TSTP Solution File: SET071+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET071+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:10:55 EDT 2024
% Result : Theorem 12.37s 2.08s
% Output : Refutation 12.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 664
% Syntax : Number of formulae : 2275 ( 132 unt; 0 def)
% Number of atoms : 7796 ( 624 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 9814 (4293 ~;4685 |; 166 &)
% ( 646 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 25 ( 2 avg)
% Number of predicates : 620 ( 618 usr; 614 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 9 con; 0-3 aty)
% Number of variables : 3392 (3361 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25073,plain,
$false,
inference(avatar_sat_refutation,[],[f273,f278,f283,f288,f293,f297,f301,f306,f310,f315,f320,f324,f328,f332,f337,f341,f345,f349,f353,f357,f362,f366,f370,f374,f378,f382,f386,f390,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f449,f453,f476,f482,f486,f490,f494,f498,f538,f542,f546,f576,f580,f584,f588,f592,f614,f618,f622,f632,f636,f640,f644,f652,f657,f661,f665,f669,f673,f683,f687,f691,f695,f708,f712,f716,f746,f750,f763,f767,f795,f799,f808,f812,f822,f826,f830,f834,f838,f842,f848,f852,f856,f866,f870,f874,f881,f885,f890,f898,f902,f958,f963,f967,f971,f995,f999,f1003,f1007,f1011,f1020,f1029,f1033,f1037,f1041,f1045,f1050,f1054,f1058,f1062,f1066,f1229,f1233,f1237,f1241,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1288,f1292,f1296,f1300,f1360,f1472,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1518,f1522,f1538,f1542,f1546,f1550,f1666,f1831,f1835,f1839,f1872,f1876,f1880,f1884,f1977,f2003,f2007,f2011,f2015,f2093,f2098,f2103,f2107,f2233,f2237,f2241,f2245,f2250,f2287,f2291,f2295,f2457,f2470,f2498,f2502,f2506,f2510,f2514,f2707,f2711,f2715,f2719,f2723,f2727,f2731,f2735,f2739,f2743,f2747,f2755,f2864,f3183,f3187,f3191,f3195,f3199,f3203,f3207,f3211,f3453,f3495,f3500,f3504,f3555,f3559,f3628,f3632,f3733,f3737,f3746,f3765,f3999,f4003,f4008,f4031,f4036,f4041,f4046,f4214,f4240,f4358,f4359,f4366,f4370,f4374,f4511,f4560,f4565,f5007,f6513,f6517,f6623,f6627,f6666,f6670,f6779,f6791,f6795,f6811,f6847,f6851,f6931,f6935,f6946,f7151,f7228,f7305,f7320,f7335,f7339,f7355,f7359,f7426,f7430,f7431,f7448,f7471,f7479,f7496,f7497,f7529,f7533,f7538,f7543,f7548,f7553,f7558,f7567,f7572,f7674,f7679,f7684,f7688,f7692,f7696,f7700,f7704,f7708,f7712,f7716,f7721,f7726,f7730,f7818,f7884,f7912,f7913,f7914,f7915,f7916,f10979,f11065,f11069,f11073,f11118,f11119,f11120,f11121,f13261,f13357,f13367,f13371,f13375,f13379,f13384,f13388,f13479,f13483,f13488,f13492,f13505,f13511,f13532,f13536,f13541,f13545,f13550,f13559,f13568,f13577,f13586,f13674,f13678,f13682,f13686,f13694,f13699,f13712,f13728,f13732,f13736,f13855,f13859,f13868,f13874,f13881,f13888,f13892,f13896,f13900,f13904,f13908,f13912,f13917,f13921,f13925,f13929,f13933,f13938,f13943,f13947,f13951,f13955,f13959,f13964,f13968,f13972,f13976,f13980,f14011,f14015,f14019,f14023,f14101,f14250,f14551,f14559,f14563,f14567,f14571,f14575,f14579,f14583,f14587,f14605,f14609,f14613,f14617,f14621,f14625,f14629,f14633,f14637,f14641,f14647,f14651,f14655,f14659,f14663,f14667,f14669,f14867,f14872,f14877,f14882,f14887,f14891,f14895,f14899,f14903,f14907,f14911,f14915,f14919,f14923,f14927,f14931,f14935,f15068,f16199,f16204,f16208,f16221,f16226,f16231,f16235,f16239,f16243,f16247,f16251,f16255,f16259,f16263,f16267,f16272,f16277,f16281,f16285,f16289,f16293,f16297,f16301,f16305,f16309,f16313,f16318,f16341,f16345,f16349,f16353,f16357,f16361,f16365,f16369,f16373,f16378,f16383,f16387,f16391,f16395,f16399,f16403,f16411,f16416,f16420,f16425,f16430,f16438,f16800,f17373,f17374,f18097,f18101,f18105,f18109,f18113,f18117,f18118,f18122,f18126,f18130,f18134,f18138,f18142,f18146,f18150,f18154,f18158,f18163,f18167,f18171,f18175,f18179,f18183,f18187,f18191,f18195,f18199,f18203,f18207,f18211,f18215,f18219,f18223,f18227,f18231,f18235,f18239,f18243,f18247,f18251,f18255,f18259,f18263,f18267,f18271,f18275,f18279,f18283,f18287,f18291,f18295,f18299,f18303,f18307,f18311,f18315,f18319,f18323,f18327,f18331,f18335,f18339,f18343,f18347,f18351,f18355,f18359,f18363,f18367,f18371,f18375,f18379,f18384,f18388,f18392,f18396,f18400,f18404,f18544,f18549,f22054,f22058,f22062,f22066,f22070,f22074,f22078,f22082,f22086,f22090,f22094,f22098,f22102,f22106,f22110,f22114,f22118,f22122,f22126,f22130,f22136,f22140,f22144,f22148,f22152,f22156,f22160,f22164,f22191,f22195,f22199,f22203,f22207,f22211,f22215,f22219,f22223,f22227,f22231,f22235,f22239,f22243,f22247,f22298,f22302,f22306,f22310,f22314,f22318,f22322,f22326,f22330,f22334,f22338,f22342,f22346,f23539,f23713,f23928,f24638,f25072]) ).
fof(f25072,plain,
( spl8_3
| spl8_2
| ~ spl8_607 ),
inference(avatar_split_clause,[],[f22926,f22336,f275,f280]) ).
fof(f280,plain,
( spl8_3
<=> null_class = unordered_pair(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f275,plain,
( spl8_2
<=> member(sK1,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f22336,plain,
( spl8_607
<=> ! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_607])]) ).
fof(f22926,plain,
( null_class = unordered_pair(sK0,sK1)
| spl8_2
| ~ spl8_607 ),
inference(resolution,[],[f22337,f277]) ).
fof(f277,plain,
( ~ member(sK1,universal_class)
| spl8_2 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f22337,plain,
( ! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(sK0,X0) )
| ~ spl8_607 ),
inference(avatar_component_clause,[],[f22336]) ).
fof(f24638,plain,
( spl8_613
| spl8_1
| ~ spl8_607 ),
inference(avatar_split_clause,[],[f22925,f22336,f270,f24635]) ).
fof(f24635,plain,
( spl8_613
<=> null_class = unordered_pair(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_613])]) ).
fof(f270,plain,
( spl8_1
<=> member(sK0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f22925,plain,
( null_class = unordered_pair(sK0,sK0)
| spl8_1
| ~ spl8_607 ),
inference(resolution,[],[f22337,f272]) ).
fof(f272,plain,
( ~ member(sK0,universal_class)
| spl8_1 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f23928,plain,
( spl8_612
| spl8_233
| ~ spl8_607 ),
inference(avatar_split_clause,[],[f22924,f22336,f4211,f23925]) ).
fof(f23925,plain,
( spl8_612
<=> null_class = unordered_pair(sK0,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_612])]) ).
fof(f4211,plain,
( spl8_233
<=> member(identity_relation,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_233])]) ).
fof(f22924,plain,
( null_class = unordered_pair(sK0,identity_relation)
| spl8_233
| ~ spl8_607 ),
inference(resolution,[],[f22337,f4212]) ).
fof(f4212,plain,
( ~ member(identity_relation,universal_class)
| spl8_233 ),
inference(avatar_component_clause,[],[f4211]) ).
fof(f23713,plain,
( spl8_611
| ~ spl8_45
| ~ spl8_250 ),
inference(avatar_split_clause,[],[f23561,f6784,f488,f23711]) ).
fof(f23711,plain,
( spl8_611
<=> ! [X0] :
( member(universal_class,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_611])]) ).
fof(f488,plain,
( spl8_45
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
fof(f6784,plain,
( spl8_250
<=> member(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_250])]) ).
fof(f23561,plain,
( ! [X0] :
( member(universal_class,X0)
| ~ subclass(universal_class,X0) )
| ~ spl8_45
| ~ spl8_250 ),
inference(resolution,[],[f6785,f489]) ).
fof(f489,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subclass(X0,X1) )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f6785,plain,
( member(universal_class,universal_class)
| ~ spl8_250 ),
inference(avatar_component_clause,[],[f6784]) ).
fof(f23539,plain,
( spl8_610
| spl8_250
| ~ spl8_607 ),
inference(avatar_split_clause,[],[f22922,f22336,f6784,f23536]) ).
fof(f23536,plain,
( spl8_610
<=> null_class = unordered_pair(sK0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_610])]) ).
fof(f22922,plain,
( null_class = unordered_pair(sK0,universal_class)
| spl8_250
| ~ spl8_607 ),
inference(resolution,[],[f22337,f6786]) ).
fof(f6786,plain,
( ~ member(universal_class,universal_class)
| spl8_250 ),
inference(avatar_component_clause,[],[f6784]) ).
fof(f22346,plain,
( spl8_609
| ~ spl8_30
| ~ spl8_69
| ~ spl8_207 ),
inference(avatar_split_clause,[],[f7525,f3197,f680,f406,f22344]) ).
fof(f22344,plain,
( spl8_609
<=> ! [X0] :
( null_class = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_609])]) ).
fof(f406,plain,
( spl8_30
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
fof(f680,plain,
( spl8_69
<=> null_class = sum_class(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
fof(f3197,plain,
( spl8_207
<=> ! [X0,X1] :
( sum_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_207])]) ).
fof(f7525,plain,
( ! [X0] :
( null_class = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))))
| ~ member(X0,universal_class) )
| ~ spl8_30
| ~ spl8_69
| ~ spl8_207 ),
inference(forward_demodulation,[],[f7509,f682]) ).
fof(f682,plain,
( null_class = sum_class(null_class)
| ~ spl8_69 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f7509,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| sum_class(null_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(null_class),sum_class(null_class))))) )
| ~ spl8_30
| ~ spl8_207 ),
inference(resolution,[],[f408,f3198]) ).
fof(f3198,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| sum_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) )
| ~ spl8_207 ),
inference(avatar_component_clause,[],[f3197]) ).
fof(f408,plain,
( member(null_class,universal_class)
| ~ spl8_30 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f22342,plain,
( spl8_608
| ~ spl8_30
| ~ spl8_69
| ~ spl8_196 ),
inference(avatar_split_clause,[],[f7524,f2733,f680,f406,f22340]) ).
fof(f22340,plain,
( spl8_608
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class)))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_608])]) ).
fof(f2733,plain,
( spl8_196
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_196])]) ).
fof(f7524,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class)))) = X0
| ~ member(X0,universal_class) )
| ~ spl8_30
| ~ spl8_69
| ~ spl8_196 ),
inference(forward_demodulation,[],[f7505,f682]) ).
fof(f7505,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(null_class),sum_class(null_class))))) = X0 )
| ~ spl8_30
| ~ spl8_196 ),
inference(resolution,[],[f408,f2734]) ).
fof(f2734,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) = X0 )
| ~ spl8_196 ),
inference(avatar_component_clause,[],[f2733]) ).
fof(f22338,plain,
( spl8_607
| ~ spl8_15
| ~ spl8_556 ),
inference(avatar_split_clause,[],[f22292,f22060,f335,f22336]) ).
fof(f335,plain,
( spl8_15
<=> ! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
fof(f22060,plain,
( spl8_556
<=> ! [X0] :
( null_class = unordered_pair(sK0,X0)
| sK2(unordered_pair(sK0,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_556])]) ).
fof(f22292,plain,
( ! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(sK0,X0) )
| ~ spl8_15
| ~ spl8_556 ),
inference(duplicate_literal_removal,[],[f22251]) ).
fof(f22251,plain,
( ! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(sK0,X0)
| null_class = unordered_pair(sK0,X0) )
| ~ spl8_15
| ~ spl8_556 ),
inference(superposition,[],[f336,f22061]) ).
fof(f22061,plain,
( ! [X0] :
( sK2(unordered_pair(sK0,X0)) = X0
| null_class = unordered_pair(sK0,X0) )
| ~ spl8_556 ),
inference(avatar_component_clause,[],[f22060]) ).
fof(f336,plain,
( ! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 )
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f22334,plain,
( spl8_606
| ~ spl8_130
| ~ spl8_184 ),
inference(avatar_split_clause,[],[f2537,f2496,f1255,f22332]) ).
fof(f22332,plain,
( spl8_606
<=> ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_606])]) ).
fof(f1255,plain,
( spl8_130
<=> ! [X2,X0,X1] :
( member(sK4(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_130])]) ).
fof(f2496,plain,
( spl8_184
<=> ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X2)
| ~ member(sK4(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_184])]) ).
fof(f2537,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2) )
| ~ spl8_130
| ~ spl8_184 ),
inference(duplicate_literal_removal,[],[f2519]) ).
fof(f2519,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X2)
| subclass(X0,intersection(X1,X2)) )
| ~ spl8_130
| ~ spl8_184 ),
inference(resolution,[],[f2497,f1256]) ).
fof(f1256,plain,
( ! [X2,X0,X1] :
( member(sK4(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) )
| ~ spl8_130 ),
inference(avatar_component_clause,[],[f1255]) ).
fof(f2497,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X2)
| ~ member(sK4(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl8_184 ),
inference(avatar_component_clause,[],[f2496]) ).
fof(f22330,plain,
( spl8_605
| ~ spl8_20
| ~ spl8_168 ),
inference(avatar_split_clause,[],[f2088,f2013,f355,f22328]) ).
fof(f22328,plain,
( spl8_605
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X2)
| ~ function(intersection(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_605])]) ).
fof(f355,plain,
( spl8_20
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
fof(f2013,plain,
( spl8_168
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subclass(intersection(X2,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_168])]) ).
fof(f2088,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X2)
| ~ function(intersection(X1,X2)) )
| ~ spl8_20
| ~ spl8_168 ),
inference(resolution,[],[f2014,f356]) ).
fof(f356,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f2014,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(intersection(X2,X1),X3)
| ~ member(X0,X2)
| member(X0,X3)
| ~ member(X0,X1) )
| ~ spl8_168 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f22326,plain,
( spl8_604
| ~ spl8_13
| ~ spl8_167 ),
inference(avatar_split_clause,[],[f2051,f2009,f326,f22324]) ).
fof(f22324,plain,
( spl8_604
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| ~ subclass(unordered_pair(X1,X2),X3)
| member(X0,sum_class(power_class(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_604])]) ).
fof(f326,plain,
( spl8_13
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
fof(f2009,plain,
( spl8_167
<=> ! [X2,X0,X1] :
( member(X0,sum_class(power_class(X1)))
| ~ member(X0,X2)
| ~ subclass(X2,X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_167])]) ).
fof(f2051,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| ~ subclass(unordered_pair(X1,X2),X3)
| member(X0,sum_class(power_class(X3))) )
| ~ spl8_13
| ~ spl8_167 ),
inference(resolution,[],[f2010,f327]) ).
fof(f327,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f2010,plain,
( ! [X2,X0,X1] :
( ~ member(X2,universal_class)
| ~ member(X0,X2)
| ~ subclass(X2,X1)
| member(X0,sum_class(power_class(X1))) )
| ~ spl8_167 ),
inference(avatar_component_clause,[],[f2009]) ).
fof(f22322,plain,
( spl8_603
| ~ spl8_13
| ~ spl8_166 ),
inference(avatar_split_clause,[],[f2016,f2005,f326,f22320]) ).
fof(f22320,plain,
( spl8_603
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(unordered_pair(X1,X2),X3)
| member(X0,sum_class(complement(X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_603])]) ).
fof(f2005,plain,
( spl8_166
<=> ! [X2,X0,X1] :
( member(X0,sum_class(complement(X1)))
| ~ member(X0,X2)
| member(X2,X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_166])]) ).
fof(f2016,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(unordered_pair(X1,X2),X3)
| member(X0,sum_class(complement(X3))) )
| ~ spl8_13
| ~ spl8_166 ),
inference(resolution,[],[f2006,f327]) ).
fof(f2006,plain,
( ! [X2,X0,X1] :
( ~ member(X2,universal_class)
| ~ member(X0,X2)
| member(X2,X1)
| member(X0,sum_class(complement(X1))) )
| ~ spl8_166 ),
inference(avatar_component_clause,[],[f2005]) ).
fof(f22318,plain,
( spl8_602
| ~ spl8_99
| ~ spl8_163 ),
inference(avatar_split_clause,[],[f1980,f1882,f896,f22316]) ).
fof(f22316,plain,
( spl8_602
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| ~ member(X3,sum_class(X2))
| ~ subclass(universal_class,sK5(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_602])]) ).
fof(f896,plain,
( spl8_99
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_99])]) ).
fof(f1882,plain,
( spl8_163
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK5(X2,X1))
| ~ member(X2,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_163])]) ).
fof(f1980,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| ~ member(X3,sum_class(X2))
| ~ subclass(universal_class,sK5(X3,X2)) )
| ~ spl8_99
| ~ spl8_163 ),
inference(resolution,[],[f1883,f897]) ).
fof(f897,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_99 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f1883,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK5(X2,X1))
| member(X0,sum_class(X1))
| ~ member(X2,sum_class(X1)) )
| ~ spl8_163 ),
inference(avatar_component_clause,[],[f1882]) ).
fof(f22314,plain,
( spl8_601
| ~ spl8_27
| ~ spl8_159 ),
inference(avatar_split_clause,[],[f1942,f1837,f384,f22312]) ).
