity_relation = intersection(singleton_relation,X0)
| member(regular(intersection(singleton_relation,X0)),element_relation) )
| ~ spl0_186
| ~ spl0_252 ),
inference(forward_demodulation,[],[f2523,f1603]) ).
fof(f2564,plain,
( ~ spl0_260
| spl0_69
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1656,f1601,f587,f2561]) ).
fof(f2561,plain,
( spl0_260
<=> member(identity_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1656,plain,
( ~ member(identity_relation,element_relation)
| spl0_69
| ~ spl0_186 ),
inference(superposition,[],[f588,f1603]) ).
fof(f2558,plain,
( spl0_259
| ~ spl0_16
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1220,f1199,f278,f2556]) ).
fof(f2556,plain,
( spl0_259
<=> ! [X0,X1] :
( member(regular(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1220,plain,
( ! [X0,X1] :
( member(regular(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_16
| ~ spl0_144 ),
inference(superposition,[],[f279,f1200]) ).
fof(f2554,plain,
( ~ spl0_258
| ~ spl0_186
| spl0_257 ),
inference(avatar_split_clause,[],[f2549,f2545,f1601,f2551]) ).
fof(f2551,plain,
( spl0_258
<=> subclass(universal_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2545,plain,
( spl0_257
<=> subclass(universal_class,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2549,plain,
( ~ subclass(universal_class,identity_relation)
| ~ spl0_186
| spl0_257 ),
inference(forward_demodulation,[],[f2547,f1603]) ).
fof(f2547,plain,
( ~ subclass(universal_class,y)
| spl0_257 ),
inference(avatar_component_clause,[],[f2545]) ).
fof(f2548,plain,
( spl0_256
| ~ spl0_257
| ~ spl0_107
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1122,f1078,f814,f2545,f2542]) ).
fof(f2542,plain,
( spl0_256
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| y = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1122,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,y)
| member(unordered_pair(X0,X1),X2)
| y = X2 )
| ~ spl0_107
| ~ spl0_137 ),
inference(resolution,[],[f1079,f815]) ).
fof(f2539,plain,
( spl0_255
| ~ spl0_112
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1031,f1009,f856,f2537]) ).
fof(f1031,plain,
( ! [X0] :
( member(regular(intersection(X0,identity_relation)),subset_relation)
| y = intersection(X0,identity_relation) )
| ~ spl0_112
| ~ spl0_131 ),
inference(resolution,[],[f1010,f857]) ).
fof(f2534,plain,
( spl0_254
| ~ spl0_111
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1028,f1009,f852,f2532]) ).
fof(f1028,plain,
( ! [X0] :
( member(regular(intersection(identity_relation,X0)),subset_relation)
| y = intersection(identity_relation,X0) )
| ~ spl0_111
| ~ spl0_131 ),
inference(resolution,[],[f1010,f853]) ).
fof(f2529,plain,
( spl0_253
| ~ spl0_112
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1024,f1005,f856,f2527]) ).
fof(f1024,plain,
( ! [X0] :
( member(regular(intersection(X0,singleton_relation)),element_relation)
| y = intersection(X0,singleton_relation) )
| ~ spl0_112
| ~ spl0_130 ),
inference(resolution,[],[f1006,f857]) ).
fof(f2524,plain,
( spl0_252
| ~ spl0_111
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1021,f1005,f852,f2522]) ).
fof(f1021,plain,
( ! [X0] :
( member(regular(intersection(singleton_relation,X0)),element_relation)
| y = intersection(singleton_relation,X0) )
| ~ spl0_111
| ~ spl0_130 ),
inference(resolution,[],[f1006,f853]) ).
fof(f2510,plain,
( spl0_21
| ~ spl0_8
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1085,f1033,f242,f301]) ).
fof(f1085,plain,
( member(y,universal_class)
| ~ spl0_8
| ~ spl0_132 ),
inference(resolution,[],[f1034,f243]) ).
fof(f2493,plain,
( spl0_251
| ~ spl0_168
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f2488,f1601,f1428,f2490]) ).
fof(f2490,plain,
( spl0_251
<=> identity_relation = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2488,plain,
( identity_relation = singleton_relation
| ~ spl0_168
| ~ spl0_186 ),
inference(forward_demodulation,[],[f1603,f1430]) ).
fof(f2485,plain,
( spl0_186
| spl0_250
| ~ spl0_50
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f872,f852,f441,f2482,f1601]) ).
fof(f872,plain,
( member(regular(identity_relation),domain_of(flip(cross_product(subset_relation,universal_class))))
| identity_relation = y
| ~ spl0_50
| ~ spl0_111 ),
inference(superposition,[],[f853,f443]) ).
fof(f2457,plain,
( spl0_168
| spl0_249
| ~ spl0_49
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f871,f852,f436,f2454,f1428]) ).
fof(f871,plain,
( member(regular(singleton_relation),complement(compose(element_relation,complement(identity_relation))))
| singleton_relation = y
| ~ spl0_49
| ~ spl0_111 ),
inference(superposition,[],[f853,f438]) ).
fof(f2452,plain,
( spl0_248
| ~ spl0_29
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f847,f831,f334,f2450]) ).
fof(f847,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| y = X0
| ~ member(regular(X0),X1) )
| ~ spl0_29
| ~ spl0_109 ),
inference(resolution,[],[f832,f335]) ).
fof(f2448,plain,
( spl0_247
| ~ spl0_34
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f821,f814,f361,f2446]) ).
fof(f821,plain,
( ! [X0,X1] :
( member(not_subclass_element(y,X0),X1)
| y = X1
| subclass(y,X0) )
| ~ spl0_34
| ~ spl0_107 ),
inference(resolution,[],[f815,f362]) ).
fof(f2428,plain,
( spl0_246
| ~ spl0_109
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1030,f1009,f831,f2426]) ).
fof(f1030,plain,
( ! [X0] :
( member(regular(X0),subset_relation)
| ~ subclass(X0,identity_relation)
| y = X0 )
| ~ spl0_109
| ~ spl0_131 ),
inference(resolution,[],[f1010,f832]) ).
fof(f2424,plain,
( spl0_245
| ~ spl0_109
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1023,f1005,f831,f2422]) ).
fof(f1023,plain,
( ! [X0] :
( member(regular(X0),element_relation)
| ~ subclass(X0,singleton_relation)
| y = X0 )
| ~ spl0_109
| ~ spl0_130 ),
inference(resolution,[],[f1006,f832]) ).
fof(f2336,plain,
( ~ spl0_5
| ~ spl0_127 ),
inference(avatar_contradiction_clause,[],[f2333]) ).
fof(f2333,plain,
( $false
| ~ spl0_5
| ~ spl0_127 ),
inference(resolution,[],[f993,f230]) ).
fof(f230,plain,
( inductive(omega)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f993,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f992,plain,
( spl0_127
<=> ! [X0] : ~ inductive(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f2335,plain,
( ~ spl0_22
| ~ spl0_127 ),
inference(avatar_contradiction_clause,[],[f2334]) ).
fof(f2334,plain,
( $false
| ~ spl0_22
| ~ spl0_127 ),
inference(resolution,[],[f993,f307]) ).
fof(f307,plain,
( inductive(universal_class)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f2325,plain,
( spl0_244
| ~ spl0_21
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2289,f2279,f301,f2322]) ).
fof(f2289,plain,
( member(subset_relation,universal_class)
| ~ spl0_21
| ~ spl0_238 ),
inference(superposition,[],[f302,f2281]) ).
fof(f2319,plain,
( spl0_243
| spl0_241
| ~ spl0_42
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f799,f789,f393,f2306,f2317]) ).
fof(f2317,plain,
( spl0_243
<=> ! [X0] : ~ inductive(flip(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f799,plain,
( ! [X0] :
( member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X0)) )
| ~ spl0_42
| ~ spl0_105 ),
inference(resolution,[],[f790,f394]) ).
fof(f2315,plain,
( ~ spl0_242
| ~ spl0_238
| spl0_241 ),
inference(avatar_split_clause,[],[f2310,f2306,f2279,f2312]) ).
fof(f2312,plain,
( spl0_242
<=> member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2310,plain,
( ~ member(subset_relation,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl0_238
| spl0_241 ),
inference(forward_demodulation,[],[f2307,f2281]) ).
fof(f2309,plain,
( spl0_240
| spl0_241
| ~ spl0_41
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f798,f789,f389,f2306,f2303]) ).
fof(f2303,plain,
( spl0_240
<=> ! [X0] : ~ inductive(rotate(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f798,plain,
( ! [X0] :
( member(y,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X0)) )
| ~ spl0_41
| ~ spl0_105 ),
inference(resolution,[],[f790,f390]) ).
fof(f2286,plain,
( spl0_238
| spl0_239
| ~ spl0_79
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f870,f852,f642,f2283,f2279]) ).