fof(f22312,plain,
( spl8_601
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(power_class(X1),X2)))
| subclass(sK5(X0,intersection(power_class(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_601])]) ).
fof(f384,plain,
( spl8_27
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
fof(f1837,plain,
( spl8_159
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK5(X0,intersection(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_159])]) ).
fof(f1942,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(power_class(X1),X2)))
| subclass(sK5(X0,intersection(power_class(X1),X2)),X1) )
| ~ spl8_27
| ~ spl8_159 ),
inference(resolution,[],[f1838,f385]) ).
fof(f385,plain,
( ! [X0,X1] :
( ~ member(X0,power_class(X1))
| subclass(X0,X1) )
| ~ spl8_27 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f1838,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,intersection(X1,X2)),X1)
| ~ member(X0,sum_class(intersection(X1,X2))) )
| ~ spl8_159 ),
inference(avatar_component_clause,[],[f1837]) ).
fof(f22310,plain,
( spl8_600
| ~ spl8_25
| ~ spl8_159 ),
inference(avatar_split_clause,[],[f1934,f1837,f376,f22308]) ).
fof(f22308,plain,
( spl8_600
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(complement(X1),X2)))
| ~ member(sK5(X0,intersection(complement(X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_600])]) ).
fof(f376,plain,
( spl8_25
<=> ! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
fof(f1934,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(complement(X1),X2)))
| ~ member(sK5(X0,intersection(complement(X1),X2)),X1) )
| ~ spl8_25
| ~ spl8_159 ),
inference(resolution,[],[f1838,f377]) ).
fof(f377,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| ~ member(X1,X0) )
| ~ spl8_25 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f22306,plain,
( spl8_599
| ~ spl8_27
| ~ spl8_158 ),
inference(avatar_split_clause,[],[f1910,f1833,f384,f22304]) ).
fof(f22304,plain,
( spl8_599
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,power_class(X2))))
| subclass(sK5(X0,intersection(X1,power_class(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_599])]) ).
fof(f1833,plain,
( spl8_158
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK5(X0,intersection(X1,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_158])]) ).
fof(f1910,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,power_class(X2))))
| subclass(sK5(X0,intersection(X1,power_class(X2))),X2) )
| ~ spl8_27
| ~ spl8_158 ),
inference(resolution,[],[f1834,f385]) ).
fof(f1834,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,intersection(X1,X2)),X2)
| ~ member(X0,sum_class(intersection(X1,X2))) )
| ~ spl8_158 ),
inference(avatar_component_clause,[],[f1833]) ).
fof(f22302,plain,
( spl8_598
| ~ spl8_25
| ~ spl8_158 ),
inference(avatar_split_clause,[],[f1902,f1833,f376,f22300]) ).
fof(f22300,plain,
( spl8_598
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,complement(X2))))
| ~ member(sK5(X0,intersection(X1,complement(X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_598])]) ).
fof(f1902,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,complement(X2))))
| ~ member(sK5(X0,intersection(X1,complement(X2))),X2) )
| ~ spl8_25
| ~ spl8_158 ),
inference(resolution,[],[f1834,f377]) ).
fof(f22298,plain,
( spl8_597
| ~ spl8_16
| ~ spl8_155 ),
inference(avatar_split_clause,[],[f1816,f1548,f339,f22296]) ).
fof(f22296,plain,
( spl8_597
<=> ! [X0,X1] :
( member(sK2(sK4(X0,X1)),sum_class(X0))
| subclass(X0,X1)
| null_class = sK4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_597])]) ).
fof(f339,plain,
( spl8_16
<=> ! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
fof(f1548,plain,
( spl8_155
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK4(X1,X2))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_155])]) ).
fof(f1816,plain,
( ! [X0,X1] :
( member(sK2(sK4(X0,X1)),sum_class(X0))
| subclass(X0,X1)
| null_class = sK4(X0,X1) )
| ~ spl8_16
| ~ spl8_155 ),
inference(resolution,[],[f1549,f340]) ).
fof(f340,plain,
( ! [X0] :
( member(sK2(X0),X0)
| null_class = X0 )
| ~ spl8_16 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f1549,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK4(X1,X2))
| member(X0,sum_class(X1))
| subclass(X1,X2) )
| ~ spl8_155 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f22247,plain,
( spl8_596
| ~ spl8_47
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1805,f1544,f496,f22245]) ).
fof(f22245,plain,
( spl8_596
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sK5(X1,X2))
| member(X0,sum_class(union(X2,X3)))
| ~ member(X1,sum_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_596])]) ).
fof(f496,plain,
( spl8_47
<=> ! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
fof(f1544,plain,
( spl8_154
<=> ! [X0,X3,X2,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_154])]) ).
fof(f1805,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sK5(X1,X2))
| member(X0,sum_class(union(X2,X3)))
| ~ member(X1,sum_class(X2)) )
| ~ spl8_47
| ~ spl8_154 ),
inference(resolution,[],[f1545,f497]) ).
fof(f497,plain,
( ! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) )
| ~ spl8_47 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f1545,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X1)
| ~ member(X0,X3)
| member(X0,sum_class(union(X1,X2))) )
| ~ spl8_154 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f22243,plain,
( spl8_595
| ~ spl8_46
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1774,f1544,f492,f22241]) ).
fof(f22241,plain,
( spl8_595
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sK5(X1,X2),X3)))
| ~ member(X1,sum_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_595])]) ).
fof(f492,plain,
( spl8_46
<=> ! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
fof(f1774,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sK5(X1,X2),X3)))
| ~ member(X1,sum_class(X2)) )
| ~ spl8_46
| ~ spl8_154 ),
inference(resolution,[],[f1545,f493]) ).
fof(f493,plain,
( ! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) )
| ~ spl8_46 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f22239,plain,
( spl8_594
| ~ spl8_47
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1757,f1540,f496,f22237]) ).
fof(f22237,plain,
( spl8_594
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sK5(X1,X2))
| member(X0,sum_class(union(X3,X2)))
| ~ member(X1,sum_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_594])]) ).
fof(f1540,plain,
( spl8_153
<=> ! [X0,X3,X2,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_153])]) ).
fof(f1757,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sK5(X1,X2))
| member(X0,sum_class(union(X3,X2)))
| ~ member(X1,sum_class(X2)) )
| ~ spl8_47
| ~ spl8_153 ),
inference(resolution,[],[f1541,f497]) ).
fof(f1541,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X2)
| ~ member(X0,X3)
| member(X0,sum_class(union(X1,X2))) )
| ~ spl8_153 ),
inference(avatar_component_clause,[],[f1540]) ).
fof(f22235,plain,
( spl8_593
| ~ spl8_46
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1726,f1540,f492,f22233]) ).
fof(f22233,plain,
( spl8_593
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sK5(X1,X3))))
| ~ member(X1,sum_class(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_593])]) ).
fof(f1726,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sK5(X1,X3))))
| ~ member(X1,sum_class(X3)) )
| ~ spl8_46
| ~ spl8_153 ),
inference(resolution,[],[f1541,f493]) ).
fof(f22231,plain,
( spl8_592
| ~ spl8_45
| ~ spl8_152 ),
inference(avatar_split_clause,[],[f1712,f1536,f488,f22229]) ).
fof(f22229,plain,
( spl8_592
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X0,X2)
| ~ subclass(sum_class(unordered_pair(X1,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_592])]) ).
fof(f1536,plain,
( spl8_152
<=> ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_152])]) ).
fof(f1712,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X0,X2)
| ~ subclass(sum_class(unordered_pair(X1,X3)),X2) )
| ~ spl8_45
| ~ spl8_152 ),
inference(resolution,[],[f1537,f489]) ).
fof(f1537,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
| ~ spl8_152 ),
inference(avatar_component_clause,[],[f1536]) ).
fof(f22227,plain,
( spl8_591
| ~ spl8_45
| ~ spl8_151 ),
inference(avatar_split_clause,[],[f1703,f1520,f488,f22225]) ).
fof(f22225,plain,
( spl8_591
<=> ! [X2,X0,X1,X3] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X0,X2)
| ~ subclass(sum_class(unordered_pair(X3,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_591])]) ).
fof(f1520,plain,
( spl8_151
<=> ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X2)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_151])]) ).
fof(f1703,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X0,X2)
| ~ subclass(sum_class(unordered_pair(X3,X1)),X2) )
| ~ spl8_45
| ~ spl8_151 ),
inference(resolution,[],[f1521,f489]) ).
fof(f1521,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X2)
| ~ member(X2,universal_class) )
| ~ spl8_151 ),
inference(avatar_component_clause,[],[f1520]) ).
fof(f22223,plain,
( spl8_590
| ~ spl8_104
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1677,f1516,f969,f22221]) ).
fof(f22221,plain,
( spl8_590
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,unordered_pair(X2,X3))
| member(sK5(X0,X1),sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_590])]) ).
fof(f969,plain,
( spl8_104
<=> ! [X2,X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_104])]) ).
fof(f1516,plain,
( spl8_150
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(sK5(X0,X1),X2)
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_150])]) ).
fof(f1677,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,unordered_pair(X2,X3))
| member(sK5(X0,X1),sum_class(universal_class)) )
| ~ spl8_104
| ~ spl8_150 ),
inference(resolution,[],[f1517,f970]) ).
fof(f970,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(universal_class)) )
| ~ spl8_104 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f1517,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,X1),X2)
| ~ member(X0,sum_class(X1))
| ~ subclass(X1,X2) )
| ~ spl8_150 ),
inference(avatar_component_clause,[],[f1516]) ).
fof(f22219,plain,
( spl8_589
| ~ spl8_45
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1674,f1516,f488,f22217]) ).
fof(f22217,plain,
( spl8_589
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,X2)
| member(sK5(X0,X1),X3)
| ~ subclass(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_589])]) ).
fof(f1674,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,X2)
| member(sK5(X0,X1),X3)
| ~ subclass(X2,X3) )
| ~ spl8_45
| ~ spl8_150 ),
inference(resolution,[],[f1517,f489]) ).
fof(f22215,plain,
( spl8_588
| ~ spl8_45
| ~ spl8_147 ),
inference(avatar_split_clause,[],[f1654,f1504,f488,f22213]) ).
fof(f22213,plain,
( spl8_588
<=> ! [X0,X3,X2,X1] :
( subclass(unordered_pair(X0,X1),X2)
| member(sK4(unordered_pair(X0,X1),X2),X3)
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_588])]) ).
fof(f1504,plain,
( spl8_147
<=> ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),X2),universal_class)
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_147])]) ).
fof(f1654,plain,
( ! [X2,X3,X0,X1] :
( subclass(unordered_pair(X0,X1),X2)
| member(sK4(unordered_pair(X0,X1),X2),X3)
| ~ subclass(universal_class,X3) )
| ~ spl8_45
| ~ spl8_147 ),
inference(resolution,[],[f1505,f489]) ).
fof(f1505,plain,
( ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),X2),universal_class)
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl8_147 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f22211,plain,
( spl8_587
| ~ spl8_45
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f1581,f1492,f488,f22209]) ).
fof(f22209,plain,
( spl8_587
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| member(sK4(intersection(X0,X1),X2),X3)
| ~ subclass(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_587])]) ).
fof(f1492,plain,
( spl8_144
<=> ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_144])]) ).
fof(f1581,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| member(sK4(intersection(X0,X1),X2),X3)
| ~ subclass(X1,X3) )
| ~ spl8_45
| ~ spl8_144 ),
inference(resolution,[],[f1493,f489]) ).
fof(f1493,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl8_144 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f22207,plain,
( spl8_586
| spl8_2
| ~ spl8_544 ),
inference(avatar_split_clause,[],[f21807,f18373,f275,f22205]) ).
fof(f22205,plain,
( spl8_586
<=> ! [X0] :
( null_class = unordered_pair(X0,sK1)
| sK2(unordered_pair(X0,sK1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_586])]) ).
fof(f18373,plain,
( spl8_544
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_544])]) ).
fof(f21807,plain,
( ! [X0] :
( null_class = unordered_pair(X0,sK1)
| sK2(unordered_pair(X0,sK1)) = X0 )
| spl8_2
| ~ spl8_544 ),
inference(resolution,[],[f18374,f277]) ).
fof(f18374,plain,
( ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X0 )
| ~ spl8_544 ),
inference(avatar_component_clause,[],[f18373]) ).
fof(f22203,plain,
( spl8_585
| ~ spl8_45
| ~ spl8_143 ),
inference(avatar_split_clause,[],[f1553,f1488,f488,f22201]) ).
fof(f22201,plain,
( spl8_585
<=> ! [X0,X3,X2,X1] :
( subclass(intersection(X0,X1),X2)
| member(sK4(intersection(X0,X1),X2),X3)
| ~ subclass(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_585])]) ).
fof(f1488,plain,
( spl8_143
<=> ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_143])]) ).
fof(f1553,plain,
( ! [X2,X3,X0,X1] :
( subclass(intersection(X0,X1),X2)
| member(sK4(intersection(X0,X1),X2),X3)
| ~ subclass(X0,X3) )
| ~ spl8_45
| ~ spl8_143 ),
inference(resolution,[],[f1489,f489]) ).
fof(f1489,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl8_143 ),
inference(avatar_component_clause,[],[f1488]) ).
fof(f22199,plain,
( spl8_584
| ~ spl8_47
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1486,f1298,f496,f22197]) ).
fof(f22197,plain,
( spl8_584
<=> ! [X0,X1] :
( member(sK5(X0,sK3(X1)),sum_class(universal_class))
| ~ member(X1,identity_relation)
| ~ member(X0,sum_class(sK3(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_584])]) ).
fof(f1298,plain,
( spl8_140
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK3(X1))
| ~ member(X1,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_140])]) ).
fof(f1486,plain,
( ! [X0,X1] :
( member(sK5(X0,sK3(X1)),sum_class(universal_class))
| ~ member(X1,identity_relation)
| ~ member(X0,sum_class(sK3(X1))) )
| ~ spl8_47
| ~ spl8_140 ),
inference(resolution,[],[f1299,f497]) ).
fof(f1299,plain,
( ! [X0,X1] :
( ~ member(X0,sK3(X1))
| member(X0,sum_class(universal_class))
| ~ member(X1,identity_relation) )
| ~ spl8_140 ),
inference(avatar_component_clause,[],[f1298]) ).
fof(f22195,plain,
( spl8_583
| ~ spl8_119
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1479,f1298,f1052,f22193]) ).
fof(f22193,plain,
( spl8_583
<=> ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| ~ member(X1,identity_relation)
| ~ subclass(X0,sK3(X1))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_583])]) ).
fof(f1052,plain,
( spl8_119
<=> ! [X0,X1] :
( member(sK2(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_119])]) ).
fof(f1479,plain,
( ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| ~ member(X1,identity_relation)
| ~ subclass(X0,sK3(X1))
| null_class = X0 )
| ~ spl8_119
| ~ spl8_140 ),
inference(resolution,[],[f1299,f1053]) ).
fof(f1053,plain,
( ! [X0,X1] :
( member(sK2(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 )
| ~ spl8_119 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f22191,plain,
( spl8_581
| spl8_582
| ~ spl8_116
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1477,f1298,f1039,f22189,f22162]) ).
fof(f22162,plain,
( spl8_581
<=> ! [X1] :
( ~ member(X1,identity_relation)
| ~ subclass(universal_class,sK3(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_581])]) ).
fof(f22189,plain,
( spl8_582
<=> ! [X0] :
( member(power_class(X0),sum_class(universal_class))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_582])]) ).
fof(f1039,plain,
( spl8_116
<=> ! [X0,X1] :
( member(power_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_116])]) ).
fof(f1477,plain,
( ! [X0,X1] :
( member(power_class(X0),sum_class(universal_class))
| ~ member(X1,identity_relation)
| ~ subclass(universal_class,sK3(X1))
| ~ member(X0,universal_class) )
| ~ spl8_116
| ~ spl8_140 ),
inference(resolution,[],[f1299,f1040]) ).
fof(f1040,plain,
( ! [X0,X1] :
( member(power_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl8_116 ),
inference(avatar_component_clause,[],[f1039]) ).
fof(f22164,plain,
( spl8_581
| spl8_573
| ~ spl8_115
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1476,f1298,f1035,f22128,f22162]) ).
fof(f22128,plain,
( spl8_573
<=> ! [X0] :
( member(sum_class(X0),sum_class(universal_class))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_573])]) ).
fof(f1035,plain,
( spl8_115
<=> ! [X0,X1] :
( member(sum_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_115])]) ).
fof(f1476,plain,
( ! [X0,X1] :
( member(sum_class(X0),sum_class(universal_class))
| ~ member(X1,identity_relation)
| ~ subclass(universal_class,sK3(X1))
| ~ member(X0,universal_class) )
| ~ spl8_115
| ~ spl8_140 ),
inference(resolution,[],[f1299,f1036]) ).
fof(f1036,plain,
( ! [X0,X1] :
( member(sum_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl8_115 ),
inference(avatar_component_clause,[],[f1035]) ).
fof(f22160,plain,
( spl8_580
| ~ spl8_47
| ~ spl8_139 ),
inference(avatar_split_clause,[],[f1468,f1294,f496,f22158]) ).
fof(f22158,plain,
( spl8_580
<=> ! [X0,X1] :
( member(sK5(X0,sK2(X1)),sum_class(X1))
| null_class = X1
| ~ member(X0,sum_class(sK2(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_580])]) ).
fof(f1294,plain,
( spl8_139
<=> ! [X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK2(X1))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_139])]) ).
fof(f1468,plain,
( ! [X0,X1] :
( member(sK5(X0,sK2(X1)),sum_class(X1))
| null_class = X1
| ~ member(X0,sum_class(sK2(X1))) )
| ~ spl8_47
| ~ spl8_139 ),
inference(resolution,[],[f1295,f497]) ).
fof(f1295,plain,
( ! [X0,X1] :
( ~ member(X0,sK2(X1))
| member(X0,sum_class(X1))
| null_class = X1 )
| ~ spl8_139 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f22156,plain,
( spl8_579
| ~ spl8_119
| ~ spl8_139 ),
inference(avatar_split_clause,[],[f1461,f1294,f1052,f22154]) ).
fof(f22154,plain,
( spl8_579
<=> ! [X0,X1] :
( member(sK2(X0),sum_class(X1))
| null_class = X1
| ~ subclass(X0,sK2(X1))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_579])]) ).
fof(f1461,plain,
( ! [X0,X1] :
( member(sK2(X0),sum_class(X1))
| null_class = X1
| ~ subclass(X0,sK2(X1))
| null_class = X0 )
| ~ spl8_119
| ~ spl8_139 ),
inference(resolution,[],[f1295,f1053]) ).
fof(f22152,plain,
( spl8_578
| ~ spl8_47
| ~ spl8_138 ),
inference(avatar_split_clause,[],[f1454,f1290,f496,f22150]) ).
fof(f22150,plain,
( spl8_578
<=> ! [X0,X1] :
( member(sK5(X0,sK2(X1)),sum_class(universal_class))
| null_class = X1
| ~ member(X0,sum_class(sK2(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_578])]) ).
fof(f1290,plain,
( spl8_138
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK2(X1))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_138])]) ).
fof(f1454,plain,
( ! [X0,X1] :
( member(sK5(X0,sK2(X1)),sum_class(universal_class))
| null_class = X1
| ~ member(X0,sum_class(sK2(X1))) )
| ~ spl8_47
| ~ spl8_138 ),
inference(resolution,[],[f1291,f497]) ).
fof(f1291,plain,
( ! [X0,X1] :
( ~ member(X0,sK2(X1))
| member(X0,sum_class(universal_class))
| null_class = X1 )
| ~ spl8_138 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f22148,plain,
( spl8_577
| spl8_1
| ~ spl8_544 ),
inference(avatar_split_clause,[],[f21806,f18373,f270,f22146]) ).
fof(f22146,plain,
( spl8_577
<=> ! [X0] :
( null_class = unordered_pair(X0,sK0)
| sK2(unordered_pair(X0,sK0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_577])]) ).
fof(f21806,plain,
( ! [X0] :
( null_class = unordered_pair(X0,sK0)
| sK2(unordered_pair(X0,sK0)) = X0 )
| spl8_1
| ~ spl8_544 ),
inference(resolution,[],[f18374,f272]) ).
fof(f22144,plain,
( spl8_576
| ~ spl8_119
| ~ spl8_138 ),
inference(avatar_split_clause,[],[f1447,f1290,f1052,f22142]) ).
fof(f22142,plain,
( spl8_576
<=> ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| null_class = X1
| ~ subclass(X0,sK2(X1))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_576])]) ).
fof(f1447,plain,
( ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| null_class = X1
| ~ subclass(X0,sK2(X1))
| null_class = X0 )
| ~ spl8_119
| ~ spl8_138 ),
inference(resolution,[],[f1291,f1053]) ).
fof(f22140,plain,
( spl8_575
| ~ spl8_47
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f1440,f1286,f496,f22138]) ).
fof(f22138,plain,
( spl8_575
<=> ! [X0,X1] :
( member(sK5(X0,power_class(X1)),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ member(X0,sum_class(power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_575])]) ).
fof(f1286,plain,
( spl8_137
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,power_class(X1))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_137])]) ).
fof(f1440,plain,
( ! [X0,X1] :
( member(sK5(X0,power_class(X1)),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl8_47
| ~ spl8_137 ),
inference(resolution,[],[f1287,f497]) ).
fof(f1287,plain,
( ! [X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,sum_class(universal_class))
| ~ member(X1,universal_class) )
| ~ spl8_137 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f22136,plain,
( spl8_574
| ~ spl8_119
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f1433,f1286,f1052,f22134]) ).
fof(f22134,plain,
( spl8_574
<=> ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ subclass(X0,power_class(X1))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_574])]) ).
fof(f1433,plain,
( ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ subclass(X0,power_class(X1))
| null_class = X0 )
| ~ spl8_119
| ~ spl8_137 ),
inference(resolution,[],[f1287,f1053]) ).
fof(f22130,plain,
( spl8_553
| spl8_573
| ~ spl8_115
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f1430,f1286,f1035,f22128,f18547]) ).
fof(f18547,plain,
( spl8_553
<=> ! [X2] :
( ~ member(X2,universal_class)
| ~ subclass(universal_class,power_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_553])]) ).
fof(f1430,plain,
( ! [X0,X1] :
( member(sum_class(X0),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ subclass(universal_class,power_class(X1))
| ~ member(X0,universal_class) )
| ~ spl8_115
| ~ spl8_137 ),
inference(resolution,[],[f1287,f1036]) ).
fof(f22126,plain,
( spl8_572
| ~ spl8_47
| ~ spl8_136 ),
inference(avatar_split_clause,[],[f1424,f1279,f496,f22124]) ).
fof(f22124,plain,
( spl8_572
<=> ! [X0,X1] :
( member(sK5(X0,sum_class(X1)),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ member(X0,sum_class(sum_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_572])]) ).
fof(f1279,plain,
( spl8_136
<=> ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sum_class(X1))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_136])]) ).
fof(f1424,plain,
( ! [X0,X1] :
( member(sK5(X0,sum_class(X1)),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ member(X0,sum_class(sum_class(X1))) )
| ~ spl8_47
| ~ spl8_136 ),
inference(resolution,[],[f1280,f497]) ).
fof(f1280,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,sum_class(universal_class))
| ~ member(X1,universal_class) )
| ~ spl8_136 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f22122,plain,
( spl8_571
| ~ spl8_119
| ~ spl8_136 ),
inference(avatar_split_clause,[],[f1417,f1279,f1052,f22120]) ).
fof(f22120,plain,
( spl8_571
<=> ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ subclass(X0,sum_class(X1))
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_571])]) ).
fof(f1417,plain,
( ! [X0,X1] :
( member(sK2(X0),sum_class(universal_class))
| ~ member(X1,universal_class)
| ~ subclass(X0,sum_class(X1))
| null_class = X0 )
| ~ spl8_119
| ~ spl8_136 ),
inference(resolution,[],[f1280,f1053]) ).
fof(f22118,plain,
( spl8_570
| ~ spl8_50
| ~ spl8_135 ),
inference(avatar_split_clause,[],[f1408,f1275,f544,f22116]) ).
fof(f22116,plain,
( spl8_570
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(X2,sum_class(universal_class))
| ~ member(X2,sK5(X0,power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_570])]) ).
fof(f544,plain,
( spl8_50
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
fof(f1275,plain,
( spl8_135
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK5(X0,power_class(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_135])]) ).
fof(f1408,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(X2,sum_class(universal_class))
| ~ member(X2,sK5(X0,power_class(X1))) )
| ~ spl8_50
| ~ spl8_135 ),
inference(resolution,[],[f1276,f545]) ).
fof(f545,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X0,sum_class(X1))
| ~ member(X0,X2) )
| ~ spl8_50 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f1276,plain,
( ! [X0,X1] :
( member(sK5(X0,power_class(X1)),universal_class)
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl8_135 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f22114,plain,
( spl8_569
| ~ spl8_50
| ~ spl8_133 ),
inference(avatar_split_clause,[],[f1401,f1267,f544,f22112]) ).
fof(f22112,plain,
( spl8_569
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(X2,sum_class(universal_class))
| ~ member(X2,sK5(X0,domain_of(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_569])]) ).
fof(f1267,plain,
( spl8_133
<=> ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK5(X0,domain_of(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_133])]) ).
fof(f1401,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(X2,sum_class(universal_class))
| ~ member(X2,sK5(X0,domain_of(X1))) )
| ~ spl8_50
| ~ spl8_133 ),
inference(resolution,[],[f1268,f545]) ).
fof(f1268,plain,
( ! [X0,X1] :
( member(sK5(X0,domain_of(X1)),universal_class)
| ~ member(X0,sum_class(domain_of(X1))) )
| ~ spl8_133 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f22110,plain,
( spl8_568
| ~ spl8_50
| ~ spl8_132 ),
inference(avatar_split_clause,[],[f1394,f1263,f544,f22108]) ).
fof(f22108,plain,
( spl8_568
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(X2,sum_class(universal_class))
| ~ member(X2,sK5(X0,complement(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_568])]) ).
fof(f1263,plain,
( spl8_132
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK5(X0,complement(X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_132])]) ).
fof(f1394,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(X2,sum_class(universal_class))
| ~ member(X2,sK5(X0,complement(X1))) )
| ~ spl8_50
| ~ spl8_132 ),
inference(resolution,[],[f1264,f545]) ).
fof(f1264,plain,
( ! [X0,X1] :
( member(sK5(X0,complement(X1)),universal_class)
| ~ member(X0,sum_class(complement(X1))) )
| ~ spl8_132 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f22106,plain,
( spl8_567
| spl8_2
| ~ spl8_543 ),
inference(avatar_split_clause,[],[f21659,f18369,f275,f22104]) ).
fof(f22104,plain,
( spl8_567
<=> ! [X0] :
( null_class = unordered_pair(sK1,X0)
| sK2(unordered_pair(sK1,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_567])]) ).
fof(f18369,plain,
( spl8_543
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_543])]) ).
fof(f21659,plain,
( ! [X0] :
( null_class = unordered_pair(sK1,X0)
| sK2(unordered_pair(sK1,X0)) = X0 )
| spl8_2
| ~ spl8_543 ),
inference(resolution,[],[f18370,f277]) ).
fof(f18370,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X1 )
| ~ spl8_543 ),
inference(avatar_component_clause,[],[f18369]) ).
fof(f22102,plain,
( spl8_566
| ~ spl8_37
| ~ spl8_131 ),
inference(avatar_split_clause,[],[f1387,f1259,f435,f22100]) ).
fof(f22100,plain,
( spl8_566
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(union(X1,X2))))
| ~ member(sK5(X0,complement(union(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_566])]) ).
fof(f435,plain,
( spl8_37
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
fof(f1259,plain,
( spl8_131
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ member(sK5(X0,complement(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_131])]) ).
fof(f1387,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(union(X1,X2))))
| ~ member(sK5(X0,complement(union(X1,X2))),X1) )
| ~ spl8_37
| ~ spl8_131 ),
inference(resolution,[],[f1260,f436]) ).
fof(f436,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) )
| ~ spl8_37 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f1260,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,complement(X1)),X1)
| ~ member(X0,sum_class(complement(X1))) )
| ~ spl8_131 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f22098,plain,
( spl8_565
| ~ spl8_38
| ~ spl8_131 ),
inference(avatar_split_clause,[],[f1386,f1259,f439,f22096]) ).
fof(f22096,plain,
( spl8_565
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(union(X1,X2))))
| ~ member(sK5(X0,complement(union(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_565])]) ).
fof(f439,plain,
( spl8_38
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
fof(f1386,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(union(X1,X2))))
| ~ member(sK5(X0,complement(union(X1,X2))),X2) )
| ~ spl8_38
| ~ spl8_131 ),
inference(resolution,[],[f1260,f440]) ).
fof(f440,plain,
( ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) )
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f22094,plain,
( spl8_564
| ~ spl8_114
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1379,f1255,f1031,f22092]) ).
fof(f22092,plain,
( spl8_564
<=> ! [X2,X0,X1] :
( ~ subclass(X0,sK2(X1))
| subclass(X0,X2)
| ~ member(sK4(X0,X2),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_564])]) ).
fof(f1031,plain,
( spl8_114
<=> ! [X0,X1] :
( ~ member(X0,sK2(X1))
| ~ member(X0,X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_114])]) ).
fof(f1379,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,sK2(X1))
| subclass(X0,X2)
| ~ member(sK4(X0,X2),X1)
| null_class = X1 )
| ~ spl8_114
| ~ spl8_130 ),
inference(resolution,[],[f1256,f1032]) ).
fof(f1032,plain,
( ! [X0,X1] :
( ~ member(X0,sK2(X1))
| ~ member(X0,X1)
| null_class = X1 )
| ~ spl8_114 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f22090,plain,
( spl8_563
| ~ spl8_50
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1363,f1255,f544,f22088]) ).
fof(f22088,plain,
( spl8_563
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| member(X3,sum_class(X1))
| ~ member(X3,sK4(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_563])]) ).
fof(f1363,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| member(X3,sum_class(X1))
| ~ member(X3,sK4(X0,X2)) )
| ~ spl8_50
| ~ spl8_130 ),
inference(resolution,[],[f1256,f545]) ).
fof(f22086,plain,
( spl8_562
| ~ spl8_35
| ~ spl8_124 ),
inference(avatar_split_clause,[],[f1332,f1231,f427,f22084]) ).
fof(f22084,plain,
( spl8_562
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(sK2(intersection(X0,intersection(X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_562])]) ).
fof(f427,plain,
( spl8_35
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
fof(f1231,plain,
( spl8_124
<=> ! [X0,X1] :
( member(sK2(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_124])]) ).
fof(f1332,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(sK2(intersection(X0,intersection(X1,X2))),X1) )
| ~ spl8_35
| ~ spl8_124 ),
inference(resolution,[],[f1232,f428]) ).
fof(f428,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) )
| ~ spl8_35 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f1232,plain,
( ! [X0,X1] :
( member(sK2(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class )
| ~ spl8_124 ),
inference(avatar_component_clause,[],[f1231]) ).
fof(f22082,plain,
( spl8_561
| ~ spl8_36
| ~ spl8_124 ),
inference(avatar_split_clause,[],[f1331,f1231,f431,f22080]) ).
fof(f22080,plain,
( spl8_561
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(sK2(intersection(X0,intersection(X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_561])]) ).
fof(f431,plain,
( spl8_36
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
fof(f1331,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,intersection(X1,X2))
| member(sK2(intersection(X0,intersection(X1,X2))),X2) )
| ~ spl8_36
| ~ spl8_124 ),
inference(resolution,[],[f1232,f432]) ).
fof(f432,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) )
| ~ spl8_36 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f22078,plain,
( spl8_560
| ~ spl8_50
| ~ spl8_124 ),
inference(avatar_split_clause,[],[f1323,f1231,f544,f22076]) ).
fof(f22076,plain,
( spl8_560
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(X2,sum_class(X1))
| ~ member(X2,sK2(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_560])]) ).
fof(f1323,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(X2,sum_class(X1))
| ~ member(X2,sK2(intersection(X0,X1))) )
| ~ spl8_50
| ~ spl8_124 ),
inference(resolution,[],[f1232,f545]) ).
fof(f22074,plain,
( spl8_559
| ~ spl8_35
| ~ spl8_123 ),
inference(avatar_split_clause,[],[f1310,f1227,f427,f22072]) ).
fof(f22072,plain,
( spl8_559
<=> ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(sK2(intersection(intersection(X0,X1),X2)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_559])]) ).
fof(f1227,plain,
( spl8_123
<=> ! [X0,X1] :
( member(sK2(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_123])]) ).
fof(f1310,plain,
( ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(sK2(intersection(intersection(X0,X1),X2)),X0) )
| ~ spl8_35
| ~ spl8_123 ),
inference(resolution,[],[f1228,f428]) ).
fof(f1228,plain,
( ! [X0,X1] :
( member(sK2(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class )
| ~ spl8_123 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f22070,plain,
( spl8_558
| ~ spl8_36
| ~ spl8_123 ),
inference(avatar_split_clause,[],[f1309,f1227,f431,f22068]) ).
fof(f22068,plain,
( spl8_558
<=> ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(sK2(intersection(intersection(X0,X1),X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_558])]) ).
fof(f1309,plain,
( ! [X2,X0,X1] :
( null_class = intersection(intersection(X0,X1),X2)
| member(sK2(intersection(intersection(X0,X1),X2)),X1) )
| ~ spl8_36
| ~ spl8_123 ),
inference(resolution,[],[f1228,f432]) ).
fof(f22066,plain,
( spl8_557
| ~ spl8_50
| ~ spl8_123 ),
inference(avatar_split_clause,[],[f1301,f1227,f544,f22064]) ).
fof(f22064,plain,
( spl8_557
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(X2,sum_class(X0))
| ~ member(X2,sK2(intersection(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_557])]) ).
fof(f1301,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(X2,sum_class(X0))
| ~ member(X2,sK2(intersection(X0,X1))) )
| ~ spl8_50
| ~ spl8_123 ),
inference(resolution,[],[f1228,f545]) ).
fof(f22062,plain,
( spl8_556
| spl8_1
| ~ spl8_543 ),
inference(avatar_split_clause,[],[f21658,f18369,f270,f22060]) ).
fof(f21658,plain,
( ! [X0] :
( null_class = unordered_pair(sK0,X0)
| sK2(unordered_pair(sK0,X0)) = X0 )
| spl8_1
| ~ spl8_543 ),
inference(resolution,[],[f18370,f272]) ).
fof(f22058,plain,
( spl8_555
| ~ spl8_96
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f1091,f1005,f879,f22056]) ).
fof(f22056,plain,
( spl8_555
<=> ! [X0] :
( subclass(power_class(sK7),X0)
| sK7 = sK4(power_class(sK7),X0)
| ~ inductive(sK4(power_class(sK7),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_555])]) ).
fof(f879,plain,
( spl8_96
<=> ! [X0] :
( sK7 = X0
| ~ subclass(X0,sK7)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_96])]) ).
fof(f1005,plain,
( spl8_108
<=> ! [X0,X1] :
( subclass(power_class(X0),X1)
| subclass(sK4(power_class(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_108])]) ).
fof(f1091,plain,
( ! [X0] :
( subclass(power_class(sK7),X0)
| sK7 = sK4(power_class(sK7),X0)
| ~ inductive(sK4(power_class(sK7),X0)) )
| ~ spl8_96
| ~ spl8_108 ),
inference(resolution,[],[f1006,f880]) ).
fof(f880,plain,
( ! [X0] :
( ~ subclass(X0,sK7)
| sK7 = X0
| ~ inductive(X0) )
| ~ spl8_96 ),
inference(avatar_component_clause,[],[f879]) ).
fof(f1006,plain,
( ! [X0,X1] :
( subclass(sK4(power_class(X0),X1),X0)
| subclass(power_class(X0),X1) )
| ~ spl8_108 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f22054,plain,
( spl8_554
| ~ spl8_52
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f932,f896,f578,f22052]) ).