fof(f870,plain,
( member(regular(subset_relation),cross_product(universal_class,universal_class))
| subset_relation = y
| ~ spl0_79
| ~ spl0_111 ),
inference(superposition,[],[f853,f644]) ).
fof(f2277,plain,
( ~ spl0_237
| spl0_235
| ~ spl0_33
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f808,f789,f352,f2263,f2274]) ).
fof(f2274,plain,
( spl0_237
<=> inductive(application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f808,plain,
( member(y,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(application_function)
| ~ spl0_33
| ~ spl0_105 ),
inference(resolution,[],[f790,f354]) ).
fof(f2272,plain,
( spl0_236
| ~ spl0_8
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2240,f2231,f242,f2269]) ).
fof(f2240,plain,
( y = complement(universal_class)
| ~ spl0_8
| ~ spl0_230 ),
inference(resolution,[],[f2232,f243]) ).
fof(f2266,plain,
( ~ spl0_234
| spl0_235
| ~ spl0_32
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f806,f789,f347,f2263,f2259]) ).
fof(f2259,plain,
( spl0_234
<=> inductive(composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f806,plain,
( member(y,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ inductive(composition_function)
| ~ spl0_32
| ~ spl0_105 ),
inference(resolution,[],[f790,f349]) ).
fof(f2250,plain,
( spl0_233
| spl0_124
| ~ spl0_31
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f794,f789,f342,f978,f2248]) ).
fof(f794,plain,
( ! [X0] :
( member(y,cross_product(universal_class,universal_class))
| ~ inductive(X0)
| ~ function(X0) )
| ~ spl0_31
| ~ spl0_105 ),
inference(resolution,[],[f790,f343]) ).
fof(f2246,plain,
( spl0_232
| ~ spl0_6
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f922,f919,f233,f2243]) ).
fof(f2243,plain,
( spl0_232
<=> single_valued_class(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f922,plain,
( single_valued_class(choice)
| ~ spl0_6
| ~ spl0_117 ),
inference(resolution,[],[f920,f235]) ).
fof(f2237,plain,
( spl0_231
| ~ spl0_46
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f2229,f978,f424,f2235]) ).
fof(f2229,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(y,X0) )
| ~ spl0_46
| ~ spl0_124 ),
inference(resolution,[],[f979,f425]) ).
fof(f2233,plain,
( spl0_230
| ~ spl0_106
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f850,f831,f810,f2231]) ).
fof(f850,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = y )
| ~ spl0_106
| ~ spl0_109 ),
inference(duplicate_literal_removal,[],[f841]) ).
fof(f841,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = y
| complement(X0) = y )
| ~ spl0_106
| ~ spl0_109 ),
inference(resolution,[],[f832,f811]) ).
fof(f2226,plain,
( spl0_229
| spl0_124
| ~ spl0_26
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f805,f789,f322,f978,f2224]) ).
fof(f2224,plain,
( spl0_229
<=> ! [X0] : ~ inductive(compose_class(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f805,plain,
( ! [X0] :
( member(y,cross_product(universal_class,universal_class))
| ~ inductive(compose_class(X0)) )
| ~ spl0_26
| ~ spl0_105 ),
inference(resolution,[],[f790,f323]) ).
fof(f2222,plain,
( spl0_227
| ~ spl0_228
| ~ spl0_7
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f519,f428,f238,f2219,f2216]) ).
fof(f2216,plain,
( spl0_227
<=> ! [X0] :
( member(y,X0)
| y = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2219,plain,
( spl0_228
<=> inductive(y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f428,plain,
( spl0_47
<=> ! [X0,X1] :
( member(y,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f519,plain,
( ! [X0] :
( ~ inductive(y)
| member(y,X0)
| y = X0 )
| ~ spl0_7
| ~ spl0_47 ),
inference(superposition,[],[f429,f239]) ).
fof(f429,plain,
( ! [X0,X1] :
( ~ inductive(intersection(X0,X1))
| member(y,X0) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f2205,plain,
( spl0_226
| ~ spl0_91
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f729,f725,f710,f2203]) ).
fof(f729,plain,
( ! [X2,X3,X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
| ~ operation(X4)
| ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
| ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
| ~ spl0_91
| ~ spl0_94 ),
inference(resolution,[],[f726,f711]) ).
fof(f2201,plain,
( spl0_225
| ~ spl0_57
| ~ spl0_91
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f783,f778,f710,f500,f2199]) ).
fof(f2199,plain,
( spl0_225
<=> ! [X2,X4,X0,X3,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
| ~ homomorphism(X0,X1,X2)
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f783,plain,
( ! [X2,X3,X0,X1,X4] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
| ~ homomorphism(X0,X1,X2)
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) )
| ~ spl0_57
| ~ spl0_91
| ~ spl0_103 ),
inference(forward_demodulation,[],[f781,f501]) ).
fof(f781,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ operation(X4)
| ~ compatible(X3,X1,X4)
| homomorphism(X3,X1,X4)
| ~ operation(X1) )
| ~ spl0_91
| ~ spl0_103 ),
inference(resolution,[],[f779,f711]) ).
fof(f2188,plain,
( spl0_224
| ~ spl0_34
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f730,f725,f361,f2186]) ).
fof(f730,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
| ~ spl0_34
| ~ spl0_94 ),
inference(resolution,[],[f726,f362]) ).
fof(f2177,plain,
( spl0_223
| ~ spl0_80
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f776,f773,f647,f2175]) ).
fof(f776,plain,
( ! [X2,X0,X1] :
( ~ member(X0,domain_of(X1))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class) )
| ~ spl0_80
| ~ spl0_102 ),
inference(resolution,[],[f774,f648]) ).
fof(f2124,plain,
( spl0_222
| ~ spl0_80
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f771,f767,f647,f2122]) ).
fof(f771,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_80
| ~ spl0_101 ),
inference(resolution,[],[f768,f648]) ).
fof(f2120,plain,
( spl0_221
| ~ spl0_80
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f770,f763,f647,f2118]) ).
fof(f770,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_80
| ~ spl0_100 ),
inference(resolution,[],[f764,f648]) ).
fof(f2110,plain,
( spl0_220
| ~ spl0_12
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f782,f778,f261,f2108]) ).
fof(f782,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ homomorphism(X0,X1,X2)
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
| ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
| y = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
| ~ spl0_12
| ~ spl0_103 ),
inference(resolution,[],[f779,f262]) ).
fof(f2106,plain,
( ~ spl0_219
| spl0_124
| ~ spl0_31
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1087,f1033,f342,f978,f2103]) ).
fof(f2103,plain,
( spl0_219
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1087,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl0_31
| ~ spl0_132 ),
inference(resolution,[],[f1034,f343]) ).
fof(f2092,plain,
( spl0_218
| ~ spl0_28
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f731,f725,f330,f2090]) ).
fof(f731,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_28
| ~ spl0_94 ),
inference(resolution,[],[f726,f331]) ).
fof(f2040,plain,
( spl0_217
| ~ spl0_80
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f668,f665,f647,f2038]) ).
fof(f668,plain,
( ! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
| ~ member(X1,X2)
| ~ member(X0,X3) )
| ~ spl0_80
| ~ spl0_82 ),
inference(resolution,[],[f666,f648]) ).
fof(f2001,plain,
( spl0_216
| ~ spl0_46
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f723,f719,f424,f1999]) ).
fof(f723,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ subclass(composition_function,X2)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) )
| ~ spl0_46
| ~ spl0_93 ),
inference(resolution,[],[f720,f425]) ).
fof(f1945,plain,
( spl0_215
| ~ spl0_57
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f737,f725,f500,f1943]) ).
fof(f737,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
| ~ spl0_57
| ~ spl0_94 ),
inference(superposition,[],[f726,f501]) ).
fof(f1941,plain,
( spl0_214
| ~ spl0_57
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f734,f725,f500,f1939]) ).
fof(f734,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
| ~ spl0_57
| ~ spl0_94 ),
inference(superposition,[],[f726,f501]) ).
fof(f1920,plain,
( spl0_213
| ~ spl0_34
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f669,f665,f361,f1918]) ).
fof(f669,plain,
( ! [X2,X0,X1] :
( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) )
| ~ spl0_34
| ~ spl0_82 ),
inference(resolution,[],[f666,f362]) ).
fof(f1891,plain,
( spl0_212
| ~ spl0_46
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f713,f710,f424,f1889]) ).
fof(f713,plain,
( ! [X2,X3,X0,X1] :
( ~ operation(X0)
| ~ compatible(X1,X2,X0)
| homomorphism(X1,X2,X0)
| ~ operation(X2)
| ~ subclass(domain_of(X2),X3)
| member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) )
| ~ spl0_46
| ~ spl0_91 ),
inference(resolution,[],[f711,f425]) ).
fof(f1885,plain,
( spl0_211
| ~ spl0_80
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f744,f741,f647,f1883]) ).
fof(f744,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_95 ),
inference(resolution,[],[f742,f648]) ).
fof(f1881,plain,
( spl0_210
| ~ spl0_28
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f670,f665,f330,f1879]) ).
fof(f1879,plain,
( spl0_210
<=> ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))))))
| ~ member(cross_product(X0,X1),universal_class)
| cross_product(X0,X1) = y ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f670,plain,
( ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))))))
| ~ member(cross_product(X0,X1),universal_class)
| cross_product(X0,X1) = y )
| ~ spl0_28
| ~ spl0_82 ),
inference(resolution,[],[f666,f331]) ).
fof(f1868,plain,
( spl0_209
| ~ spl0_2
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f732,f725,f213,f1866]) ).
fof(f732,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
| y = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_2
| ~ spl0_94 ),
inference(resolution,[],[f726,f214]) ).
fof(f1862,plain,
( spl0_208
| ~ spl0_48
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f581,f577,f432,f1860]) ).
fof(f581,plain,
( ! [X0] :
( ~ inductive(X0)
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
| ~ spl0_48
| ~ spl0_67 ),
inference(resolution,[],[f578,f433]) ).
fof(f1858,plain,
( ~ spl0_205
| ~ spl0_206
| spl0_207
| ~ spl0_77
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f650,f642,f629,f1855,f1851,f1847]) ).
fof(f1847,plain,
( spl0_205
<=> function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1851,plain,
( spl0_206
<=> member(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1855,plain,
( spl0_207
<=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f629,plain,
( spl0_77
<=> ! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f650,plain,
( member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
| ~ member(universal_class,universal_class)
| ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ spl0_77
| ~ spl0_79 ),
inference(superposition,[],[f630,f644]) ).
fof(f630,plain,
( ! [X0,X8] :
( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X8) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f1843,plain,
( spl0_204
| ~ spl0_80
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f704,f701,f647,f1841]) ).
fof(f704,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
| ~ member(compose(X1,X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_89 ),
inference(resolution,[],[f702,f648]) ).
fof(f1818,plain,
( spl0_203
| ~ spl0_56
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f652,f642,f496,f1816]) ).
fof(f652,plain,
( ! [X0] :
( member(X0,subset_relation)
| ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
| ~ member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_56
| ~ spl0_79 ),
inference(superposition,[],[f497,f644]) ).
fof(f1811,plain,
( spl0_202
| ~ spl0_46
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f659,f647,f424,f1809]) ).
fof(f659,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ subclass(cross_product(X3,X1),X4)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
| ~ spl0_46
| ~ spl0_80 ),
inference(resolution,[],[f648,f425]) ).
fof(f1807,plain,
( spl0_201
| ~ spl0_48
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f567,f555,f432,f1805]) ).
fof(f1805,plain,
( spl0_201
<=> ! [X0] :
( ~ operation(X0)
| ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f567,plain,
( ! [X0] :
( ~ operation(X0)
| ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
| domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
| ~ spl0_48
| ~ spl0_63 ),
inference(resolution,[],[f556,f433]) ).
fof(f1800,plain,
( spl0_200
| ~ spl0_67
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f600,f596,f577,f1798]) ).
fof(f1798,plain,
( spl0_200
<=> ! [X0] :
( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
| maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f596,plain,
( spl0_71
<=> ! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f600,plain,
( ! [X0] :
( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
| maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
| ~ inductive(X0) )
| ~ spl0_67
| ~ spl0_71 ),
inference(resolution,[],[f597,f578]) ).
fof(f597,plain,
( ! [X1,X8] :
( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| ~ function(X8)
| maps(X8,domain_of(X8),X1) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f1761,plain,
( spl0_199
| ~ spl0_21
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1655,f1601,f301,f1758]) ).
fof(f1655,plain,
( member(identity_relation,universal_class)
| ~ spl0_21
| ~ spl0_186 ),
inference(superposition,[],[f302,f1603]) ).
fof(f1756,plain,
( spl0_198
| ~ spl0_80
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f691,f683,f647,f1754]) ).
fof(f691,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_80
| ~ spl0_85 ),
inference(resolution,[],[f684,f648]) ).
fof(f1752,plain,
( spl0_197
| ~ spl0_46
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f640,f633,f424,f1750]) ).
fof(f633,plain,
( spl0_78
<=> ! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f640,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) )
| ~ spl0_46
| ~ spl0_78 ),
inference(resolution,[],[f634,f425]) ).
fof(f634,plain,
( ! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f1748,plain,
( spl0_196
| ~ spl0_46
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f636,f629,f424,f1746]) ).
fof(f636,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ function(X1)
| ~ subclass(universal_class,X2)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) )
| ~ spl0_46
| ~ spl0_77 ),
inference(resolution,[],[f630,f425]) ).
fof(f1744,plain,
( spl0_195
| ~ spl0_48
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f546,f508,f432,f1742]) ).
fof(f1742,plain,
( spl0_195
<=> ! [X0] :
( ~ function(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f546,plain,
( ! [X0] :
( ~ function(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
| ~ spl0_48
| ~ spl0_59 ),
inference(resolution,[],[f509,f433]) ).
fof(f1740,plain,
( spl0_194
| ~ spl0_48
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f545,f504,f432,f1738]) ).
fof(f1738,plain,
( spl0_194
<=> ! [X0] :
( ~ single_valued_class(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f545,plain,
( ! [X0] :
( ~ single_valued_class(X0)
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
| ~ spl0_48
| ~ spl0_58 ),
inference(resolution,[],[f505,f433]) ).
fof(f1652,plain,
( spl0_193
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f677,f674,f1650]) ).
fof(f674,plain,
( spl0_83
<=> ! [X9,X11,X10] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f677,plain,
( ! [X0,X1] :
( compatible(domain_of(X0),X0,X1)
| ~ function(domain_of(X0))
| ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
| ~ spl0_83 ),
inference(equality_resolution,[],[f675]) ).
fof(f675,plain,
( ! [X10,X11,X9] :
( domain_of(domain_of(X10)) != domain_of(X9)
| compatible(X9,X10,X11)
| ~ function(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f1648,plain,
( spl0_192
| ~ spl0_46
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f621,f605,f424,f1646]) ).
fof(f621,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(domain_relation,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) )
| ~ spl0_46
| ~ spl0_72 ),
inference(resolution,[],[f606,f425]) ).
fof(f1644,plain,
( spl0_191
| ~ spl0_35
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f531,f496,f365,f1642]) ).
fof(f531,plain,
( ! [X2,X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl0_35
| ~ spl0_56 ),
inference(resolution,[],[f497,f366]) ).
fof(f1640,plain,
( spl0_190
| ~ spl0_34
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f524,f492,f361,f1638]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( not_subclass_element(unordered_pair(X0,X1),X2) = X0
| not_subclass_element(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl0_34
| ~ spl0_55 ),
inference(resolution,[],[f493,f362]) ).
fof(f1627,plain,
( spl0_189
| ~ spl0_40
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f654,f642,f385,f1625]) ).
fof(f654,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
| ~ spl0_40
| ~ spl0_79 ),
inference(superposition,[],[f386,f644]) ).
fof(f1620,plain,
( spl0_188
| ~ spl0_57
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f637,f629,f500,f1618]) ).
fof(f637,plain,
( ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(X1) )
| ~ spl0_57
| ~ spl0_77 ),
inference(superposition,[],[f630,f501]) ).
fof(f1608,plain,
( spl0_186
| spl0_187
| ~ spl0_50
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f886,f856,f441,f1605,f1601]) ).
fof(f886,plain,
( member(regular(identity_relation),subset_relation)
| identity_relation = y
| ~ spl0_50
| ~ spl0_112 ),
inference(superposition,[],[f857,f443]) ).
fof(f1599,plain,
( spl0_185
| ~ spl0_31
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f603,f596,f342,f1597]) ).
fof(f1597,plain,
( spl0_185
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f603,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
| ~ spl0_31
| ~ spl0_71 ),
inference(resolution,[],[f597,f343]) ).
fof(f1595,plain,
( spl0_184
| ~ spl0_35
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f489,f472,f365,f1593]) ).
fof(f489,plain,
( ! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) )
| ~ spl0_35
| ~ spl0_51 ),
inference(resolution,[],[f473,f366]) ).
fof(f1591,plain,
( spl0_183
| ~ spl0_42
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f459,f432,f393,f1589]) ).
fof(f459,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
| ~ spl0_42
| ~ spl0_48 ),
inference(resolution,[],[f433,f394]) ).
fof(f1587,plain,
( spl0_182
| ~ spl0_41
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f458,f432,f389,f1585]) ).
fof(f458,plain,
( ! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
| ~ spl0_41
| ~ spl0_48 ),
inference(resolution,[],[f433,f390]) ).