fof(f22052,plain,
( spl8_554
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,union(X0,X1))
| member(unordered_pair(X2,X3),X0)
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_554])]) ).
fof(f578,plain,
( spl8_52
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
fof(f932,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,union(X0,X1))
| member(unordered_pair(X2,X3),X0)
| member(unordered_pair(X2,X3),X1) )
| ~ spl8_52
| ~ spl8_99 ),
inference(resolution,[],[f897,f579]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) )
| ~ spl8_52 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f18549,plain,
( spl8_553
| spl8_349
| ~ spl8_99
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f1427,f1286,f896,f13879,f18547]) ).
fof(f13879,plain,
( spl8_349
<=> ! [X0,X1] : member(unordered_pair(X0,X1),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_349])]) ).
fof(f1427,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ member(X2,universal_class)
| ~ subclass(universal_class,power_class(X2)) )
| ~ spl8_99
| ~ spl8_137 ),
inference(resolution,[],[f1287,f897]) ).
fof(f18544,plain,
( spl8_552
| ~ spl8_224
| ~ spl8_349 ),
inference(avatar_split_clause,[],[f16337,f13879,f3743,f18541]) ).
fof(f18541,plain,
( spl8_552
<=> member(sK2(identity_relation),sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_552])]) ).
fof(f3743,plain,
( spl8_224
<=> sK2(identity_relation) = unordered_pair(unordered_pair(sK3(sK2(identity_relation)),sK3(sK2(identity_relation))),unordered_pair(sK3(sK2(identity_relation)),unordered_pair(sK3(sK2(identity_relation)),sK3(sK2(identity_relation))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_224])]) ).
fof(f16337,plain,
( member(sK2(identity_relation),sum_class(universal_class))
| ~ spl8_224
| ~ spl8_349 ),
inference(superposition,[],[f13880,f3745]) ).
fof(f3745,plain,
( sK2(identity_relation) = unordered_pair(unordered_pair(sK3(sK2(identity_relation)),sK3(sK2(identity_relation))),unordered_pair(sK3(sK2(identity_relation)),unordered_pair(sK3(sK2(identity_relation)),sK3(sK2(identity_relation)))))
| ~ spl8_224 ),
inference(avatar_component_clause,[],[f3743]) ).
fof(f13880,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ spl8_349 ),
inference(avatar_component_clause,[],[f13879]) ).
fof(f18404,plain,
( spl8_551
| ~ spl8_67
| ~ spl8_194 ),
inference(avatar_split_clause,[],[f2981,f2725,f667,f18402]) ).
fof(f18402,plain,
( spl8_551
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ subclass(element_relation,cross_product(X2,X3))
| member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_551])]) ).
fof(f667,plain,
( spl8_67
<=> ! [X0,X3,X2,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
fof(f2725,plain,
( spl8_194
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ subclass(element_relation,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_194])]) ).
fof(f2981,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ subclass(element_relation,cross_product(X2,X3))
| member(X0,X3) )
| ~ spl8_67
| ~ spl8_194 ),
inference(resolution,[],[f2726,f668]) ).
fof(f668,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X1,X3) )
| ~ spl8_67 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f2726,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ member(X1,universal_class)
| ~ member(X0,X1)
| ~ subclass(element_relation,X2) )
| ~ spl8_194 ),
inference(avatar_component_clause,[],[f2725]) ).
fof(f18400,plain,
( spl8_550
| ~ spl8_68
| ~ spl8_194 ),
inference(avatar_split_clause,[],[f2980,f2725,f671,f18398]) ).
fof(f18398,plain,
( spl8_550
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ subclass(element_relation,cross_product(X2,X3))
| member(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_550])]) ).
fof(f671,plain,
( spl8_68
<=> ! [X0,X3,X2,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
fof(f2980,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ subclass(element_relation,cross_product(X2,X3))
| member(X1,X2) )
| ~ spl8_68
| ~ spl8_194 ),
inference(resolution,[],[f2726,f672]) ).
fof(f672,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) )
| ~ spl8_68 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f18396,plain,
( spl8_549
| ~ spl8_106
| ~ spl8_184 ),
inference(avatar_split_clause,[],[f2540,f2496,f997,f18394]) ).
fof(f18394,plain,
( spl8_549
<=> ! [X0,X1] :
( ~ member(sK4(complement(X0),intersection(X1,universal_class)),X1)
| subclass(complement(X0),intersection(X1,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_549])]) ).
fof(f997,plain,
( spl8_106
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| member(sK4(complement(X0),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_106])]) ).
fof(f2540,plain,
( ! [X0,X1] :
( ~ member(sK4(complement(X0),intersection(X1,universal_class)),X1)
| subclass(complement(X0),intersection(X1,universal_class)) )
| ~ spl8_106
| ~ spl8_184 ),
inference(duplicate_literal_removal,[],[f2516]) ).
fof(f2516,plain,
( ! [X0,X1] :
( ~ member(sK4(complement(X0),intersection(X1,universal_class)),X1)
| subclass(complement(X0),intersection(X1,universal_class))
| subclass(complement(X0),intersection(X1,universal_class)) )
| ~ spl8_106
| ~ spl8_184 ),
inference(resolution,[],[f2497,f998]) ).
fof(f998,plain,
( ! [X0,X1] :
( member(sK4(complement(X0),X1),universal_class)
| subclass(complement(X0),X1) )
| ~ spl8_106 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f18392,plain,
( spl8_548
| ~ spl8_107
| ~ spl8_184 ),
inference(avatar_split_clause,[],[f2539,f2496,f1001,f18390]) ).
fof(f18390,plain,
( spl8_548
<=> ! [X0,X1] :
( ~ member(sK4(domain_of(X0),intersection(X1,universal_class)),X1)
| subclass(domain_of(X0),intersection(X1,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_548])]) ).
fof(f1001,plain,
( spl8_107
<=> ! [X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK4(domain_of(X0),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_107])]) ).
fof(f2539,plain,
( ! [X0,X1] :
( ~ member(sK4(domain_of(X0),intersection(X1,universal_class)),X1)
| subclass(domain_of(X0),intersection(X1,universal_class)) )
| ~ spl8_107
| ~ spl8_184 ),
inference(duplicate_literal_removal,[],[f2517]) ).
fof(f2517,plain,
( ! [X0,X1] :
( ~ member(sK4(domain_of(X0),intersection(X1,universal_class)),X1)
| subclass(domain_of(X0),intersection(X1,universal_class))
| subclass(domain_of(X0),intersection(X1,universal_class)) )
| ~ spl8_107
| ~ spl8_184 ),
inference(resolution,[],[f2497,f1002]) ).
fof(f1002,plain,
( ! [X0,X1] :
( member(sK4(domain_of(X0),X1),universal_class)
| subclass(domain_of(X0),X1) )
| ~ spl8_107 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f18388,plain,
( spl8_547
| ~ spl8_109
| ~ spl8_184 ),
inference(avatar_split_clause,[],[f2538,f2496,f1009,f18386]) ).
fof(f18386,plain,
( spl8_547
<=> ! [X0,X1] :
( ~ member(sK4(power_class(X0),intersection(X1,universal_class)),X1)
| subclass(power_class(X0),intersection(X1,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_547])]) ).
fof(f1009,plain,
( spl8_109
<=> ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(sK4(power_class(X0),X1),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_109])]) ).
fof(f2538,plain,
( ! [X0,X1] :
( ~ member(sK4(power_class(X0),intersection(X1,universal_class)),X1)
| subclass(power_class(X0),intersection(X1,universal_class)) )
| ~ spl8_109
| ~ spl8_184 ),
inference(duplicate_literal_removal,[],[f2518]) ).
fof(f2518,plain,
( ! [X0,X1] :
( ~ member(sK4(power_class(X0),intersection(X1,universal_class)),X1)
| subclass(power_class(X0),intersection(X1,universal_class))
| subclass(power_class(X0),intersection(X1,universal_class)) )
| ~ spl8_109
| ~ spl8_184 ),
inference(resolution,[],[f2497,f1010]) ).
fof(f1010,plain,
( ! [X0,X1] :
( member(sK4(power_class(X0),X1),universal_class)
| subclass(power_class(X0),X1) )
| ~ spl8_109 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f18384,plain,
( ~ spl8_546
| ~ spl8_314
| ~ spl8_349 ),
inference(avatar_split_clause,[],[f16333,f13879,f13477,f18381]) ).
fof(f18381,plain,
( spl8_546
<=> subclass(universal_class,complement(sum_class(universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_546])]) ).
fof(f13477,plain,
( spl8_314
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_314])]) ).
fof(f16333,plain,
( ~ subclass(universal_class,complement(sum_class(universal_class)))
| ~ spl8_314
| ~ spl8_349 ),
inference(resolution,[],[f13880,f13478]) ).
fof(f13478,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,complement(X0)) )
| ~ spl8_314 ),
inference(avatar_component_clause,[],[f13477]) ).
fof(f18379,plain,
( spl8_545
| ~ spl8_41
| ~ spl8_181 ),
inference(avatar_split_clause,[],[f2472,f2455,f451,f18377]) ).
fof(f18377,plain,
( spl8_545
<=> ! [X0] :
( member(unordered_pair(X0,X0),sum_class(identity_relation))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(X0,X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_545])]) ).
fof(f451,plain,
( spl8_41
<=> ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
fof(f2455,plain,
( spl8_181
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X1,sum_class(identity_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_181])]) ).
fof(f2472,plain,
( ! [X0] :
( member(unordered_pair(X0,X0),sum_class(identity_relation))
| ~ member(X0,universal_class)
| ~ member(unordered_pair(X0,X0),universal_class) )
| ~ spl8_41
| ~ spl8_181 ),
inference(resolution,[],[f2456,f452]) ).
fof(f452,plain,
( ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) )
| ~ spl8_41 ),
inference(avatar_component_clause,[],[f451]) ).
fof(f2456,plain,
( ! [X0,X1] :
( ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))))
| member(X1,sum_class(identity_relation))
| ~ member(X0,universal_class) )
| ~ spl8_181 ),
inference(avatar_component_clause,[],[f2455]) ).
fof(f18375,plain,
( spl8_544
| ~ spl8_15
| ~ spl8_179 ),
inference(avatar_split_clause,[],[f2404,f2289,f335,f18373]) ).
fof(f2289,plain,
( spl8_179
<=> ! [X0,X1] :
( sK2(unordered_pair(X0,X1)) = X0
| sK2(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_179])]) ).
fof(f2404,plain,
( ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X0 )
| ~ spl8_15
| ~ spl8_179 ),
inference(duplicate_literal_removal,[],[f2371]) ).
fof(f2371,plain,
( ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl8_15
| ~ spl8_179 ),
inference(superposition,[],[f336,f2290]) ).
fof(f2290,plain,
( ! [X0,X1] :
( sK2(unordered_pair(X0,X1)) = X1
| sK2(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl8_179 ),
inference(avatar_component_clause,[],[f2289]) ).
fof(f18371,plain,
( spl8_543
| ~ spl8_15
| ~ spl8_179 ),
inference(avatar_split_clause,[],[f2396,f2289,f335,f18369]) ).
fof(f2396,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X1 )
| ~ spl8_15
| ~ spl8_179 ),
inference(duplicate_literal_removal,[],[f2379]) ).
fof(f2379,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| sK2(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl8_15
| ~ spl8_179 ),
inference(superposition,[],[f336,f2290]) ).
fof(f18367,plain,
( spl8_542
| ~ spl8_179 ),
inference(avatar_split_clause,[],[f2388,f2289,f18365]) ).
fof(f18365,plain,
( spl8_542
<=> ! [X0,X1] :
( X0 != X1
| sK2(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_542])]) ).
fof(f2388,plain,
( ! [X0,X1] :
( X0 != X1
| sK2(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl8_179 ),
inference(equality_factoring,[],[f2290]) ).
fof(f18363,plain,
( spl8_541
| ~ spl8_179 ),
inference(avatar_split_clause,[],[f2387,f2289,f18361]) ).
fof(f18361,plain,
( spl8_541
<=> ! [X0,X1] :
( X0 != X1
| sK2(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_541])]) ).
fof(f2387,plain,
( ! [X0,X1] :
( X0 != X1
| sK2(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class )
| ~ spl8_179 ),
inference(equality_factoring,[],[f2290]) ).
fof(f18359,plain,
( spl8_540
| ~ spl8_143
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2278,f2243,f1488,f18357]) ).
fof(f18357,plain,
( spl8_540
<=> ! [X0,X1] :
( ~ subclass(sK4(intersection(universal_class,X0),power_class(X1)),X1)
| subclass(intersection(universal_class,X0),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_540])]) ).
fof(f2243,plain,
( spl8_176
<=> ! [X0,X1] :
( ~ subclass(sK4(X0,power_class(X1)),X1)
| ~ member(sK4(X0,power_class(X1)),universal_class)
| subclass(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_176])]) ).
fof(f2278,plain,
( ! [X0,X1] :
( ~ subclass(sK4(intersection(universal_class,X0),power_class(X1)),X1)
| subclass(intersection(universal_class,X0),power_class(X1)) )
| ~ spl8_143
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2273]) ).
fof(f2273,plain,
( ! [X0,X1] :
( ~ subclass(sK4(intersection(universal_class,X0),power_class(X1)),X1)
| subclass(intersection(universal_class,X0),power_class(X1))
| subclass(intersection(universal_class,X0),power_class(X1)) )
| ~ spl8_143
| ~ spl8_176 ),
inference(resolution,[],[f2244,f1489]) ).
fof(f2244,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,power_class(X1)),universal_class)
| ~ subclass(sK4(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1)) )
| ~ spl8_176 ),
inference(avatar_component_clause,[],[f2243]) ).
fof(f18355,plain,
( spl8_539
| ~ spl8_144
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2277,f2243,f1492,f18353]) ).
fof(f18353,plain,
( spl8_539
<=> ! [X0,X1] :
( ~ subclass(sK4(intersection(X0,universal_class),power_class(X1)),X1)
| subclass(intersection(X0,universal_class),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_539])]) ).
fof(f2277,plain,
( ! [X0,X1] :
( ~ subclass(sK4(intersection(X0,universal_class),power_class(X1)),X1)
| subclass(intersection(X0,universal_class),power_class(X1)) )
| ~ spl8_144
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2274]) ).
fof(f2274,plain,
( ! [X0,X1] :
( ~ subclass(sK4(intersection(X0,universal_class),power_class(X1)),X1)
| subclass(intersection(X0,universal_class),power_class(X1))
| subclass(intersection(X0,universal_class),power_class(X1)) )
| ~ spl8_144
| ~ spl8_176 ),
inference(resolution,[],[f2244,f1493]) ).
fof(f18351,plain,
( spl8_538
| ~ spl8_147
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2276,f2243,f1504,f18349]) ).
fof(f18349,plain,
( spl8_538
<=> ! [X2,X0,X1] :
( ~ subclass(sK4(unordered_pair(X0,X1),power_class(X2)),X2)
| subclass(unordered_pair(X0,X1),power_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_538])]) ).
fof(f2276,plain,
( ! [X2,X0,X1] :
( ~ subclass(sK4(unordered_pair(X0,X1),power_class(X2)),X2)
| subclass(unordered_pair(X0,X1),power_class(X2)) )
| ~ spl8_147
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2275]) ).
fof(f2275,plain,
( ! [X2,X0,X1] :
( ~ subclass(sK4(unordered_pair(X0,X1),power_class(X2)),X2)
| subclass(unordered_pair(X0,X1),power_class(X2))
| subclass(unordered_pair(X0,X1),power_class(X2)) )
| ~ spl8_147
| ~ spl8_176 ),
inference(resolution,[],[f2244,f1505]) ).
fof(f18347,plain,
( spl8_537
| ~ spl8_143
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2262,f2239,f1488,f18345]) ).
fof(f18345,plain,
( spl8_537
<=> ! [X0,X1] :
( member(sK4(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_537])]) ).
fof(f2239,plain,
( spl8_175
<=> ! [X0,X1] :
( member(sK4(X0,complement(X1)),X1)
| ~ member(sK4(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_175])]) ).
fof(f2262,plain,
( ! [X0,X1] :
( member(sK4(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl8_143
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2256]) ).
fof(f2256,plain,
( ! [X0,X1] :
( member(sK4(intersection(universal_class,X0),complement(X1)),X1)
| subclass(intersection(universal_class,X0),complement(X1))
| subclass(intersection(universal_class,X0),complement(X1)) )
| ~ spl8_143
| ~ spl8_175 ),
inference(resolution,[],[f2240,f1489]) ).
fof(f2240,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,complement(X1)),universal_class)
| member(sK4(X0,complement(X1)),X1)
| subclass(X0,complement(X1)) )
| ~ spl8_175 ),
inference(avatar_component_clause,[],[f2239]) ).
fof(f18343,plain,
( spl8_536
| ~ spl8_144
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2261,f2239,f1492,f18341]) ).
fof(f18341,plain,
( spl8_536
<=> ! [X0,X1] :
( member(sK4(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_536])]) ).
fof(f2261,plain,
( ! [X0,X1] :
( member(sK4(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl8_144
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2257]) ).
fof(f2257,plain,
( ! [X0,X1] :
( member(sK4(intersection(X0,universal_class),complement(X1)),X1)
| subclass(intersection(X0,universal_class),complement(X1))
| subclass(intersection(X0,universal_class),complement(X1)) )
| ~ spl8_144
| ~ spl8_175 ),
inference(resolution,[],[f2240,f1493]) ).
fof(f18339,plain,
( spl8_535
| ~ spl8_34
| ~ spl8_417 ),
inference(avatar_split_clause,[],[f15874,f14925,f423,f18337]) ).
fof(f18337,plain,
( spl8_535
<=> ! [X0] : subclass(union(X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_535])]) ).
fof(f423,plain,
( spl8_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
fof(f14925,plain,
( spl8_417
<=> ! [X0,X1] :
( member(sK4(union(X0,X0),X1),X0)
| subclass(union(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_417])]) ).
fof(f15874,plain,
( ! [X0] : subclass(union(X0,X0),X0)
| ~ spl8_34
| ~ spl8_417 ),
inference(duplicate_literal_removal,[],[f15788]) ).