fof(f1577,plain,
( spl0_181
| ~ spl0_7
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f738,f725,f238,f1575]) ).
fof(f738,plain,
( ! [X2,X0,X1] :
( ~ member(X2,domain_of(domain_of(flip(cross_product(y,universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
| y = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
| ~ spl0_7
| ~ spl0_94 ),
inference(superposition,[],[f726,f239]) ).
fof(f1568,plain,
( spl0_180
| ~ spl0_12
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f728,f725,f261,f1566]) ).
fof(f728,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| ~ member(X1,universal_class)
| y = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
| ~ spl0_12
| ~ spl0_94 ),
inference(resolution,[],[f726,f262]) ).
fof(f1539,plain,
( spl0_179
| ~ spl0_46
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f549,f516,f424,f1537]) ).
fof(f516,plain,
( spl0_61
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f549,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(universal_class,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
| ~ spl0_46
| ~ spl0_61 ),
inference(resolution,[],[f517,f425]) ).
fof(f517,plain,
( ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1535,plain,
( spl0_178
| ~ spl0_46
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f530,f496,f424,f1533]) ).
fof(f530,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| ~ subclass(intersection(X2,X1),X3)
| member(X0,X3) )
| ~ spl0_46
| ~ spl0_56 ),
inference(resolution,[],[f497,f425]) ).
fof(f1531,plain,
( spl0_176
| ~ spl0_177
| ~ spl0_33
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f466,f432,f352,f1528,f1524]) ).
fof(f1524,plain,
( spl0_176
<=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f466,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
| ~ spl0_33
| ~ spl0_48 ),
inference(resolution,[],[f433,f354]) ).
fof(f1522,plain,
( spl0_174
| ~ spl0_175
| ~ spl0_32
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f464,f432,f347,f1519,f1515]) ).
fof(f464,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
| ~ spl0_32
| ~ spl0_48 ),
inference(resolution,[],[f433,f349]) ).
fof(f1513,plain,
( spl0_173
| ~ spl0_30
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f462,f432,f338,f1511]) ).
fof(f462,plain,
( ! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) )
| ~ spl0_30
| ~ spl0_48 ),
inference(resolution,[],[f433,f339]) ).
fof(f1506,plain,
( spl0_172
| ~ spl0_28
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f525,f492,f330,f1504]) ).
fof(f525,plain,
( ! [X0,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
| domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1
| ~ member(unordered_pair(X0,X1),universal_class)
| unordered_pair(X0,X1) = y )
| ~ spl0_28
| ~ spl0_55 ),
inference(resolution,[],[f493,f331]) ).
fof(f1499,plain,
( spl0_171
| ~ spl0_168
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1495,f1491,f1428,f1497]) ).
fof(f1495,plain,
( ! [X2,X0,X1] :
( singleton_relation = cross_product(unordered_pair(X0,X0),universal_class)
| ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
| ~ spl0_168
| ~ spl0_170 ),
inference(forward_demodulation,[],[f1494,f1430]) ).
fof(f1494,plain,
( ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(singleton_relation,universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_168
| ~ spl0_170 ),
inference(forward_demodulation,[],[f1492,f1430]) ).
fof(f1493,plain,
( spl0_170
| ~ spl0_7
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f735,f725,f238,f1491]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class),X2),universal_class)))))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_94 ),
inference(superposition,[],[f726,f239]) ).
fof(f1435,plain,
( spl0_168
| spl0_169
| ~ spl0_49
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f885,f856,f436,f1432,f1428]) ).
fof(f885,plain,
( member(regular(singleton_relation),element_relation)
| singleton_relation = y
| ~ spl0_49
| ~ spl0_112 ),
inference(superposition,[],[f857,f438]) ).
fof(f1426,plain,
( spl0_167
| ~ spl0_50
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f534,f496,f441,f1424]) ).
fof(f534,plain,
( ! [X0] :
( member(X0,identity_relation)
| ~ member(X0,subset_relation)
| ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_50
| ~ spl0_56 ),
inference(superposition,[],[f497,f443]) ).
fof(f1422,plain,
( spl0_166
| ~ spl0_49
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f533,f496,f436,f1420]) ).
fof(f533,plain,
( ! [X0] :
( member(X0,singleton_relation)
| ~ member(X0,element_relation)
| ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_49
| ~ spl0_56 ),
inference(superposition,[],[f497,f438]) ).
fof(f1418,plain,
( spl0_165
| ~ spl0_46
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f488,f472,f424,f1416]) ).
fof(f488,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(complement(X1),X2)
| member(X0,X2) )
| ~ spl0_46
| ~ spl0_51 ),
inference(resolution,[],[f473,f425]) ).
fof(f1365,plain,
( spl0_164
| ~ spl0_10
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f602,f596,f251,f1363]) ).
fof(f1363,plain,
( spl0_164
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f602,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
| ~ spl0_10
| ~ spl0_71 ),
inference(resolution,[],[f597,f252]) ).
fof(f1361,plain,
( spl0_163
| ~ spl0_26
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f463,f432,f322,f1359]) ).
fof(f463,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
| cross_product(universal_class,universal_class) = compose_class(X0) )
| ~ spl0_26
| ~ spl0_48 ),
inference(resolution,[],[f433,f323]) ).
fof(f1357,plain,
( spl0_162
| ~ spl0_31
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f456,f432,f342,f1355]) ).
fof(f456,plain,
( ! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) )
| ~ spl0_31
| ~ spl0_48 ),
inference(resolution,[],[f433,f343]) ).
fof(f1353,plain,
( spl0_161
| ~ spl0_34
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f418,f385,f361,f1351]) ).
fof(f418,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_34
| ~ spl0_40 ),
inference(resolution,[],[f386,f362]) ).
fof(f1349,plain,
( spl0_160
| ~ spl0_34
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f413,f381,f361,f1347]) ).
fof(f413,plain,
( ! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl0_34
| ~ spl0_39 ),
inference(resolution,[],[f382,f362]) ).
fof(f1339,plain,
( spl0_159
| ~ spl0_1
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f733,f725,f209,f1337]) ).
fof(f733,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),compose(X1,X2))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(y,y))),cross_product(universal_class,universal_class))
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
| ~ spl0_1
| ~ spl0_94 ),
inference(resolution,[],[f726,f210]) ).
fof(f1306,plain,
( spl0_158
| ~ spl0_63
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f599,f596,f555,f1304]) ).
fof(f1304,plain,
( spl0_158
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(X0)))
| ~ operation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f599,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),domain_of(domain_of(X0)))
| ~ operation(X0) )
| ~ spl0_63
| ~ spl0_71 ),
inference(resolution,[],[f597,f556]) ).
fof(f1302,plain,
( ~ spl0_157
| spl0_124
| ~ spl0_20
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f807,f789,f296,f978,f1299]) ).
fof(f1299,plain,
( spl0_157
<=> inductive(domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f807,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ inductive(domain_relation)
| ~ spl0_20
| ~ spl0_105 ),
inference(resolution,[],[f790,f298]) ).
fof(f1297,plain,
( spl0_156
| ~ spl0_38
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f452,f424,f377,f1295]) ).
fof(f452,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) )
| ~ spl0_38
| ~ spl0_46 ),
inference(resolution,[],[f425,f378]) ).
fof(f1293,plain,
( spl0_155
| ~ spl0_36
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f451,f424,f369,f1291]) ).
fof(f451,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) )
| ~ spl0_36
| ~ spl0_46 ),
inference(resolution,[],[f425,f370]) ).
fof(f1289,plain,
( spl0_154
| ~ spl0_34
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f445,f424,f361,f1287]) ).
fof(f445,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) )
| ~ spl0_34
| ~ spl0_46 ),
inference(resolution,[],[f425,f362]) ).
fof(f1266,plain,
( spl0_153
| ~ spl0_39
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f470,f441,f381,f1264]) ).
fof(f470,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
| ~ spl0_39
| ~ spl0_50 ),
inference(superposition,[],[f382,f443]) ).
fof(f1262,plain,
( spl0_152
| ~ spl0_39
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f468,f436,f381,f1260]) ).
fof(f468,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,complement(compose(element_relation,complement(identity_relation)))) )
| ~ spl0_39
| ~ spl0_49 ),
inference(superposition,[],[f382,f438]) ).
fof(f1258,plain,
( spl0_150
| ~ spl0_151
| ~ spl0_20
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f465,f432,f296,f1255,f1251]) ).
fof(f465,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| cross_product(universal_class,universal_class) = domain_relation
| ~ spl0_20
| ~ spl0_48 ),
inference(resolution,[],[f433,f298]) ).
fof(f1249,plain,
( spl0_148
| ~ spl0_149
| ~ spl0_18
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f460,f432,f287,f1246,f1242]) ).
fof(f460,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| cross_product(universal_class,universal_class) = successor_relation
| ~ spl0_18
| ~ spl0_48 ),
inference(resolution,[],[f433,f289]) ).
fof(f1240,plain,
( spl0_146
| ~ spl0_147
| ~ spl0_17
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f457,f432,f282,f1237,f1233]) ).
fof(f457,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| element_relation = cross_product(universal_class,universal_class)
| ~ spl0_17
| ~ spl0_48 ),
inference(resolution,[],[f433,f284]) ).
fof(f1231,plain,
( spl0_145
| ~ spl0_29
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f408,f361,f334,f1229]) ).
fof(f408,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) )
| ~ spl0_29
| ~ spl0_34 ),
inference(resolution,[],[f362,f335]) ).
fof(f1201,plain,
( spl0_144
| ~ spl0_2
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f671,f665,f213,f1199]) ).
fof(f671,plain,
( ! [X0,X1] :
( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
| cross_product(X0,X1) = y )
| ~ spl0_2
| ~ spl0_82 ),
inference(resolution,[],[f666,f214]) ).
fof(f1197,plain,
( ~ spl0_143
| spl0_124
| ~ spl0_18
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f800,f789,f287,f978,f1194]) ).
fof(f1194,plain,
( spl0_143
<=> inductive(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f800,plain,
( member(y,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation)
| ~ spl0_18
| ~ spl0_105 ),
inference(resolution,[],[f790,f289]) ).
fof(f1183,plain,
( spl0_142
| ~ spl0_58
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f623,f617,f504,f1181]) ).
fof(f617,plain,
( spl0_75
<=> ! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f623,plain,
( ! [X0] :
( ~ subclass(X0,cross_product(universal_class,universal_class))
| function(X0)
| ~ single_valued_class(X0) )
| ~ spl0_58
| ~ spl0_75 ),
inference(resolution,[],[f618,f505]) ).
fof(f618,plain,
( ! [X8] :
( ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| function(X8) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f1145,plain,
( spl0_141
| ~ spl0_28
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f419,f385,f330,f1143]) ).
fof(f419,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y )
| ~ spl0_28
| ~ spl0_40 ),
inference(resolution,[],[f386,f331]) ).
fof(f1141,plain,
( spl0_140
| ~ spl0_28
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f414,f381,f330,f1139]) ).
fof(f414,plain,
( ! [X0,X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0)
| ~ member(intersection(X0,X1),universal_class)
| intersection(X0,X1) = y )
| ~ spl0_28
| ~ spl0_39 ),
inference(resolution,[],[f382,f331]) ).
fof(f1091,plain,
( spl0_139
| ~ spl0_39
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f655,f642,f381,f1089]) ).
fof(f655,plain,
( ! [X0] :
( ~ member(X0,subset_relation)
| member(X0,cross_product(universal_class,universal_class)) )
| ~ spl0_39
| ~ spl0_79 ),
inference(superposition,[],[f382,f644]) ).
fof(f1084,plain,
( spl0_138
| ~ spl0_19
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f461,f432,f292,f1082]) ).
fof(f461,plain,
( ! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) )
| ~ spl0_19
| ~ spl0_48 ),
inference(resolution,[],[f433,f293]) ).
fof(f1080,plain,
( spl0_137
| ~ spl0_16
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f450,f424,f278,f1078]) ).
fof(f450,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X0) )
| ~ spl0_16
| ~ spl0_46 ),
inference(resolution,[],[f425,f279]) ).
fof(f1068,plain,
( spl0_136
| ~ spl0_28
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f358,f334,f330,f1066]) ).
fof(f358,plain,
( ! [X0] :
( ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0)
| ~ member(complement(X0),universal_class)
| complement(X0) = y )
| ~ spl0_28
| ~ spl0_29 ),
inference(resolution,[],[f335,f331]) ).
fof(f1061,plain,
( spl0_135
| ~ spl0_8
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f601,f596,f242,f1059]) ).
fof(f1059,plain,
( spl0_135
<=> ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f601,plain,
( ! [X0] :
( ~ function(X0)
| maps(X0,domain_of(X0),universal_class) )
| ~ spl0_8
| ~ spl0_71 ),
inference(resolution,[],[f597,f243]) ).
fof(f1045,plain,
( spl0_134
| ~ spl0_28
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f446,f424,f330,f1043]) ).
fof(f446,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1)
| ~ member(X0,universal_class)
| y = X0 )
| ~ spl0_28
| ~ spl0_46 ),
inference(resolution,[],[f425,f331]) ).
fof(f1039,plain,
( spl0_133
| ~ spl0_12
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f412,f365,f261,f1037]) ).
fof(f412,plain,
( ! [X0,X1] :
( y = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
| subclass(X0,domain_of(X1))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class) )
| ~ spl0_12
| ~ spl0_35 ),
inference(forward_demodulation,[],[f410,f130]) ).
fof(f130,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f410,plain,
( ! [X0,X1] :
( subclass(X0,domain_of(X1))
| ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
| y = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1) )
| ~ spl0_12
| ~ spl0_35 ),
inference(resolution,[],[f366,f262]) ).
fof(f1035,plain,
( spl0_132
| ~ spl0_21
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f995,f424,f301,f1033]) ).
fof(f995,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(y,X0) )
| ~ spl0_21
| ~ spl0_46 ),
inference(resolution,[],[f302,f425]) ).
fof(f1011,plain,
( spl0_131
| ~ spl0_40
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f469,f441,f385,f1009]) ).
fof(f469,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_40
| ~ spl0_50 ),
inference(superposition,[],[f386,f443]) ).
fof(f1007,plain,
( spl0_130
| ~ spl0_40
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f467,f436,f385,f1005]) ).
fof(f467,plain,
( ! [X0] :
( ~ member(X0,singleton_relation)
| member(X0,element_relation) )
| ~ spl0_40
| ~ spl0_49 ),
inference(superposition,[],[f386,f438]) ).
fof(f1003,plain,
( spl0_129
| ~ spl0_8
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f454,f432,f242,f1001]) ).
fof(f454,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_8
| ~ spl0_48 ),
inference(resolution,[],[f433,f243]) ).
fof(f999,plain,
( spl0_128
| ~ spl0_9
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f449,f424,f246,f997]) ).
fof(f997,plain,
( spl0_128
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f449,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_9
| ~ spl0_46 ),
inference(resolution,[],[f425,f248]) ).
fof(f994,plain,
( spl0_127
| spl0_21
| ~ spl0_8
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f792,f789,f242,f301,f992]) ).
fof(f792,plain,
( ! [X0] :
( member(y,universal_class)
| ~ inductive(X0) )
| ~ spl0_8
| ~ spl0_105 ),
inference(resolution,[],[f790,f243]) ).
fof(f989,plain,
( ~ spl0_124
| spl0_125
| ~ spl0_126
| ~ spl0_15
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f359,f342,f273,f986,f982,f978]) ).
fof(f982,plain,
( spl0_125
<=> inductive(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f273,plain,
( spl0_15
<=> ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(y,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f359,plain,
( ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
| inductive(cross_product(universal_class,universal_class))
| ~ member(y,cross_product(universal_class,universal_class))
| ~ spl0_15
| ~ spl0_31 ),
inference(resolution,[],[f343,f274]) ).
fof(f274,plain,
( ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(y,X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f976,plain,
( spl0_122
| spl0_123
| ~ spl0_7
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f638,f629,f238,f973,f970]) ).
fof(f638,plain,
( ! [X0] :
( member(domain_of(domain_of(flip(cross_product(y,universal_class)))),universal_class)
| ~ member(X0,universal_class)
| ~ function(regular(cross_product(X0,universal_class)))
| y = cross_product(X0,universal_class) )
| ~ spl0_7
| ~ spl0_77 ),
inference(superposition,[],[f630,f239]) ).
fof(f968,plain,
( spl0_120
| spl0_121
| ~ spl0_1
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f672,f665,f209,f965,f962]) ).
fof(f962,plain,
( spl0_120
<=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f672,plain,
( ! [X0,X1] :
( y = unordered_pair(unordered_pair(first(y),first(y)),unordered_pair(first(y),unordered_pair(second(y),second(y))))
| ~ inductive(cross_product(X0,X1)) )
| ~ spl0_1
| ~ spl0_82 ),
inference(resolution,[],[f666,f210]) ).
fof(f955,plain,
( spl0_119
| ~ spl0_12
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f453,f424,f261,f953]) ).
fof(f453,plain,
( ! [X2,X0,X1] :
( ~ subclass(domain_of(X0),X1)
| member(X2,X1)
| ~ member(X2,universal_class)
| y = intersection(cross_product(unordered_pair(X2,X2),universal_class),X0) )
| ~ spl0_12
| ~ spl0_46 ),
inference(resolution,[],[f425,f262]) ).
fof(f927,plain,
( spl0_118
| ~ spl0_2
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f526,f492,f213,f925]) ).