fof(f15788,plain,
( ! [X0] :
( subclass(union(X0,X0),X0)
| subclass(union(X0,X0),X0) )
| ~ spl8_34
| ~ spl8_417 ),
inference(resolution,[],[f14926,f424]) ).
fof(f424,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,X1),X1)
| subclass(X0,X1) )
| ~ spl8_34 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f14926,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X0),X1),X0)
| subclass(union(X0,X0),X1) )
| ~ spl8_417 ),
inference(avatar_component_clause,[],[f14925]) ).
fof(f18335,plain,
( spl8_534
| ~ spl8_147
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2260,f2239,f1504,f18333]) ).
fof(f18333,plain,
( spl8_534
<=> ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),complement(X2)),X2)
| subclass(unordered_pair(X0,X1),complement(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_534])]) ).
fof(f2260,plain,
( ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),complement(X2)),X2)
| subclass(unordered_pair(X0,X1),complement(X2)) )
| ~ spl8_147
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2258]) ).
fof(f2258,plain,
( ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),complement(X2)),X2)
| subclass(unordered_pair(X0,X1),complement(X2))
| subclass(unordered_pair(X0,X1),complement(X2)) )
| ~ spl8_147
| ~ spl8_175 ),
inference(resolution,[],[f2240,f1505]) ).
fof(f18331,plain,
( spl8_533
| ~ spl8_12
| ~ spl8_169 ),
inference(avatar_split_clause,[],[f2127,f2091,f322,f18329]) ).
fof(f18329,plain,
( spl8_533
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(null_class,sum_class(intersection(X1,X2)))
| ~ member(X0,X2)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_533])]) ).
fof(f322,plain,
( spl8_12
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f2091,plain,
( spl8_169
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X3,sum_class(intersection(X2,X1)))
| ~ member(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_169])]) ).
fof(f2127,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(null_class,sum_class(intersection(X1,X2)))
| ~ member(X0,X2)
| ~ inductive(X0) )
| ~ spl8_12
| ~ spl8_169 ),
inference(resolution,[],[f2092,f323]) ).
fof(f323,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f2092,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,X0)
| ~ member(X0,X2)
| member(X3,sum_class(intersection(X2,X1)))
| ~ member(X0,X1) )
| ~ spl8_169 ),
inference(avatar_component_clause,[],[f2091]) ).
fof(f18327,plain,
( spl8_532
| ~ spl8_13
| ~ spl8_169 ),
inference(avatar_split_clause,[],[f2122,f2091,f326,f18325]) ).
fof(f18325,plain,
( spl8_532
<=> ! [X0,X3,X2,X1] :
( ~ member(universal_class,X0)
| member(unordered_pair(X1,X2),sum_class(intersection(X0,X3)))
| ~ member(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_532])]) ).
fof(f2122,plain,
( ! [X2,X3,X0,X1] :
( ~ member(universal_class,X0)
| member(unordered_pair(X1,X2),sum_class(intersection(X0,X3)))
| ~ member(universal_class,X3) )
| ~ spl8_13
| ~ spl8_169 ),
inference(resolution,[],[f2092,f327]) ).
fof(f18323,plain,
( spl8_531
| ~ spl8_20
| ~ spl8_161 ),
inference(avatar_split_clause,[],[f1961,f1874,f355,f18321]) ).
fof(f18321,plain,
( spl8_531
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,X1)
| ~ function(power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_531])]) ).
fof(f1874,plain,
( spl8_161
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(power_class(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_161])]) ).
fof(f1961,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class))
| ~ subclass(X0,X1)
| ~ function(power_class(X1)) )
| ~ spl8_20
| ~ spl8_161 ),
inference(resolution,[],[f1875,f356]) ).
fof(f1875,plain,
( ! [X2,X0,X1] :
( ~ subclass(power_class(X1),X2)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(X0,X1) )
| ~ spl8_161 ),
inference(avatar_component_clause,[],[f1874]) ).
fof(f18319,plain,
( spl8_530
| ~ spl8_20
| ~ spl8_160 ),
inference(avatar_split_clause,[],[f1957,f1870,f355,f18317]) ).
fof(f18317,plain,
( spl8_530
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class))
| member(X0,X1)
| ~ function(complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_530])]) ).
fof(f1870,plain,
( spl8_160
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(complement(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_160])]) ).
fof(f1957,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,cross_product(universal_class,universal_class))
| member(X0,X1)
| ~ function(complement(X1)) )
| ~ spl8_20
| ~ spl8_160 ),
inference(resolution,[],[f1871,f356]) ).
fof(f1871,plain,
( ! [X2,X0,X1] :
( ~ subclass(complement(X1),X2)
| ~ member(X0,universal_class)
| member(X0,X2)
| member(X0,X1) )
| ~ spl8_160 ),
inference(avatar_component_clause,[],[f1870]) ).
fof(f18315,plain,
( spl8_529
| ~ spl8_99
| ~ spl8_155 ),
inference(avatar_split_clause,[],[f1811,f1548,f896,f18313]) ).
fof(f18313,plain,
( spl8_529
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| subclass(X2,X3)
| ~ subclass(universal_class,sK4(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_529])]) ).
fof(f1811,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| subclass(X2,X3)
| ~ subclass(universal_class,sK4(X2,X3)) )
| ~ spl8_99
| ~ spl8_155 ),
inference(resolution,[],[f1549,f897]) ).
fof(f18311,plain,
( spl8_528
| ~ spl8_33
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1797,f1544,f419,f18309]) ).
fof(f18309,plain,
( spl8_528
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sK4(X1,X2))
| member(X0,sum_class(union(X1,X3)))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_528])]) ).
fof(f419,plain,
( spl8_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
fof(f1797,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sK4(X1,X2))
| member(X0,sum_class(union(X1,X3)))
| subclass(X1,X2) )
| ~ spl8_33
| ~ spl8_154 ),
inference(resolution,[],[f1545,f420]) ).
fof(f420,plain,
( ! [X0,X1] :
( member(sK4(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f18307,plain,
( spl8_527
| ~ spl8_99
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1775,f1544,f896,f18305]) ).
fof(f18305,plain,
( spl8_527
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,X4)))
| ~ subclass(universal_class,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_527])]) ).
fof(f1775,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,X4)))
| ~ subclass(universal_class,X3) )
| ~ spl8_99
| ~ spl8_154 ),
inference(resolution,[],[f1545,f897]) ).
fof(f18303,plain,
( spl8_526
| ~ spl8_37
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1769,f1544,f435,f18301]) ).
fof(f18301,plain,
( spl8_526
<=> ! [X2,X4,X0,X3,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(union(X2,X3),X4)))
| ~ member(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_526])]) ).
fof(f1769,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| member(X0,sum_class(union(union(X2,X3),X4)))
| ~ member(X1,X2) )
| ~ spl8_37
| ~ spl8_154 ),
inference(resolution,[],[f1545,f436]) ).
fof(f18299,plain,
( spl8_525
| ~ spl8_38
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1768,f1544,f439,f18297]) ).
fof(f18297,plain,
( spl8_525
<=> ! [X2,X4,X0,X3,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(union(X2,X3),X4)))
| ~ member(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_525])]) ).
fof(f1768,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| member(X0,sum_class(union(union(X2,X3),X4)))
| ~ member(X1,X3) )
| ~ spl8_38
| ~ spl8_154 ),
inference(resolution,[],[f1545,f440]) ).
fof(f18295,plain,
( spl8_524
| ~ spl8_34
| ~ spl8_416 ),
inference(avatar_split_clause,[],[f15736,f14921,f423,f18293]) ).
fof(f18293,plain,
( spl8_524
<=> ! [X0] : subclass(union(null_class,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_524])]) ).
fof(f14921,plain,
( spl8_416
<=> ! [X0,X1] :
( member(sK4(union(null_class,X0),X1),X0)
| subclass(union(null_class,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_416])]) ).
fof(f15736,plain,
( ! [X0] : subclass(union(null_class,X0),X0)
| ~ spl8_34
| ~ spl8_416 ),
inference(duplicate_literal_removal,[],[f15651]) ).
fof(f15651,plain,
( ! [X0] :
( subclass(union(null_class,X0),X0)
| subclass(union(null_class,X0),X0) )
| ~ spl8_34
| ~ spl8_416 ),
inference(resolution,[],[f14922,f424]) ).
fof(f14922,plain,
( ! [X0,X1] :
( member(sK4(union(null_class,X0),X1),X0)
| subclass(union(null_class,X0),X1) )
| ~ spl8_416 ),
inference(avatar_component_clause,[],[f14921]) ).
fof(f18291,plain,
( spl8_523
| ~ spl8_41
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1764,f1544,f451,f18289]) ).
fof(f18289,plain,
( spl8_523
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(unordered_pair(X1,X2),X3)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_523])]) ).
fof(f1764,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(unordered_pair(X1,X2),X3)))
| ~ member(X1,universal_class) )
| ~ spl8_41
| ~ spl8_154 ),
inference(resolution,[],[f1545,f452]) ).
fof(f18287,plain,
( spl8_522
| ~ spl8_40
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1763,f1544,f447,f18285]) ).
fof(f18285,plain,
( spl8_522
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(unordered_pair(X2,X1),X3)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_522])]) ).
fof(f447,plain,
( spl8_40
<=> ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
fof(f1763,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(unordered_pair(X2,X1),X3)))
| ~ member(X1,universal_class) )
| ~ spl8_40
| ~ spl8_154 ),
inference(resolution,[],[f1545,f448]) ).
fof(f448,plain,
( ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) )
| ~ spl8_40 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f18283,plain,
( spl8_521
| ~ spl8_33
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1749,f1540,f419,f18281]) ).
fof(f18281,plain,
( spl8_521
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sK4(X1,X2))
| member(X0,sum_class(union(X3,X1)))
| subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_521])]) ).
fof(f1749,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sK4(X1,X2))
| member(X0,sum_class(union(X3,X1)))
| subclass(X1,X2) )
| ~ spl8_33
| ~ spl8_153 ),
inference(resolution,[],[f1541,f420]) ).
fof(f18279,plain,
( spl8_520
| ~ spl8_99
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1727,f1540,f896,f18277]) ).
fof(f18277,plain,
( spl8_520
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,X4)))
| ~ subclass(universal_class,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_520])]) ).
fof(f1727,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,X4)))
| ~ subclass(universal_class,X4) )
| ~ spl8_99
| ~ spl8_153 ),
inference(resolution,[],[f1541,f897]) ).
fof(f18275,plain,
( spl8_519
| ~ spl8_37
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1721,f1540,f435,f18273]) ).
fof(f18273,plain,
( spl8_519
<=> ! [X2,X4,X0,X3,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,union(X3,X4))))
| ~ member(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_519])]) ).
fof(f1721,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,union(X3,X4))))
| ~ member(X1,X3) )
| ~ spl8_37
| ~ spl8_153 ),
inference(resolution,[],[f1541,f436]) ).
fof(f18271,plain,
( spl8_518
| ~ spl8_38
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1720,f1540,f439,f18269]) ).
fof(f18269,plain,
( spl8_518
<=> ! [X2,X4,X0,X3,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,union(X3,X4))))
| ~ member(X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_518])]) ).
fof(f1720,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,union(X3,X4))))
| ~ member(X1,X4) )
| ~ spl8_38
| ~ spl8_153 ),
inference(resolution,[],[f1541,f440]) ).
fof(f18267,plain,
( spl8_517
| ~ spl8_41
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1716,f1540,f451,f18265]) ).
fof(f18265,plain,
( spl8_517
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,unordered_pair(X1,X3))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_517])]) ).
fof(f1716,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,unordered_pair(X1,X3))))
| ~ member(X1,universal_class) )
| ~ spl8_41
| ~ spl8_153 ),
inference(resolution,[],[f1541,f452]) ).
fof(f18263,plain,
( spl8_516
| ~ spl8_40
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1715,f1540,f447,f18261]) ).
fof(f18261,plain,
( spl8_516
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,unordered_pair(X3,X1))))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_516])]) ).
fof(f1715,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,unordered_pair(X3,X1))))
| ~ member(X1,universal_class) )
| ~ spl8_40
| ~ spl8_153 ),
inference(resolution,[],[f1541,f448]) ).
fof(f18259,plain,
( spl8_515
| ~ spl8_35
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1681,f1516,f427,f18257]) ).
fof(f18257,plain,
( spl8_515
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK5(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_515])]) ).
fof(f1681,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK5(X0,X1),X2) )
| ~ spl8_35
| ~ spl8_150 ),
inference(resolution,[],[f1517,f428]) ).
fof(f18255,plain,
( spl8_514
| ~ spl8_36
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1680,f1516,f431,f18253]) ).
fof(f18253,plain,
( spl8_514
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK5(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_514])]) ).
fof(f1680,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,intersection(X2,X3))
| member(sK5(X0,X1),X3) )
| ~ spl8_36
| ~ spl8_150 ),
inference(resolution,[],[f1517,f432]) ).
fof(f18251,plain,
( spl8_513
| ~ spl8_34
| ~ spl8_415 ),
inference(avatar_split_clause,[],[f15599,f14917,f423,f18249]) ).
fof(f18249,plain,
( spl8_513
<=> ! [X0] : subclass(union(X0,null_class),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_513])]) ).
fof(f14917,plain,
( spl8_415
<=> ! [X0,X1] :
( member(sK4(union(X0,null_class),X1),X0)
| subclass(union(X0,null_class),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_415])]) ).
fof(f15599,plain,
( ! [X0] : subclass(union(X0,null_class),X0)
| ~ spl8_34
| ~ spl8_415 ),
inference(duplicate_literal_removal,[],[f15514]) ).
fof(f15514,plain,
( ! [X0] :
( subclass(union(X0,null_class),X0)
| subclass(union(X0,null_class),X0) )
| ~ spl8_34
| ~ spl8_415 ),
inference(resolution,[],[f14918,f424]) ).
fof(f14918,plain,
( ! [X0,X1] :
( member(sK4(union(X0,null_class),X1),X0)
| subclass(union(X0,null_class),X1) )
| ~ spl8_415 ),
inference(avatar_component_clause,[],[f14917]) ).
fof(f18247,plain,
( spl8_512
| ~ spl8_95
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1640,f1500,f872,f18245]) ).
fof(f18245,plain,
( spl8_512
<=> ! [X0,X1] :
( subclass(X0,union(X1,sum_class(universal_class)))
| ~ member(sK4(X0,union(X1,sum_class(universal_class))),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_512])]) ).
fof(f872,plain,
( spl8_95
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_95])]) ).
fof(f1500,plain,
( spl8_146
<=> ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X2)
| subclass(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_146])]) ).
fof(f1640,plain,
( ! [X0,X1] :
( subclass(X0,union(X1,sum_class(universal_class)))
| ~ member(sK4(X0,union(X1,sum_class(universal_class))),sK7) )
| ~ spl8_95
| ~ spl8_146 ),
inference(resolution,[],[f1501,f873]) ).
fof(f873,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK7) )
| ~ spl8_95 ),
inference(avatar_component_clause,[],[f872]) ).
fof(f1501,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X2)
| subclass(X0,union(X1,X2)) )
| ~ spl8_146 ),
inference(avatar_component_clause,[],[f1500]) ).
fof(f18243,plain,
( spl8_511
| ~ spl8_95
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1619,f1496,f872,f18241]) ).
fof(f18241,plain,
( spl8_511
<=> ! [X0,X1] :
( subclass(X0,union(sum_class(universal_class),X1))
| ~ member(sK4(X0,union(sum_class(universal_class),X1)),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_511])]) ).
fof(f1496,plain,
( spl8_145
<=> ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X1)
| subclass(X0,union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_145])]) ).
fof(f1619,plain,
( ! [X0,X1] :
( subclass(X0,union(sum_class(universal_class),X1))
| ~ member(sK4(X0,union(sum_class(universal_class),X1)),sK7) )
| ~ spl8_95
| ~ spl8_145 ),
inference(resolution,[],[f1497,f873]) ).
fof(f1497,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X1)
| subclass(X0,union(X1,X2)) )
| ~ spl8_145 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f18239,plain,
( spl8_510
| ~ spl8_27
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f1596,f1492,f384,f18237]) ).
fof(f18237,plain,
( spl8_510
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,power_class(X1)),X2)
| subclass(sK4(intersection(X0,power_class(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_510])]) ).
fof(f1596,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,power_class(X1)),X2)
| subclass(sK4(intersection(X0,power_class(X1)),X2),X1) )
| ~ spl8_27
| ~ spl8_144 ),
inference(resolution,[],[f1493,f385]) ).
fof(f18235,plain,
( spl8_509
| ~ spl8_25
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f1589,f1492,f376,f18233]) ).
fof(f18233,plain,
( spl8_509
<=> ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(sK4(intersection(X0,complement(X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_509])]) ).
fof(f1589,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,complement(X1)),X2)
| ~ member(sK4(intersection(X0,complement(X1)),X2),X1) )
| ~ spl8_25
| ~ spl8_144 ),
inference(resolution,[],[f1493,f377]) ).
fof(f18231,plain,
( spl8_508
| ~ spl8_27
| ~ spl8_143 ),
inference(avatar_split_clause,[],[f1568,f1488,f384,f18229]) ).
fof(f18229,plain,
( spl8_508
<=> ! [X2,X0,X1] :
( subclass(intersection(power_class(X0),X1),X2)
| subclass(sK4(intersection(power_class(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_508])]) ).
fof(f1568,plain,
( ! [X2,X0,X1] :
( subclass(intersection(power_class(X0),X1),X2)
| subclass(sK4(intersection(power_class(X0),X1),X2),X0) )
| ~ spl8_27
| ~ spl8_143 ),
inference(resolution,[],[f1489,f385]) ).
fof(f18227,plain,
( spl8_507
| ~ spl8_25
| ~ spl8_143 ),
inference(avatar_split_clause,[],[f1561,f1488,f376,f18225]) ).
fof(f18225,plain,
( spl8_507
<=> ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(sK4(intersection(complement(X0),X1),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_507])]) ).
fof(f1561,plain,
( ! [X2,X0,X1] :
( subclass(intersection(complement(X0),X1),X2)
| ~ member(sK4(intersection(complement(X0),X1),X2),X0) )
| ~ spl8_25
| ~ spl8_143 ),
inference(resolution,[],[f1489,f377]) ).
fof(f18223,plain,
( spl8_506
| ~ spl8_33
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1484,f1298,f419,f18221]) ).
fof(f18221,plain,
( spl8_506
<=> ! [X0,X1] :
( member(sK4(sK3(X0),X1),sum_class(universal_class))
| ~ member(X0,identity_relation)
| subclass(sK3(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_506])]) ).
fof(f1484,plain,
( ! [X0,X1] :
( member(sK4(sK3(X0),X1),sum_class(universal_class))
| ~ member(X0,identity_relation)
| subclass(sK3(X0),X1) )
| ~ spl8_33
| ~ spl8_140 ),
inference(resolution,[],[f1299,f420]) ).
fof(f18219,plain,
( spl8_505
| ~ spl8_33
| ~ spl8_139 ),
inference(avatar_split_clause,[],[f1466,f1294,f419,f18217]) ).
fof(f18217,plain,
( spl8_505
<=> ! [X0,X1] :
( member(sK4(sK2(X0),X1),sum_class(X0))
| null_class = X0
| subclass(sK2(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_505])]) ).
fof(f1466,plain,
( ! [X0,X1] :
( member(sK4(sK2(X0),X1),sum_class(X0))
| null_class = X0
| subclass(sK2(X0),X1) )
| ~ spl8_33
| ~ spl8_139 ),
inference(resolution,[],[f1295,f420]) ).
fof(f18215,plain,
( spl8_504
| ~ spl8_33
| ~ spl8_138 ),
inference(avatar_split_clause,[],[f1452,f1290,f419,f18213]) ).
fof(f18213,plain,
( spl8_504
<=> ! [X0,X1] :
( member(sK4(sK2(X0),X1),sum_class(universal_class))
| null_class = X0
| subclass(sK2(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_504])]) ).
fof(f1452,plain,
( ! [X0,X1] :
( member(sK4(sK2(X0),X1),sum_class(universal_class))
| null_class = X0
| subclass(sK2(X0),X1) )
| ~ spl8_33
| ~ spl8_138 ),
inference(resolution,[],[f1291,f420]) ).
fof(f18211,plain,
( spl8_503
| ~ spl8_33
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f1438,f1286,f419,f18209]) ).
fof(f18209,plain,
( spl8_503
<=> ! [X0,X1] :
( member(sK4(power_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(power_class(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_503])]) ).
fof(f1438,plain,
( ! [X0,X1] :
( member(sK4(power_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(power_class(X0),X1) )
| ~ spl8_33
| ~ spl8_137 ),
inference(resolution,[],[f1287,f420]) ).
fof(f18207,plain,
( spl8_502
| ~ spl8_33
| ~ spl8_414 ),
inference(avatar_split_clause,[],[f15513,f14913,f419,f18205]) ).
fof(f18205,plain,
( spl8_502
<=> ! [X0] : subclass(X0,intersection(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_502])]) ).
fof(f14913,plain,
( spl8_414
<=> ! [X0,X1] :
( ~ member(sK4(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_414])]) ).
fof(f15513,plain,
( ! [X0] : subclass(X0,intersection(X0,X0))
| ~ spl8_33
| ~ spl8_414 ),
inference(duplicate_literal_removal,[],[f15487]) ).
fof(f15487,plain,
( ! [X0] :
( subclass(X0,intersection(X0,X0))
| subclass(X0,intersection(X0,X0)) )
| ~ spl8_33
| ~ spl8_414 ),
inference(resolution,[],[f14914,f420]) ).
fof(f14914,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl8_414 ),
inference(avatar_component_clause,[],[f14913]) ).
fof(f18203,plain,
( spl8_501
| ~ spl8_33
| ~ spl8_136 ),
inference(avatar_split_clause,[],[f1422,f1279,f419,f18201]) ).
fof(f18201,plain,
( spl8_501
<=> ! [X0,X1] :
( member(sK4(sum_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(sum_class(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_501])]) ).
fof(f1422,plain,
( ! [X0,X1] :
( member(sK4(sum_class(X0),X1),sum_class(universal_class))
| ~ member(X0,universal_class)
| subclass(sum_class(X0),X1) )
| ~ spl8_33
| ~ spl8_136 ),
inference(resolution,[],[f1280,f420]) ).
fof(f18199,plain,
( spl8_500
| ~ spl8_45
| ~ spl8_135 ),
inference(avatar_split_clause,[],[f1409,f1275,f488,f18197]) ).
fof(f18197,plain,
( spl8_500
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK5(X0,power_class(X1)),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_500])]) ).
fof(f1409,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK5(X0,power_class(X1)),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_45
| ~ spl8_135 ),
inference(resolution,[],[f1276,f489]) ).
fof(f18195,plain,
( spl8_499
| ~ spl8_45
| ~ spl8_133 ),
inference(avatar_split_clause,[],[f1402,f1267,f488,f18193]) ).
fof(f18193,plain,
( spl8_499
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK5(X0,domain_of(X1)),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_499])]) ).
fof(f1402,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK5(X0,domain_of(X1)),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_45
| ~ spl8_133 ),
inference(resolution,[],[f1268,f489]) ).
fof(f18191,plain,
( spl8_498
| ~ spl8_45
| ~ spl8_132 ),
inference(avatar_split_clause,[],[f1395,f1263,f488,f18189]) ).
fof(f18189,plain,
( spl8_498
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK5(X0,complement(X1)),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_498])]) ).
fof(f1395,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK5(X0,complement(X1)),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_45
| ~ spl8_132 ),
inference(resolution,[],[f1264,f489]) ).
fof(f18187,plain,
( spl8_497
| ~ spl8_104
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1367,f1255,f969,f18185]) ).
fof(f18185,plain,
( spl8_497
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| member(sK4(X0,X3),sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_497])]) ).
fof(f1367,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| subclass(X0,X3)
| member(sK4(X0,X3),sum_class(universal_class)) )
| ~ spl8_104
| ~ spl8_130 ),
inference(resolution,[],[f1256,f970]) ).
fof(f18183,plain,
( spl8_496
| ~ spl8_45
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1364,f1255,f488,f18181]) ).
fof(f18181,plain,
( spl8_496
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| member(sK4(X0,X2),X3)
| ~ subclass(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_496])]) ).
fof(f1364,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,X1)
| subclass(X0,X2)
| member(sK4(X0,X2),X3)
| ~ subclass(X1,X3) )
| ~ spl8_45
| ~ spl8_130 ),
inference(resolution,[],[f1256,f489]) ).
fof(f18179,plain,
( spl8_495
| ~ spl8_45
| ~ spl8_124 ),
inference(avatar_split_clause,[],[f1324,f1231,f488,f18177]) ).
fof(f18177,plain,
( spl8_495
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK2(intersection(X0,X1)),X2)
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_495])]) ).
fof(f1324,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK2(intersection(X0,X1)),X2)
| ~ subclass(X1,X2) )
| ~ spl8_45
| ~ spl8_124 ),
inference(resolution,[],[f1232,f489]) ).
fof(f18175,plain,
( spl8_494
| ~ spl8_45
| ~ spl8_123 ),
inference(avatar_split_clause,[],[f1302,f1227,f488,f18173]) ).
fof(f18173,plain,
( spl8_494
<=> ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK2(intersection(X0,X1)),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_494])]) ).
fof(f1302,plain,
( ! [X2,X0,X1] :
( intersection(X0,X1) = null_class
| member(sK2(intersection(X0,X1)),X2)
| ~ subclass(X0,X2) )
| ~ spl8_45
| ~ spl8_123 ),
inference(resolution,[],[f1228,f489]) ).
fof(f18171,plain,
( spl8_493
| ~ spl8_114
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f1224,f1056,f1031,f18169]) ).
fof(f18169,plain,
( spl8_493
<=> ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| ~ member(X1,identity_relation)
| ~ member(sK3(X1),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_493])]) ).
fof(f1056,plain,
( spl8_120
<=> ! [X0,X1] :
( member(sK3(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_120])]) ).
fof(f1224,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| ~ member(X1,identity_relation)
| ~ member(sK3(X1),X0)
| null_class = X0 )
| ~ spl8_114
| ~ spl8_120 ),
inference(resolution,[],[f1057,f1032]) ).
fof(f1057,plain,
( ! [X0,X1] :
( member(sK3(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,identity_relation) )
| ~ spl8_120 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f18167,plain,
( spl8_492
| ~ spl8_50
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f1204,f1056,f544,f18165]) ).
fof(f18165,plain,
( spl8_492
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(X2,sum_class(X0))
| ~ member(X2,sK3(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_492])]) ).
fof(f1204,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(X2,sum_class(X0))
| ~ member(X2,sK3(X1)) )
| ~ spl8_50
| ~ spl8_120 ),
inference(resolution,[],[f1057,f545]) ).
fof(f18163,plain,
( spl8_491
| ~ spl8_6
| ~ spl8_366 ),
inference(avatar_split_clause,[],[f14369,f13953,f295,f18160]) ).
fof(f18160,plain,
( spl8_491
<=> null_class = union(null_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_491])]) ).
fof(f295,plain,
( spl8_6
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f13953,plain,
( spl8_366
<=> ! [X0] :
( member(sK2(union(X0,null_class)),X0)
| null_class = union(X0,null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_366])]) ).
fof(f14369,plain,
( null_class = union(null_class,null_class)
| ~ spl8_6
| ~ spl8_366 ),
inference(resolution,[],[f13954,f296]) ).
fof(f296,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f13954,plain,
( ! [X0] :
( member(sK2(union(X0,null_class)),X0)
| null_class = union(X0,null_class) )
| ~ spl8_366 ),
inference(avatar_component_clause,[],[f13953]) ).
fof(f18158,plain,
( spl8_490
| ~ spl8_114
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1201,f1052,f1031,f18156]) ).
fof(f18156,plain,
( spl8_490
<=> ! [X0,X1] :
( ~ subclass(X0,sK2(X1))
| null_class = X0
| ~ member(sK2(X0),X1)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_490])]) ).
fof(f1201,plain,
( ! [X0,X1] :
( ~ subclass(X0,sK2(X1))
| null_class = X0
| ~ member(sK2(X0),X1)
| null_class = X1 )
| ~ spl8_114
| ~ spl8_119 ),
inference(resolution,[],[f1053,f1032]) ).
fof(f18154,plain,
( spl8_489
| ~ spl8_50
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1181,f1052,f544,f18152]) ).
fof(f18152,plain,
( spl8_489
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(X2,sum_class(X1))
| ~ member(X2,sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_489])]) ).
fof(f1181,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(X2,sum_class(X1))
| ~ member(X2,sK2(X0)) )
| ~ spl8_50
| ~ spl8_119 ),
inference(resolution,[],[f1053,f545]) ).
fof(f18150,plain,
( spl8_488
| ~ spl8_114
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1177,f1043,f1031,f18148]) ).
fof(f18148,plain,
( spl8_488
<=> ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| null_class = X1
| ~ member(sK2(X1),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_488])]) ).
fof(f1043,plain,
( spl8_117
<=> ! [X0,X1] :
( member(sK2(X0),X1)
| ~ subclass(universal_class,X1)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_117])]) ).
fof(f1177,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| null_class = X1
| ~ member(sK2(X1),X0)
| null_class = X0 )
| ~ spl8_114
| ~ spl8_117 ),
inference(resolution,[],[f1044,f1032]) ).
fof(f1044,plain,
( ! [X0,X1] :
( member(sK2(X0),X1)
| ~ subclass(universal_class,X1)
| null_class = X0 )
| ~ spl8_117 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f18146,plain,
( spl8_487
| ~ spl8_50
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1157,f1043,f544,f18144]) ).
fof(f18144,plain,
( spl8_487
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(X2,sum_class(X0))
| ~ member(X2,sK2(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_487])]) ).
fof(f1157,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(X2,sum_class(X0))
| ~ member(X2,sK2(X1)) )
| ~ spl8_50
| ~ spl8_117 ),
inference(resolution,[],[f1044,f545]) ).
fof(f18142,plain,
( spl8_486
| ~ spl8_114
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1154,f1039,f1031,f18140]) ).
fof(f18140,plain,
( spl8_486
<=> ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_486])]) ).
fof(f1154,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),X0)
| null_class = X0 )
| ~ spl8_114
| ~ spl8_116 ),
inference(resolution,[],[f1040,f1032]) ).
fof(f18138,plain,
( spl8_485
| ~ spl8_50
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1134,f1039,f544,f18136]) ).
fof(f18136,plain,
( spl8_485
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_485])]) ).
fof(f1134,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,power_class(X1)) )
| ~ spl8_50
| ~ spl8_116 ),
inference(resolution,[],[f1040,f545]) ).
fof(f18134,plain,
( spl8_484
| ~ spl8_114
| ~ spl8_115 ),
inference(avatar_split_clause,[],[f1131,f1035,f1031,f18132]) ).
fof(f18132,plain,
( spl8_484
<=> ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_484])]) ).
fof(f1131,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,sK2(X0))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),X0)
| null_class = X0 )
| ~ spl8_114
| ~ spl8_115 ),
inference(resolution,[],[f1036,f1032]) ).
fof(f18130,plain,
( spl8_483
| ~ spl8_50
| ~ spl8_115 ),
inference(avatar_split_clause,[],[f1111,f1035,f544,f18128]) ).
fof(f18128,plain,
( spl8_483
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_483])]) ).
fof(f1111,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(X0))
| ~ member(X2,sum_class(X1)) )
| ~ spl8_50
| ~ spl8_115 ),
inference(resolution,[],[f1036,f545]) ).
fof(f18126,plain,
( spl8_482
| ~ spl8_47
| ~ spl8_114 ),
inference(avatar_split_clause,[],[f1103,f1031,f496,f18124]) ).
fof(f18124,plain,
( spl8_482
<=> ! [X0,X1] :
( ~ member(sK5(X0,sK2(X1)),X1)
| null_class = X1
| ~ member(X0,sum_class(sK2(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_482])]) ).
fof(f1103,plain,
( ! [X0,X1] :
( ~ member(sK5(X0,sK2(X1)),X1)
| null_class = X1
| ~ member(X0,sum_class(sK2(X1))) )
| ~ spl8_47
| ~ spl8_114 ),
inference(resolution,[],[f1032,f497]) ).
fof(f18122,plain,
( spl8_481
| ~ spl8_50
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f1095,f1009,f544,f18120]) ).
fof(f18120,plain,
( spl8_481
<=> ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK4(power_class(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_481])]) ).
fof(f1095,plain,
( ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK4(power_class(X0),X1)) )
| ~ spl8_50
| ~ spl8_109 ),
inference(resolution,[],[f1010,f545]) ).
fof(f18118,plain,
( ~ spl8_80
| ~ spl8_98
| ~ spl8_474 ),
inference(avatar_split_clause,[],[f17687,f16797,f888,f792]) ).
fof(f792,plain,
( spl8_80
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).
fof(f888,plain,
( spl8_98
<=> ! [X0] : ~ inductive(power_class(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).
fof(f16797,plain,
( spl8_474
<=> universal_class = power_class(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_474])]) ).
fof(f17687,plain,
( ~ inductive(universal_class)
| ~ spl8_98
| ~ spl8_474 ),
inference(superposition,[],[f889,f16799]) ).
fof(f16799,plain,
( universal_class = power_class(universal_class)
| ~ spl8_474 ),
inference(avatar_component_clause,[],[f16797]) ).
fof(f889,plain,
( ! [X0] : ~ inductive(power_class(X0))
| ~ spl8_98 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f18117,plain,
( spl8_480
| ~ spl8_50
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f1086,f1001,f544,f18115]) ).
fof(f18115,plain,
( spl8_480
<=> ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK4(domain_of(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_480])]) ).
fof(f1086,plain,
( ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK4(domain_of(X0),X1)) )
| ~ spl8_50
| ~ spl8_107 ),
inference(resolution,[],[f1002,f545]) ).
fof(f18113,plain,
( spl8_479
| ~ spl8_50
| ~ spl8_106 ),
inference(avatar_split_clause,[],[f1078,f997,f544,f18111]) ).
fof(f18111,plain,
( spl8_479
<=> ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK4(complement(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_479])]) ).
fof(f1078,plain,
( ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(X2,sum_class(universal_class))
| ~ member(X2,sK4(complement(X0),X1)) )
| ~ spl8_50
| ~ spl8_106 ),
inference(resolution,[],[f998,f545]) ).
fof(f18109,plain,
( spl8_478
| ~ spl8_37
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1071,f993,f435,f18107]) ).
fof(f18107,plain,
( spl8_478
<=> ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK4(complement(union(X0,X1)),X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_478])]) ).
fof(f993,plain,
( spl8_105
<=> ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(sK4(complement(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_105])]) ).
fof(f1071,plain,
( ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK4(complement(union(X0,X1)),X2),X0) )
| ~ spl8_37
| ~ spl8_105 ),
inference(resolution,[],[f994,f436]) ).
fof(f994,plain,
( ! [X0,X1] :
( ~ member(sK4(complement(X0),X1),X0)
| subclass(complement(X0),X1) )
| ~ spl8_105 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f18105,plain,
( spl8_477
| ~ spl8_38
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1070,f993,f439,f18103]) ).
fof(f18103,plain,
( spl8_477
<=> ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK4(complement(union(X0,X1)),X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_477])]) ).
fof(f1070,plain,
( ! [X2,X0,X1] :
( subclass(complement(union(X0,X1)),X2)
| ~ member(sK4(complement(union(X0,X1)),X2),X1) )
| ~ spl8_38
| ~ spl8_105 ),
inference(resolution,[],[f994,f440]) ).
fof(f18101,plain,
( spl8_476
| ~ spl8_47
| ~ spl8_104 ),
inference(avatar_split_clause,[],[f991,f969,f496,f18099]) ).
fof(f18099,plain,
( spl8_476
<=> ! [X2,X0,X1] :
( member(sK5(X0,unordered_pair(X1,X2)),sum_class(universal_class))
| ~ member(X0,sum_class(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_476])]) ).