fof(f526,plain,
( ! [X0,X1] :
( regular(unordered_pair(X0,X1)) = X0
| regular(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = y )
| ~ spl0_2
| ~ spl0_55 ),
inference(resolution,[],[f493,f214]) ).
fof(f921,plain,
( spl0_117
| ~ spl0_59
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f547,f512,f508,f919]) ).
fof(f512,plain,
( spl0_60
<=> ! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f547,plain,
( ! [X0] :
( single_valued_class(X0)
| ~ function(X0) )
| ~ spl0_59
| ~ spl0_60 ),
inference(resolution,[],[f513,f509]) ).
fof(f513,plain,
( ! [X0] :
( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| single_valued_class(X0) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f914,plain,
( spl0_116
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f259,f255,f238,f912]) ).
fof(f255,plain,
( spl0_11
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| y != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f259,plain,
( ! [X0] :
( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f258]) ).
fof(f258,plain,
( ! [X0] :
( y != y
| ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
| y = cross_product(unordered_pair(X0,X0),universal_class) )
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f256,f239]) ).
fof(f256,plain,
( ! [X0,X4] :
( y != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
| ~ member(X4,domain_of(X0)) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f899,plain,
( spl0_115
| ~ spl0_11
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f540,f500,f255,f897]) ).
fof(f540,plain,
( ! [X0,X1] :
( y != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
| ~ member(X0,domain_of(X1)) )
| ~ spl0_11
| ~ spl0_57 ),
inference(superposition,[],[f256,f501]) ).
fof(f895,plain,
( ~ spl0_114
| ~ spl0_1
| spl0_97 ),
inference(avatar_split_clause,[],[f829,f750,f209,f892]) ).
fof(f892,plain,
( spl0_114
<=> inductive(subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f829,plain,
( ~ inductive(subset_relation)
| ~ spl0_1
| spl0_97 ),
inference(resolution,[],[f751,f210]) ).
fof(f890,plain,
( spl0_113
| ~ spl0_7
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f532,f496,f238,f888]) ).
fof(f532,plain,
( ! [X0,X1] :
( member(X1,y)
| ~ member(X1,regular(X0))
| ~ member(X1,X0)
| y = X0 )
| ~ spl0_7
| ~ spl0_56 ),
inference(superposition,[],[f497,f239]) ).
fof(f858,plain,
( spl0_112
| ~ spl0_2
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f420,f385,f213,f856]) ).
fof(f420,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = y )
| ~ spl0_2
| ~ spl0_40 ),
inference(resolution,[],[f386,f214]) ).
fof(f854,plain,
( spl0_111
| ~ spl0_2
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f415,f381,f213,f852]) ).
fof(f415,plain,
( ! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = y )
| ~ spl0_2
| ~ spl0_39 ),
inference(resolution,[],[f382,f214]) ).
fof(f837,plain,
( spl0_110
| ~ spl0_1
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f527,f492,f209,f835]) ).
fof(f527,plain,
( ! [X0,X1] :
( y = X0
| y = X1
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl0_1
| ~ spl0_55 ),
inference(resolution,[],[f493,f210]) ).
fof(f833,plain,
( spl0_109
| ~ spl0_2
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f447,f424,f213,f831]) ).
fof(f447,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| y = X0 )
| ~ spl0_2
| ~ spl0_46 ),
inference(resolution,[],[f425,f214]) ).
fof(f828,plain,
( spl0_108
| ~ spl0_7
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f422,f385,f238,f826]) ).
fof(f422,plain,
( ! [X0,X1] :
( ~ member(X1,y)
| member(X1,regular(X0))
| y = X0 )
| ~ spl0_7
| ~ spl0_40 ),
inference(superposition,[],[f386,f239]) ).
fof(f816,plain,
( spl0_107
| ~ spl0_7
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f417,f381,f238,f814]) ).
fof(f417,plain,
( ! [X0,X1] :
( ~ member(X1,y)
| member(X1,X0)
| y = X0 )
| ~ spl0_7
| ~ spl0_39 ),
inference(superposition,[],[f382,f239]) ).
fof(f812,plain,
( spl0_106
| ~ spl0_2
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f357,f334,f213,f810]) ).
fof(f357,plain,
( ! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = y )
| ~ spl0_2
| ~ spl0_29 ),
inference(resolution,[],[f335,f214]) ).
fof(f791,plain,
( spl0_105
| ~ spl0_1
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f448,f424,f209,f789]) ).
fof(f448,plain,
( ! [X0,X1] :
( ~ subclass(X0,X1)
| member(y,X1)
| ~ inductive(X0) )
| ~ spl0_1
| ~ spl0_46 ),
inference(resolution,[],[f425,f210]) ).
fof(f787,plain,
spl0_104,
inference(avatar_split_clause,[],[f207,f785]) ).
fof(f785,plain,
( spl0_104
<=> ! [X9,X11,X10] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f207,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f206,f130]) ).
fof(f206,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f205,f130]) ).
fof(f205,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f204,f130]) ).
fof(f204,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f203,f130]) ).
fof(f203,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f202,f130]) ).
fof(f202,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f201,f130]) ).
fof(f201,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f200,f130]) ).
fof(f200,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f199,f130]) ).
fof(f199,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f198,f130]) ).
fof(f198,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f180,f130]) ).
fof(f180,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f91,f118,f119,f118,f118,f118,f118,f119]) ).
fof(f119,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f118,plain,
! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
inference(definition_unfolding,[],[f68,f115,f117,f12]) ).
fof(f117,plain,
! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
inference(definition_unfolding,[],[f42,f116,f29]) ).
fof(f116,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f115,plain,
! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
inference(definition_unfolding,[],[f53,f29]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
fof(f91,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).
fof(f780,plain,
spl0_103,
inference(avatar_split_clause,[],[f197,f778]) ).
fof(f197,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f196,f130]) ).
fof(f196,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f195,f130]) ).
fof(f195,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f194,f130]) ).
fof(f194,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f193,f130]) ).
fof(f193,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f172,f130]) ).
fof(f172,plain,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f89,f119,f118,f119,f118,f118,f118,f118,f119]) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).
fof(f775,plain,
spl0_102,
inference(avatar_split_clause,[],[f192,f773]) ).
fof(f192,plain,
! [X0,X1,X4] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
| ~ member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(forward_demodulation,[],[f171,f130]) ).
fof(f171,plain,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
inference(definition_unfolding,[],[f108,f119,f119,f118,f119,f119]) ).
fof(f108,axiom,
! [X0,X1,X4] :
( ~ member(X1,domain_of(X0))
| member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).
fof(f769,plain,
spl0_101,
inference(avatar_split_clause,[],[f176,f767]) ).
fof(f176,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f37,f119,f119,f119,f119,f119,f119]) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).
fof(f765,plain,
spl0_100,
inference(avatar_split_clause,[],[f175,f763]) ).
fof(f175,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f34,f119,f119,f119,f119,f119,f119]) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).
fof(f761,plain,
spl0_99,
inference(avatar_split_clause,[],[f160,f759]) ).
fof(f160,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
inference(definition_unfolding,[],[f36,f119,f119,f119,f119]) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).
fof(f757,plain,
( spl0_97
| ~ spl0_98
| ~ spl0_50
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f566,f484,f441,f754,f750]) ).
fof(f754,plain,
( spl0_98
<=> inductive(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f484,plain,
( spl0_54
<=> ! [X0,X1] :
( member(y,X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f566,plain,
( ~ inductive(identity_relation)
| member(y,subset_relation)
| ~ spl0_50
| ~ spl0_54 ),
inference(superposition,[],[f485,f443]) ).
fof(f485,plain,
( ! [X0,X1] :
( ~ inductive(intersection(X1,X0))
| member(y,X0) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f748,plain,
spl0_96,
inference(avatar_split_clause,[],[f159,f746]) ).
fof(f159,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
inference(definition_unfolding,[],[f33,f119,f119,f119,f119]) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).
fof(f743,plain,
spl0_95,
inference(avatar_split_clause,[],[f183,f741]) ).
fof(f183,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f170]) ).
fof(f170,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f46,f125,f119,f119]) ).
fof(f125,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f43,f26,f12]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).
fof(f727,plain,
spl0_94,
inference(avatar_split_clause,[],[f174,f725]) ).
fof(f174,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f59,f119,f119,f117,f117,f12]) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).
fof(f721,plain,
spl0_93,
inference(avatar_split_clause,[],[f157,f719]) ).
fof(f157,plain,
! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
inference(definition_unfolding,[],[f97,f119,f119,f119]) ).
fof(f97,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).
fof(f717,plain,
spl0_92,
inference(avatar_split_clause,[],[f188,f715]) ).
fof(f188,plain,
! [X0,X1,X4] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(forward_demodulation,[],[f154,f130]) ).
fof(f154,plain,
! [X0,X1,X4] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(definition_unfolding,[],[f107,f118,f119,f119]) ).
fof(f107,axiom,
! [X0,X1,X4] :
( apply(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).
fof(f712,plain,
spl0_91,
inference(avatar_split_clause,[],[f179,f710]) ).
fof(f179,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
inference(definition_unfolding,[],[f90,f119]) ).
fof(f90,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).
fof(f708,plain,
spl0_90,
inference(avatar_split_clause,[],[f158,f706]) ).
fof(f158,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f58,f119,f117,f117,f12]) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
fof(f703,plain,
spl0_89,
inference(avatar_split_clause,[],[f184,f701]) ).
fof(f184,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f173]) ).
fof(f173,plain,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f94,f119,f119]) ).
fof(f94,axiom,
! [X0,X1,X4] :
( compose(X0,X1) != X4
| member(ordered_pair(X1,X4),compose_class(X0))
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).
fof(f699,plain,
spl0_88,
inference(avatar_split_clause,[],[f156,f697]) ).
fof(f156,plain,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
inference(definition_unfolding,[],[f96,f119,f119]) ).
fof(f96,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).
fof(f695,plain,
spl0_87,
inference(avatar_split_clause,[],[f152,f693]) ).
fof(f152,plain,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
inference(definition_unfolding,[],[f106,f119,f119]) ).
fof(f106,axiom,
! [X0,X1,X4] :
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).
fof(f690,plain,
( ~ spl0_86
| ~ spl0_1
| spl0_69 ),
inference(avatar_split_clause,[],[f656,f587,f209,f687]) ).
fof(f687,plain,
( spl0_86
<=> inductive(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f656,plain,
( ~ inductive(element_relation)
| ~ spl0_1
| spl0_69 ),
inference(resolution,[],[f588,f210]) ).
fof(f685,plain,
spl0_85,
inference(avatar_split_clause,[],[f167,f683]) ).
fof(f167,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f20,f119,f119]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
fof(f681,plain,
spl0_84,
inference(avatar_split_clause,[],[f177,f679]) ).
fof(f679,plain,
( spl0_84
<=> ! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f177,plain,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f81,f116]) ).
fof(f81,axiom,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).
fof(f676,plain,
spl0_83,
inference(avatar_split_clause,[],[f178,f674]) ).
fof(f178,plain,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f85,f116]) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).
fof(f667,plain,
spl0_82,
inference(avatar_split_clause,[],[f153,f665]) ).
fof(f153,plain,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
inference(definition_unfolding,[],[f17,f119]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f663,plain,
spl0_81,
inference(avatar_split_clause,[],[f150,f661]) ).
fof(f150,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f45,f125,f119]) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).
fof(f649,plain,
spl0_80,
inference(avatar_split_clause,[],[f166,f647]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f16,f119]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f645,plain,
spl0_79,
inference(avatar_split_clause,[],[f131,f642]) ).
fof(f131,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f74,f38]) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).
fof(f635,plain,
spl0_78,
inference(avatar_split_clause,[],[f186,f633]) ).
fof(f186,plain,
! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ),
inference(forward_demodulation,[],[f139,f130]) ).
fof(f139,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
inference(definition_unfolding,[],[f56,f126]) ).
fof(f126,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
inference(definition_unfolding,[],[f55,f117]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).
fof(f631,plain,
spl0_77,
inference(avatar_split_clause,[],[f162,f629]) ).
fof(f162,plain,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
inference(definition_unfolding,[],[f65,f117]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
fof(f627,plain,
spl0_76,
inference(avatar_split_clause,[],[f155,f625]) ).
fof(f155,plain,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
inference(definition_unfolding,[],[f93,f119]) ).
fof(f93,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).
fof(f619,plain,
spl0_75,
inference(avatar_split_clause,[],[f165,f617]) ).
fof(f165,plain,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f64,f38]) ).
fof(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).
fof(f615,plain,
spl0_74,
inference(avatar_split_clause,[],[f146,f613]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f14,f119]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f611,plain,
spl0_73,
inference(avatar_split_clause,[],[f145,f609]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f15,f119]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f607,plain,
spl0_72,
inference(avatar_split_clause,[],[f141,f605]) ).
fof(f141,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
inference(definition_unfolding,[],[f100,f119]) ).
fof(f100,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
fof(f598,plain,
spl0_71,
inference(avatar_split_clause,[],[f163,f596]) ).
fof(f163,plain,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ),
inference(definition_unfolding,[],[f112,f116]) ).
fof(f112,axiom,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).
fof(f594,plain,
( spl0_69
| ~ spl0_70
| ~ spl0_49
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f565,f484,f436,f591,f587]) ).
fof(f591,plain,
( spl0_70
<=> inductive(singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f565,plain,
( ~ inductive(singleton_relation)
| member(y,element_relation)
| ~ spl0_49
| ~ spl0_54 ),
inference(superposition,[],[f485,f438]) ).
fof(f585,plain,
spl0_68,
inference(avatar_split_clause,[],[f151,f583]) ).
fof(f151,plain,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
inference(definition_unfolding,[],[f99,f119]) ).
fof(f99,axiom,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
fof(f579,plain,
spl0_67,
inference(avatar_split_clause,[],[f185,f577]) ).
fof(f185,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(forward_demodulation,[],[f135,f130]) ).
fof(f135,plain,
! [X0] :
( ~ inductive(X0)
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f48,f117]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
fof(f575,plain,
spl0_66,
inference(avatar_split_clause,[],[f149,f573]) ).
fof(f573,plain,
( spl0_66
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f149,plain,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f84,f116]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).
fof(f571,plain,
spl0_65,
inference(avatar_split_clause,[],[f144,f569]) ).
fof(f144,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f19,f119]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
fof(f561,plain,
spl0_64,
inference(avatar_split_clause,[],[f148,f559]) ).
fof(f559,plain,
( spl0_64
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f148,plain,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
inference(definition_unfolding,[],[f111,f116]) ).
fof(f111,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).
fof(f557,plain,
spl0_63,
inference(avatar_split_clause,[],[f136,f555]) ).
fof(f136,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f116]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).
fof(f553,plain,
spl0_62,
inference(avatar_split_clause,[],[f79,f551]) ).
fof(f551,plain,
( spl0_62
<=> ! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).
fof(f518,plain,
spl0_61,
inference(avatar_split_clause,[],[f187,f516]) ).
fof(f187,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f140,f130]) ).
fof(f140,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f115]) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
fof(f514,plain,
spl0_60,
inference(avatar_split_clause,[],[f138,f512]) ).
fof(f138,plain,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f61,f38]) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f510,plain,
spl0_59,
inference(avatar_split_clause,[],[f137,f508]) ).
fof(f137,plain,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f63,f38]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
fof(f506,plain,
spl0_58,
inference(avatar_split_clause,[],[f132,f504]) ).
fof(f132,plain,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f60,f38]) ).
fof(f60,axiom,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).
fof(f502,plain,
spl0_57,
inference(avatar_split_clause,[],[f130,f500]) ).
fof(f498,plain,
spl0_56,
inference(avatar_split_clause,[],[f23,f496]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f494,plain,
spl0_55,
inference(avatar_split_clause,[],[f8,f492]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f486,plain,
( spl0_54
| ~ spl0_1
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f421,f385,f209,f484]) ).
fof(f421,plain,
( ! [X0,X1] :
( member(y,X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl0_1
| ~ spl0_40 ),
inference(resolution,[],[f386,f210]) ).
fof(f482,plain,
spl0_53,
inference(avatar_split_clause,[],[f161,f480]) ).
fof(f480,plain,
( spl0_53
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f161,plain,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f73,f38]) ).
fof(f73,axiom,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).
fof(f478,plain,
spl0_52,
inference(avatar_split_clause,[],[f83,f476]) ).
fof(f476,plain,
( spl0_52
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).
fof(f474,plain,
spl0_51,
inference(avatar_split_clause,[],[f25,f472]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f444,plain,
spl0_50,
inference(avatar_split_clause,[],[f129,f441]) ).
fof(f129,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f75,f38]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
fof(f439,plain,
spl0_49,
inference(avatar_split_clause,[],[f104,f436]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).
fof(f434,plain,
spl0_48,
inference(avatar_split_clause,[],[f7,f432]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f430,plain,
( spl0_47
| ~ spl0_1
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f416,f381,f209,f428]) ).
fof(f416,plain,
( ! [X0,X1] :
( member(y,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl0_1
| ~ spl0_39 ),
inference(resolution,[],[f382,f210]) ).
fof(f426,plain,
spl0_46,
inference(avatar_split_clause,[],[f1,f424]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f407,plain,
spl0_45,
inference(avatar_split_clause,[],[f133,f405]) ).
fof(f133,plain,
! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f72,f38]) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).