fof(f991,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,unordered_pair(X1,X2)),sum_class(universal_class))
| ~ member(X0,sum_class(unordered_pair(X1,X2))) )
| ~ spl8_47
| ~ spl8_104 ),
inference(resolution,[],[f970,f497]) ).
fof(f18097,plain,
( spl8_475
| ~ spl8_43
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f982,f965,f480,f18095]) ).
fof(f18095,plain,
( spl8_475
<=> ! [X0] :
( null_class = power_class(X0)
| sK2(power_class(X0)) = X0
| ~ subclass(X0,sK2(power_class(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_475])]) ).
fof(f480,plain,
( spl8_43
<=> ! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
fof(f965,plain,
( spl8_103
<=> ! [X0] :
( subclass(sK2(power_class(X0)),X0)
| null_class = power_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).
fof(f982,plain,
( ! [X0] :
( null_class = power_class(X0)
| sK2(power_class(X0)) = X0
| ~ subclass(X0,sK2(power_class(X0))) )
| ~ spl8_43
| ~ spl8_103 ),
inference(resolution,[],[f966,f481]) ).
fof(f481,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| X0 = X1
| ~ subclass(X0,X1) )
| ~ spl8_43 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f966,plain,
( ! [X0] :
( subclass(sK2(power_class(X0)),X0)
| null_class = power_class(X0) )
| ~ spl8_103 ),
inference(avatar_component_clause,[],[f965]) ).
fof(f17374,plain,
( spl8_90
| ~ spl8_12
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f14725,f376,f322,f846]) ).
fof(f846,plain,
( spl8_90
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
fof(f14725,plain,
( ! [X0] :
( ~ inductive(complement(X0))
| ~ member(null_class,X0) )
| ~ spl8_12
| ~ spl8_25 ),
inference(resolution,[],[f323,f377]) ).
fof(f17373,plain,
( ~ spl8_80
| ~ spl8_29
| ~ spl8_449 ),
inference(avatar_split_clause,[],[f17180,f16315,f403,f792]) ).
fof(f403,plain,
( spl8_29
<=> ! [X0] : ~ inductive(complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
fof(f16315,plain,
( spl8_449
<=> universal_class = complement(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_449])]) ).
fof(f17180,plain,
( ~ inductive(universal_class)
| ~ spl8_29
| ~ spl8_449 ),
inference(superposition,[],[f404,f16317]) ).
fof(f16317,plain,
( universal_class = complement(null_class)
| ~ spl8_449 ),
inference(avatar_component_clause,[],[f16315]) ).
fof(f404,plain,
( ! [X0] : ~ inductive(complement(X0))
| ~ spl8_29 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f16800,plain,
( spl8_474
| ~ spl8_91
| ~ spl8_377 ),
inference(avatar_split_clause,[],[f15302,f14247,f850,f16797]) ).
fof(f850,plain,
( spl8_91
<=> ! [X0] :
( universal_class = X0
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).
fof(f14247,plain,
( spl8_377
<=> subclass(universal_class,power_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_377])]) ).
fof(f15302,plain,
( universal_class = power_class(universal_class)
| ~ spl8_91
| ~ spl8_377 ),
inference(resolution,[],[f14249,f851]) ).
fof(f851,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl8_91 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f14249,plain,
( subclass(universal_class,power_class(universal_class))
| ~ spl8_377 ),
inference(avatar_component_clause,[],[f14247]) ).
fof(f16438,plain,
( ~ spl8_472
| spl8_473
| ~ spl8_6
| ~ spl8_243 ),
inference(avatar_split_clause,[],[f6586,f6515,f295,f16436,f16432]) ).
fof(f16432,plain,
( spl8_472
<=> subclass(successor_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_472])]) ).
fof(f16436,plain,
( spl8_473
<=> ! [X0] :
( ~ member(X0,universal_class)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_473])]) ).
fof(f6515,plain,
( spl8_243
<=> ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),X1)
| ~ subclass(successor_relation,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_243])]) ).
fof(f6586,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ subclass(successor_relation,null_class) )
| ~ spl8_6
| ~ spl8_243 ),
inference(resolution,[],[f6516,f296]) ).
fof(f6516,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),X1)
| ~ member(X0,universal_class)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ subclass(successor_relation,X1) )
| ~ spl8_243 ),
inference(avatar_component_clause,[],[f6515]) ).
fof(f16430,plain,
( spl8_471
| ~ spl8_189 ),
inference(avatar_split_clause,[],[f2824,f2705,f16428]) ).
fof(f16428,plain,
( spl8_471
<=> ! [X0,X1] :
( member(sK5(X0,union(X1,X1)),X1)
| ~ member(X0,sum_class(union(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_471])]) ).
fof(f2705,plain,
( spl8_189
<=> ! [X2,X0,X1] :
( member(sK5(X0,union(X1,X2)),X1)
| member(sK5(X0,union(X1,X2)),X2)
| ~ member(X0,sum_class(union(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_189])]) ).
fof(f2824,plain,
( ! [X0,X1] :
( member(sK5(X0,union(X1,X1)),X1)
| ~ member(X0,sum_class(union(X1,X1))) )
| ~ spl8_189 ),
inference(factoring,[],[f2706]) ).
fof(f2706,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,union(X1,X2)),X2)
| member(sK5(X0,union(X1,X2)),X1)
| ~ member(X0,sum_class(union(X1,X2))) )
| ~ spl8_189 ),
inference(avatar_component_clause,[],[f2705]) ).
fof(f16425,plain,
( spl8_470
| ~ spl8_92
| ~ spl8_377 ),
inference(avatar_split_clause,[],[f15300,f14247,f854,f16422]) ).
fof(f16422,plain,
( spl8_470
<=> member(sK7,power_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_470])]) ).
fof(f854,plain,
( spl8_92
<=> ! [X0] :
( member(sK7,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).
fof(f15300,plain,
( member(sK7,power_class(universal_class))
| ~ spl8_92
| ~ spl8_377 ),
inference(resolution,[],[f14249,f855]) ).
fof(f855,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(sK7,X0) )
| ~ spl8_92 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f16420,plain,
( spl8_469
| ~ spl8_6
| ~ spl8_189 ),
inference(avatar_split_clause,[],[f2809,f2705,f295,f16418]) ).
fof(f16418,plain,
( spl8_469
<=> ! [X0,X1] :
( member(sK5(X0,union(null_class,X1)),X1)
| ~ member(X0,sum_class(union(null_class,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_469])]) ).
fof(f2809,plain,
( ! [X0,X1] :
( member(sK5(X0,union(null_class,X1)),X1)
| ~ member(X0,sum_class(union(null_class,X1))) )
| ~ spl8_6
| ~ spl8_189 ),
inference(resolution,[],[f2706,f296]) ).
fof(f16416,plain,
( spl8_468
| ~ spl8_6
| ~ spl8_189 ),
inference(avatar_split_clause,[],[f2775,f2705,f295,f16414]) ).
fof(f16414,plain,
( spl8_468
<=> ! [X0,X1] :
( member(sK5(X0,union(X1,null_class)),X1)
| ~ member(X0,sum_class(union(X1,null_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_468])]) ).
fof(f2775,plain,
( ! [X0,X1] :
( member(sK5(X0,union(X1,null_class)),X1)
| ~ member(X0,sum_class(union(X1,null_class))) )
| ~ spl8_6
| ~ spl8_189 ),
inference(resolution,[],[f2706,f296]) ).
fof(f16411,plain,
( ~ spl8_466
| spl8_467
| ~ spl8_75
| ~ spl8_180 ),
inference(avatar_split_clause,[],[f2436,f2293,f714,f16409,f16405]) ).
fof(f16405,plain,
( spl8_466
<=> subclass(identity_relation,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_466])]) ).
fof(f16409,plain,
( spl8_467
<=> ! [X0] :
( ~ member(X0,universal_class)
| union(X0,unordered_pair(X0,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_467])]) ).
fof(f714,plain,
( spl8_75
<=> ! [X0,X1] :
( union(X0,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,[spl8_75])]) ).
fof(f2293,plain,
( spl8_180
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),X1)
| ~ subclass(identity_relation,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_180])]) ).
fof(f2436,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,successor_relation)
| union(X0,unordered_pair(X0,X0)) = X0 )
| ~ spl8_75
| ~ spl8_180 ),
inference(resolution,[],[f2294,f715]) ).
fof(f715,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| union(X0,unordered_pair(X0,X0)) = X1 )
| ~ spl8_75 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f2294,plain,
( ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),X1)
| ~ member(X0,universal_class)
| ~ subclass(identity_relation,X1) )
| ~ spl8_180 ),
inference(avatar_component_clause,[],[f2293]) ).
fof(f16403,plain,
( spl8_465
| ~ spl8_130
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2279,f2243,f1255,f16401]) ).
fof(f16401,plain,
( spl8_465
<=> ! [X0,X1] :
( ~ subclass(sK4(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_465])]) ).
fof(f2279,plain,
( ! [X0,X1] :
( ~ subclass(sK4(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1))
| ~ subclass(X0,universal_class) )
| ~ spl8_130
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2272]) ).
fof(f2272,plain,
( ! [X0,X1] :
( ~ subclass(sK4(X0,power_class(X1)),X1)
| subclass(X0,power_class(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,power_class(X1)) )
| ~ spl8_130
| ~ spl8_176 ),
inference(resolution,[],[f2244,f1256]) ).
fof(f16399,plain,
( spl8_464
| ~ spl8_130
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2263,f2239,f1255,f16397]) ).
fof(f16397,plain,
( spl8_464
<=> ! [X0,X1] :
( member(sK4(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_464])]) ).
fof(f2263,plain,
( ! [X0,X1] :
( member(sK4(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class) )
| ~ spl8_130
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2255]) ).
fof(f2255,plain,
( ! [X0,X1] :
( member(sK4(X0,complement(X1)),X1)
| subclass(X0,complement(X1))
| ~ subclass(X0,universal_class)
| subclass(X0,complement(X1)) )
| ~ spl8_130
| ~ spl8_175 ),
inference(resolution,[],[f2240,f1256]) ).
fof(f16395,plain,
( spl8_463
| ~ spl8_16
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1790,f1544,f339,f16393]) ).
fof(f16393,plain,
( spl8_463
<=> ! [X2,X0,X1] :
( ~ member(X0,sK2(X1))
| member(X0,sum_class(union(X1,X2)))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_463])]) ).
fof(f1790,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK2(X1))
| member(X0,sum_class(union(X1,X2)))
| null_class = X1 )
| ~ spl8_16
| ~ spl8_154 ),
inference(resolution,[],[f1545,f340]) ).
fof(f16391,plain,
( spl8_462
| ~ spl8_95
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1770,f1544,f872,f16389]) ).
fof(f16389,plain,
( spl8_462
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sum_class(universal_class),X2)))
| ~ member(X1,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_462])]) ).
fof(f1770,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(sum_class(universal_class),X2)))
| ~ member(X1,sK7) )
| ~ spl8_95
| ~ spl8_154 ),
inference(resolution,[],[f1545,f873]) ).
fof(f16387,plain,
( spl8_461
| ~ spl8_16
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1742,f1540,f339,f16385]) ).
fof(f16385,plain,
( spl8_461
<=> ! [X2,X0,X1] :
( ~ member(X0,sK2(X1))
| member(X0,sum_class(union(X2,X1)))
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_461])]) ).
fof(f1742,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK2(X1))
| member(X0,sum_class(union(X2,X1)))
| null_class = X1 )
| ~ spl8_16
| ~ spl8_153 ),
inference(resolution,[],[f1541,f340]) ).
fof(f16383,plain,
( spl8_460
| ~ spl8_95
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1722,f1540,f872,f16381]) ).
fof(f16381,plain,
( spl8_460
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sum_class(universal_class))))
| ~ member(X1,sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_460])]) ).
fof(f1722,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| member(X0,sum_class(union(X2,sum_class(universal_class))))
| ~ member(X1,sK7) )
| ~ spl8_95
| ~ spl8_153 ),
inference(resolution,[],[f1541,f873]) ).
fof(f16378,plain,
( spl8_459
| ~ spl8_97
| ~ spl8_377 ),
inference(avatar_split_clause,[],[f15298,f14247,f883,f16375]) ).
fof(f16375,plain,
( spl8_459
<=> member(null_class,power_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_459])]) ).
fof(f883,plain,
( spl8_97
<=> ! [X0] :
( member(null_class,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_97])]) ).
fof(f15298,plain,
( member(null_class,power_class(universal_class))
| ~ spl8_97
| ~ spl8_377 ),
inference(resolution,[],[f14249,f884]) ).
fof(f884,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) )
| ~ spl8_97 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f16373,plain,
( spl8_458
| ~ spl8_27
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1689,f1516,f384,f16371]) ).
fof(f16371,plain,
( spl8_458
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,power_class(X2))
| subclass(sK5(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_458])]) ).
fof(f1689,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,power_class(X2))
| subclass(sK5(X0,X1),X2) )
| ~ spl8_27
| ~ spl8_150 ),
inference(resolution,[],[f1517,f385]) ).
fof(f16369,plain,
( spl8_457
| ~ spl8_25
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1682,f1516,f376,f16367]) ).
fof(f16367,plain,
( spl8_457
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,complement(X2))
| ~ member(sK5(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_457])]) ).
fof(f1682,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,complement(X2))
| ~ member(sK5(X0,X1),X2) )
| ~ spl8_25
| ~ spl8_150 ),
inference(resolution,[],[f1517,f377]) ).
fof(f16365,plain,
( spl8_456
| ~ spl8_20
| ~ spl8_149 ),
inference(avatar_split_clause,[],[f1670,f1512,f355,f16363]) ).
fof(f16363,plain,
( spl8_456
<=> ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,sum_class(X1))
| ~ function(sK5(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_456])]) ).
fof(f1512,plain,
( spl8_149
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,X2)
| ~ subclass(sK5(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_149])]) ).
fof(f1670,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,sum_class(X1))
| ~ function(sK5(X0,X1)) )
| ~ spl8_20
| ~ spl8_149 ),
inference(resolution,[],[f1513,f356]) ).
fof(f1513,plain,
( ! [X2,X0,X1] :
( ~ subclass(sK5(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,sum_class(X1)) )
| ~ spl8_149 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f16361,plain,
( spl8_455
| ~ spl8_16
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1478,f1298,f339,f16359]) ).
fof(f16359,plain,
( spl8_455
<=> ! [X0] :
( member(sK2(sK3(X0)),sum_class(universal_class))
| ~ member(X0,identity_relation)
| null_class = sK3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_455])]) ).
fof(f1478,plain,
( ! [X0] :
( member(sK2(sK3(X0)),sum_class(universal_class))
| ~ member(X0,identity_relation)
| null_class = sK3(X0) )
| ~ spl8_16
| ~ spl8_140 ),
inference(resolution,[],[f1299,f340]) ).
fof(f16357,plain,
( spl8_454
| ~ spl8_16
| ~ spl8_139 ),
inference(avatar_split_clause,[],[f1460,f1294,f339,f16355]) ).
fof(f16355,plain,
( spl8_454
<=> ! [X0] :
( member(sK2(sK2(X0)),sum_class(X0))
| null_class = X0
| null_class = sK2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_454])]) ).
fof(f1460,plain,
( ! [X0] :
( member(sK2(sK2(X0)),sum_class(X0))
| null_class = X0
| null_class = sK2(X0) )
| ~ spl8_16
| ~ spl8_139 ),
inference(resolution,[],[f1295,f340]) ).
fof(f16353,plain,
( spl8_453
| ~ spl8_99
| ~ spl8_139 ),
inference(avatar_split_clause,[],[f1455,f1294,f896,f16351]) ).
fof(f16351,plain,
( spl8_453
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| null_class = X2
| ~ subclass(universal_class,sK2(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_453])]) ).
fof(f1455,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(X2))
| null_class = X2
| ~ subclass(universal_class,sK2(X2)) )
| ~ spl8_99
| ~ spl8_139 ),
inference(resolution,[],[f1295,f897]) ).
fof(f16349,plain,
( spl8_452
| ~ spl8_16
| ~ spl8_138 ),
inference(avatar_split_clause,[],[f1446,f1290,f339,f16347]) ).
fof(f16347,plain,
( spl8_452
<=> ! [X0] :
( member(sK2(sK2(X0)),sum_class(universal_class))
| null_class = X0
| null_class = sK2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_452])]) ).
fof(f1446,plain,
( ! [X0] :
( member(sK2(sK2(X0)),sum_class(universal_class))
| null_class = X0
| null_class = sK2(X0) )
| ~ spl8_16
| ~ spl8_138 ),
inference(resolution,[],[f1291,f340]) ).
fof(f16345,plain,
( spl8_451
| ~ spl8_16
| ~ spl8_137 ),
inference(avatar_split_clause,[],[f1432,f1286,f339,f16343]) ).
fof(f16343,plain,
( spl8_451
<=> ! [X0] :
( member(sK2(power_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = power_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_451])]) ).
fof(f1432,plain,
( ! [X0] :
( member(sK2(power_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = power_class(X0) )
| ~ spl8_16
| ~ spl8_137 ),
inference(resolution,[],[f1287,f340]) ).
fof(f16341,plain,
( spl8_450
| ~ spl8_16
| ~ spl8_136 ),
inference(avatar_split_clause,[],[f1416,f1279,f339,f16339]) ).
fof(f16339,plain,
( spl8_450
<=> ! [X0] :
( member(sK2(sum_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = sum_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_450])]) ).
fof(f1416,plain,
( ! [X0] :
( member(sK2(sum_class(X0)),sum_class(universal_class))
| ~ member(X0,universal_class)
| null_class = sum_class(X0) )
| ~ spl8_16
| ~ spl8_136 ),
inference(resolution,[],[f1280,f340]) ).
fof(f16318,plain,
( spl8_449
| ~ spl8_91
| ~ spl8_376 ),
inference(avatar_split_clause,[],[f15149,f14098,f850,f16315]) ).
fof(f14098,plain,
( spl8_376
<=> subclass(universal_class,complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_376])]) ).