fof(f403,plain,
spl0_44,
inference(avatar_split_clause,[],[f110,f401]) ).
fof(f401,plain,
( spl0_44
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f110,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).
fof(f399,plain,
spl0_43,
inference(avatar_split_clause,[],[f88,f397]) ).
fof(f397,plain,
( spl0_43
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
fof(f395,plain,
spl0_42,
inference(avatar_split_clause,[],[f35,f393]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).
fof(f391,plain,
spl0_41,
inference(avatar_split_clause,[],[f32,f389]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).
fof(f387,plain,
spl0_40,
inference(avatar_split_clause,[],[f22,f385]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f383,plain,
spl0_39,
inference(avatar_split_clause,[],[f21,f381]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f379,plain,
spl0_38,
inference(avatar_split_clause,[],[f10,f377]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f375,plain,
( spl0_37
| ~ spl0_1
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f356,f334,f209,f373]) ).
fof(f373,plain,
( spl0_37
<=> ! [X0] :
( ~ member(y,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f356,plain,
( ! [X0] :
( ~ member(y,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_1
| ~ spl0_29 ),
inference(resolution,[],[f335,f210]) ).
fof(f371,plain,
spl0_36,
inference(avatar_split_clause,[],[f9,f369]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f367,plain,
spl0_35,
inference(avatar_split_clause,[],[f3,f365]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f363,plain,
spl0_34,
inference(avatar_split_clause,[],[f2,f361]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f355,plain,
spl0_33,
inference(avatar_split_clause,[],[f105,f352]) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).
fof(f350,plain,
spl0_32,
inference(avatar_split_clause,[],[f95,f347]) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).
fof(f344,plain,
spl0_31,
inference(avatar_split_clause,[],[f62,f342]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
fof(f340,plain,
spl0_30,
inference(avatar_split_clause,[],[f57,f338]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f336,plain,
spl0_29,
inference(avatar_split_clause,[],[f24,f334]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f332,plain,
spl0_28,
inference(avatar_split_clause,[],[f191,f330]) ).
fof(f191,plain,
! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| y = X1 ),
inference(forward_demodulation,[],[f190,f130]) ).
fof(f190,plain,
! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
| ~ member(X1,universal_class)
| y = X1 ),
inference(forward_demodulation,[],[f168,f130]) ).
fof(f168,plain,
! [X1] :
( ~ member(X1,universal_class)
| y = X1
| member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
inference(definition_unfolding,[],[f70,f113,f118]) ).
fof(f113,axiom,
null_class = y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lemma_1_to_restricted_domain_1) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
fof(f328,plain,
spl0_27,
inference(avatar_split_clause,[],[f109,f326]) ).
fof(f326,plain,
( spl0_27
<=> ! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).
fof(f324,plain,
spl0_26,
inference(avatar_split_clause,[],[f92,f322]) ).
fof(f92,axiom,
! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).
fof(f320,plain,
spl0_25,
inference(avatar_split_clause,[],[f87,f318]) ).
fof(f318,plain,
( spl0_25
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f316,plain,
spl0_24,
inference(avatar_split_clause,[],[f86,f314]) ).
fof(f314,plain,
( spl0_24
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f312,plain,
spl0_23,
inference(avatar_split_clause,[],[f82,f310]) ).
fof(f310,plain,
( spl0_23
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
fof(f308,plain,
( ~ spl0_21
| spl0_22
| ~ spl0_8
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f276,f273,f242,f305,f301]) ).
fof(f276,plain,
( inductive(universal_class)
| ~ member(y,universal_class)
| ~ spl0_8
| ~ spl0_15 ),
inference(resolution,[],[f274,f243]) ).
fof(f299,plain,
spl0_20,
inference(avatar_split_clause,[],[f98,f296]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
fof(f294,plain,
spl0_19,
inference(avatar_split_clause,[],[f51,f292]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f290,plain,
spl0_18,
inference(avatar_split_clause,[],[f44,f287]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
fof(f285,plain,
spl0_17,
inference(avatar_split_clause,[],[f18,f282]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
fof(f280,plain,
spl0_16,
inference(avatar_split_clause,[],[f11,f278]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f275,plain,
spl0_15,
inference(avatar_split_clause,[],[f189,f273]) ).
fof(f189,plain,
! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(y,X0) ),
inference(forward_demodulation,[],[f164,f130]) ).
fof(f164,plain,
! [X0] :
( inductive(X0)
| ~ member(y,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f49,f113,f117]) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).
fof(f271,plain,
spl0_14,
inference(avatar_split_clause,[],[f78,f269]) ).
fof(f269,plain,
( spl0_14
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
fof(f267,plain,
spl0_13,
inference(avatar_split_clause,[],[f71,f265]) ).
fof(f265,plain,
( spl0_13
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
fof(f263,plain,
spl0_12,
inference(avatar_split_clause,[],[f169,f261]) ).
fof(f169,plain,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| y = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f31,f29,f12,f113]) ).
fof(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f257,plain,
spl0_11,
inference(avatar_split_clause,[],[f147,f255]) ).
fof(f147,plain,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| y != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f30,f29,f12,f113]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f253,plain,
spl0_10,
inference(avatar_split_clause,[],[f181,f251]) ).
fof(f181,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).
fof(f249,plain,
spl0_9,
inference(avatar_split_clause,[],[f52,f246]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f244,plain,
spl0_8,
inference(avatar_split_clause,[],[f4,f242]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f240,plain,
spl0_7,
inference(avatar_split_clause,[],[f143,f238]) ).
fof(f143,plain,
! [X0] :
( y = X0
| intersection(X0,regular(X0)) = y ),
inference(definition_unfolding,[],[f67,f113,f113]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f236,plain,
spl0_6,
inference(avatar_split_clause,[],[f69,f233]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f231,plain,
spl0_5,
inference(avatar_split_clause,[],[f50,f228]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f226,plain,
( ~ spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f221,f217,f223]) ).
fof(f217,plain,
( spl0_3
<=> y = domain_of(intersection(cross_product(y,y),x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f221,plain,
( y != domain_of(intersection(x,cross_product(y,y)))
| spl0_3 ),
inference(forward_demodulation,[],[f219,f130]) ).
fof(f219,plain,
( y != domain_of(intersection(cross_product(y,y),x))
| spl0_3 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f220,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f128,f217]) ).
fof(f128,plain,
y != domain_of(intersection(cross_product(y,y),x)),
inference(definition_unfolding,[],[f114,f29]) ).
fof(f114,axiom,
y != domain_of(restrict(x,y,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lemma_1_to_restricted_domain_2) ).
fof(f215,plain,
spl0_2,
inference(avatar_split_clause,[],[f142,f213]) ).
fof(f142,plain,
! [X0] :
( y = X0
| member(regular(X0),X0) ),
inference(definition_unfolding,[],[f66,f113]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f211,plain,
spl0_1,
inference(avatar_split_clause,[],[f134,f209]) ).
fof(f134,plain,
! [X0] :
( ~ inductive(X0)
| member(y,X0) ),
inference(definition_unfolding,[],[f47,f113]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET473-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon May 20 12:21:08 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (17083)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (17086)WARNING: value z3 for option sas not known
% 0.11/0.35 % (17084)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (17085)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (17088)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.35 % (17087)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (17086)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35 % (17089)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.35 % (17090)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.38 TRYING [1]
% 0.11/0.38 TRYING [2]
% 0.17/0.44 TRYING [3]
% 1.49/0.54 TRYING [1]
% 1.49/0.55 TRYING [2]
% 1.49/0.59 TRYING [4]
% 2.16/0.68 TRYING [3]
% 4.99/1.09 TRYING [5]
% 7.77/1.46 TRYING [1]
% 7.77/1.46 TRYING [2]
% 7.77/1.47 TRYING [3]
% 8.55/1.54 TRYING [4]
% 9.33/1.73 TRYING [4]
% 9.88/1.77 TRYING [5]
% 14.96/2.49 TRYING [6]
% 18.96/3.11 TRYING [6]
% 29.93/4.62 TRYING [7]
% 53.84/8.02 % (17088)First to succeed.
% 54.43/8.10 % (17088)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-17083"
% 54.43/8.11 % (17088)Refutation found. Thanks to Tanya!
% 54.43/8.11 % SZS status Unsatisfiable for theBenchmark
% 54.43/8.11 % SZS output start Proof for theBenchmark
% See solution above
% 54.43/8.13 % (17088)------------------------------
% 54.43/8.13 % (17088)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 54.43/8.13 % (17088)Termination reason: Refutation
% 54.43/8.13
% 54.43/8.13 % (17088)Memory used [KB]: 37045
% 54.43/8.13 % (17088)Time elapsed: 7.753 s
% 54.43/8.13 % (17088)Instructions burned: 15689 (million)
% 54.43/8.13 % (17083)Success in time 7.789 s
%------------------------------------------------------------------------------