fof(f15149,plain,
( universal_class = complement(null_class)
| ~ spl8_91
| ~ spl8_376 ),
inference(resolution,[],[f14100,f851]) ).
fof(f14100,plain,
( subclass(universal_class,complement(null_class))
| ~ spl8_376 ),
inference(avatar_component_clause,[],[f14098]) ).
fof(f16313,plain,
( spl8_448
| spl8_349
| ~ spl8_99
| ~ spl8_136 ),
inference(avatar_split_clause,[],[f1411,f1279,f896,f13879,f16311]) ).
fof(f16311,plain,
( spl8_448
<=> ! [X2] :
( ~ member(X2,universal_class)
| ~ subclass(universal_class,sum_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_448])]) ).
fof(f1411,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ member(X2,universal_class)
| ~ subclass(universal_class,sum_class(X2)) )
| ~ spl8_99
| ~ spl8_136 ),
inference(resolution,[],[f1280,f897]) ).
fof(f16309,plain,
( spl8_447
| ~ spl8_100
| ~ spl8_134 ),
inference(avatar_split_clause,[],[f1403,f1271,f900,f16307]) ).
fof(f16307,plain,
( spl8_447
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(null_class,X1)
| ~ inductive(sK5(X0,power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_447])]) ).
fof(f900,plain,
( spl8_100
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ subclass(X1,X0)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_100])]) ).
fof(f1271,plain,
( spl8_134
<=> ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| subclass(sK5(X0,power_class(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_134])]) ).
fof(f1403,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(null_class,X1)
| ~ inductive(sK5(X0,power_class(X1))) )
| ~ spl8_100
| ~ spl8_134 ),
inference(resolution,[],[f1272,f901]) ).
fof(f901,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| member(null_class,X0)
| ~ inductive(X1) )
| ~ spl8_100 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f1272,plain,
( ! [X0,X1] :
( subclass(sK5(X0,power_class(X1)),X1)
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl8_134 ),
inference(avatar_component_clause,[],[f1271]) ).
fof(f16305,plain,
( spl8_446
| ~ spl8_95
| ~ spl8_131 ),
inference(avatar_split_clause,[],[f1388,f1259,f872,f16303]) ).
fof(f16303,plain,
( spl8_446
<=> ! [X0] :
( ~ member(X0,sum_class(complement(sum_class(universal_class))))
| ~ member(sK5(X0,complement(sum_class(universal_class))),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_446])]) ).
fof(f1388,plain,
( ! [X0] :
( ~ member(X0,sum_class(complement(sum_class(universal_class))))
| ~ member(sK5(X0,complement(sum_class(universal_class))),sK7) )
| ~ spl8_95
| ~ spl8_131 ),
inference(resolution,[],[f1260,f873]) ).
fof(f16301,plain,
( spl8_445
| ~ spl8_35
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1371,f1255,f427,f16299]) ).
fof(f16299,plain,
( spl8_445
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK4(X0,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_445])]) ).
fof(f1371,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK4(X0,X3),X1) )
| ~ spl8_35
| ~ spl8_130 ),
inference(resolution,[],[f1256,f428]) ).
fof(f16297,plain,
( spl8_444
| ~ spl8_36
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1370,f1255,f431,f16295]) ).
fof(f16295,plain,
( spl8_444
<=> ! [X0,X3,X2,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK4(X0,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_444])]) ).
fof(f1370,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| subclass(X0,X3)
| member(sK4(X0,X3),X2) )
| ~ spl8_36
| ~ spl8_130 ),
inference(resolution,[],[f1256,f432]) ).
fof(f16293,plain,
( spl8_443
| ~ spl8_27
| ~ spl8_124 ),
inference(avatar_split_clause,[],[f1340,f1231,f384,f16291]) ).
fof(f16291,plain,
( spl8_443
<=> ! [X0,X1] :
( null_class = intersection(X0,power_class(X1))
| subclass(sK2(intersection(X0,power_class(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_443])]) ).
fof(f1340,plain,
( ! [X0,X1] :
( null_class = intersection(X0,power_class(X1))
| subclass(sK2(intersection(X0,power_class(X1))),X1) )
| ~ spl8_27
| ~ spl8_124 ),
inference(resolution,[],[f1232,f385]) ).
fof(f16289,plain,
( spl8_442
| ~ spl8_25
| ~ spl8_124 ),
inference(avatar_split_clause,[],[f1333,f1231,f376,f16287]) ).
fof(f16287,plain,
( spl8_442
<=> ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(sK2(intersection(X0,complement(X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_442])]) ).
fof(f1333,plain,
( ! [X0,X1] :
( null_class = intersection(X0,complement(X1))
| ~ member(sK2(intersection(X0,complement(X1))),X1) )
| ~ spl8_25
| ~ spl8_124 ),
inference(resolution,[],[f1232,f377]) ).
fof(f16285,plain,
( spl8_441
| ~ spl8_27
| ~ spl8_123 ),
inference(avatar_split_clause,[],[f1318,f1227,f384,f16283]) ).
fof(f16283,plain,
( spl8_441
<=> ! [X0,X1] :
( null_class = intersection(power_class(X0),X1)
| subclass(sK2(intersection(power_class(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_441])]) ).
fof(f1318,plain,
( ! [X0,X1] :
( null_class = intersection(power_class(X0),X1)
| subclass(sK2(intersection(power_class(X0),X1)),X0) )
| ~ spl8_27
| ~ spl8_123 ),
inference(resolution,[],[f1228,f385]) ).
fof(f16281,plain,
( spl8_440
| ~ spl8_25
| ~ spl8_123 ),
inference(avatar_split_clause,[],[f1311,f1227,f376,f16279]) ).
fof(f16279,plain,
( spl8_440
<=> ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(sK2(intersection(complement(X0),X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_440])]) ).
fof(f1311,plain,
( ! [X0,X1] :
( null_class = intersection(complement(X0),X1)
| ~ member(sK2(intersection(complement(X0),X1)),X0) )
| ~ spl8_25
| ~ spl8_123 ),
inference(resolution,[],[f1228,f377]) ).
fof(f16277,plain,
( spl8_439
| ~ spl8_45
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f1205,f1056,f488,f16275]) ).
fof(f16275,plain,
( spl8_439
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(sK3(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_439])]) ).
fof(f1205,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,identity_relation)
| member(sK3(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl8_45
| ~ spl8_120 ),
inference(resolution,[],[f1057,f489]) ).
fof(f16272,plain,
( spl8_438
| ~ spl8_92
| ~ spl8_376 ),
inference(avatar_split_clause,[],[f15147,f14098,f854,f16269]) ).
fof(f16269,plain,
( spl8_438
<=> member(sK7,complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_438])]) ).
fof(f15147,plain,
( member(sK7,complement(null_class))
| ~ spl8_92
| ~ spl8_376 ),
inference(resolution,[],[f14100,f855]) ).
fof(f16267,plain,
( spl8_437
| ~ spl8_104
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1185,f1052,f969,f16265]) ).
fof(f16265,plain,
( spl8_437
<=> ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| null_class = X0
| member(sK2(X0),sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_437])]) ).
fof(f1185,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,unordered_pair(X1,X2))
| null_class = X0
| member(sK2(X0),sum_class(universal_class)) )
| ~ spl8_104
| ~ spl8_119 ),
inference(resolution,[],[f1053,f970]) ).
fof(f16263,plain,
( spl8_436
| ~ spl8_45
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1182,f1052,f488,f16261]) ).
fof(f16261,plain,
( spl8_436
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(sK2(X0),X2)
| ~ subclass(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_436])]) ).
fof(f1182,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| null_class = X0
| member(sK2(X0),X2)
| ~ subclass(X1,X2) )
| ~ spl8_45
| ~ spl8_119 ),
inference(resolution,[],[f1053,f489]) ).
fof(f16259,plain,
( spl8_435
| ~ spl8_45
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1158,f1043,f488,f16257]) ).
fof(f16257,plain,
( spl8_435
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(sK2(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_435])]) ).
fof(f1158,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| null_class = X1
| member(sK2(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl8_45
| ~ spl8_117 ),
inference(resolution,[],[f1044,f489]) ).
fof(f16255,plain,
( spl8_434
| ~ spl8_45
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1135,f1039,f488,f16253]) ).
fof(f16253,plain,
( spl8_434
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(power_class(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_434])]) ).
fof(f1135,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(power_class(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl8_45
| ~ spl8_116 ),
inference(resolution,[],[f1040,f489]) ).
fof(f16251,plain,
( spl8_433
| ~ spl8_45
| ~ spl8_115 ),
inference(avatar_split_clause,[],[f1112,f1035,f488,f16249]) ).
fof(f16249,plain,
( spl8_433
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(sum_class(X1),X2)
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_433])]) ).
fof(f1112,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ member(X1,universal_class)
| member(sum_class(X1),X2)
| ~ subclass(X0,X2) )
| ~ spl8_45
| ~ spl8_115 ),
inference(resolution,[],[f1036,f489]) ).
fof(f16247,plain,
( spl8_432
| ~ spl8_33
| ~ spl8_114 ),
inference(avatar_split_clause,[],[f1102,f1031,f419,f16245]) ).
fof(f16245,plain,
( spl8_432
<=> ! [X0,X1] :
( ~ member(sK4(sK2(X0),X1),X0)
| null_class = X0
| subclass(sK2(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_432])]) ).
fof(f1102,plain,
( ! [X0,X1] :
( ~ member(sK4(sK2(X0),X1),X0)
| null_class = X0
| subclass(sK2(X0),X1) )
| ~ spl8_33
| ~ spl8_114 ),
inference(resolution,[],[f1032,f420]) ).
fof(f16243,plain,
( spl8_431
| ~ spl8_45
| ~ spl8_109 ),
inference(avatar_split_clause,[],[f1096,f1009,f488,f16241]) ).
fof(f16241,plain,
( spl8_431
<=> ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(sK4(power_class(X0),X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_431])]) ).
fof(f1096,plain,
( ! [X2,X0,X1] :
( subclass(power_class(X0),X1)
| member(sK4(power_class(X0),X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_45
| ~ spl8_109 ),
inference(resolution,[],[f1010,f489]) ).
fof(f16239,plain,
( spl8_430
| ~ spl8_45
| ~ spl8_107 ),
inference(avatar_split_clause,[],[f1087,f1001,f488,f16237]) ).
fof(f16237,plain,
( spl8_430
<=> ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK4(domain_of(X0),X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_430])]) ).
fof(f1087,plain,
( ! [X2,X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK4(domain_of(X0),X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_45
| ~ spl8_107 ),
inference(resolution,[],[f1002,f489]) ).
fof(f16235,plain,
( spl8_429
| ~ spl8_45
| ~ spl8_106 ),
inference(avatar_split_clause,[],[f1079,f997,f488,f16233]) ).
fof(f16233,plain,
( spl8_429
<=> ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(sK4(complement(X0),X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_429])]) ).
fof(f1079,plain,
( ! [X2,X0,X1] :
( subclass(complement(X0),X1)
| member(sK4(complement(X0),X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_45
| ~ spl8_106 ),
inference(resolution,[],[f998,f489]) ).
fof(f16231,plain,
( spl8_428
| ~ spl8_33
| ~ spl8_104 ),
inference(avatar_split_clause,[],[f990,f969,f419,f16229]) ).
fof(f16229,plain,
( spl8_428
<=> ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),X2),sum_class(universal_class))
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_428])]) ).
fof(f990,plain,
( ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),X2),sum_class(universal_class))
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl8_33
| ~ spl8_104 ),
inference(resolution,[],[f970,f420]) ).
fof(f16226,plain,
( spl8_427
| ~ spl8_97
| ~ spl8_376 ),
inference(avatar_split_clause,[],[f15145,f14098,f883,f16223]) ).
fof(f16223,plain,
( spl8_427
<=> member(null_class,complement(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_427])]) ).
fof(f15145,plain,
( member(null_class,complement(null_class))
| ~ spl8_97
| ~ spl8_376 ),
inference(resolution,[],[f14100,f884]) ).
fof(f16221,plain,
( ~ spl8_424
| spl8_425
| spl8_426
| ~ spl8_96
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f983,f965,f879,f16218,f16214,f16210]) ).
fof(f16210,plain,
( spl8_424
<=> inductive(sK2(power_class(sK7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_424])]) ).
fof(f16214,plain,
( spl8_425
<=> sK7 = sK2(power_class(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_425])]) ).
fof(f16218,plain,
( spl8_426
<=> null_class = power_class(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_426])]) ).
fof(f983,plain,
( null_class = power_class(sK7)
| sK7 = sK2(power_class(sK7))
| ~ inductive(sK2(power_class(sK7)))
| ~ spl8_96
| ~ spl8_103 ),
inference(resolution,[],[f966,f880]) ).
fof(f16208,plain,
( spl8_423
| ~ spl8_37
| ~ spl8_101 ),
inference(avatar_split_clause,[],[f977,f956,f435,f16206]) ).
fof(f16206,plain,
( spl8_423
<=> ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK2(complement(union(X0,X1))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_423])]) ).
fof(f956,plain,
( spl8_101
<=> ! [X0] :
( ~ member(sK2(complement(X0)),X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_101])]) ).
fof(f977,plain,
( ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK2(complement(union(X0,X1))),X0) )
| ~ spl8_37
| ~ spl8_101 ),
inference(resolution,[],[f957,f436]) ).
fof(f957,plain,
( ! [X0] :
( ~ member(sK2(complement(X0)),X0)
| complement(X0) = null_class )
| ~ spl8_101 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f16204,plain,
( spl8_422
| ~ spl8_38
| ~ spl8_101 ),
inference(avatar_split_clause,[],[f976,f956,f439,f16202]) ).
fof(f16202,plain,
( spl8_422
<=> ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK2(complement(union(X0,X1))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_422])]) ).
fof(f976,plain,
( ! [X0,X1] :
( null_class = complement(union(X0,X1))
| ~ member(sK2(complement(union(X0,X1))),X1) )
| ~ spl8_38
| ~ spl8_101 ),
inference(resolution,[],[f957,f440]) ).
fof(f16199,plain,
( spl8_420
| spl8_421
| ~ spl8_55
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f953,f900,f590,f16196,f16193]) ).
fof(f16193,plain,
( spl8_420
<=> ! [X0] :
( ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_420])]) ).
fof(f16196,plain,
( spl8_421
<=> member(null_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_421])]) ).
fof(f590,plain,
( spl8_55
<=> ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
fof(f953,plain,
( ! [X0] :
( member(null_class,identity_relation)
| ~ inductive(compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
| ~ function(X0) )
| ~ spl8_55
| ~ spl8_100 ),
inference(resolution,[],[f901,f591]) ).
fof(f591,plain,
( ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) )
| ~ spl8_55 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f15068,plain,
( spl8_30
| ~ spl8_274
| ~ spl8_307 ),
inference(avatar_split_clause,[],[f13724,f13354,f7494,f406]) ).
fof(f7494,plain,
( spl8_274
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_274])]) ).
fof(f13354,plain,
( spl8_307
<=> member(null_class,sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_307])]) ).
fof(f13724,plain,
( member(null_class,universal_class)
| ~ spl8_274
| ~ spl8_307 ),
inference(resolution,[],[f13356,f7495]) ).
fof(f7495,plain,
( ! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) )
| ~ spl8_274 ),
inference(avatar_component_clause,[],[f7494]) ).
fof(f13356,plain,
( member(null_class,sum_class(universal_class))
| ~ spl8_307 ),
inference(avatar_component_clause,[],[f13354]) ).
fof(f14935,plain,
( spl8_419
| ~ spl8_34
| ~ spl8_185 ),
inference(avatar_split_clause,[],[f2645,f2500,f423,f14933]) ).
fof(f14933,plain,
( spl8_419
<=> ! [X0,X1] :
( member(sK4(union(X0,X1),X1),X0)
| subclass(union(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_419])]) ).
fof(f2500,plain,
( spl8_185
<=> ! [X2,X0,X1] :
( member(sK4(union(X0,X1),X2),X0)
| member(sK4(union(X0,X1),X2),X1)
| subclass(union(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_185])]) ).
fof(f2645,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X1),X0)
| subclass(union(X0,X1),X1) )
| ~ spl8_34
| ~ spl8_185 ),
inference(duplicate_literal_removal,[],[f2555]) ).
fof(f2555,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X1),X0)
| subclass(union(X0,X1),X1)
| subclass(union(X0,X1),X1) )
| ~ spl8_34
| ~ spl8_185 ),
inference(resolution,[],[f2501,f424]) ).
fof(f2501,plain,
( ! [X2,X0,X1] :
( member(sK4(union(X0,X1),X2),X1)
| member(sK4(union(X0,X1),X2),X0)
| subclass(union(X0,X1),X2) )
| ~ spl8_185 ),
inference(avatar_component_clause,[],[f2500]) ).
fof(f14931,plain,
( spl8_418
| ~ spl8_34
| ~ spl8_185 ),
inference(avatar_split_clause,[],[f2639,f2500,f423,f14929]) ).
fof(f14929,plain,
( spl8_418
<=> ! [X0,X1] :
( member(sK4(union(X0,X1),X0),X1)
| subclass(union(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_418])]) ).
fof(f2639,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X0),X1)
| subclass(union(X0,X1),X0) )
| ~ spl8_34
| ~ spl8_185 ),
inference(duplicate_literal_removal,[],[f2594]) ).
fof(f2594,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X1),X0),X1)
| subclass(union(X0,X1),X0)
| subclass(union(X0,X1),X0) )
| ~ spl8_34
| ~ spl8_185 ),
inference(resolution,[],[f2501,f424]) ).
fof(f14927,plain,
( spl8_417
| ~ spl8_185 ),
inference(avatar_split_clause,[],[f2633,f2500,f14925]) ).
fof(f2633,plain,
( ! [X0,X1] :
( member(sK4(union(X0,X0),X1),X0)
| subclass(union(X0,X0),X1) )
| ~ spl8_185 ),
inference(factoring,[],[f2501]) ).
fof(f14923,plain,
( spl8_416
| ~ spl8_6
| ~ spl8_185 ),
inference(avatar_split_clause,[],[f2618,f2500,f295,f14921]) ).
fof(f2618,plain,
( ! [X0,X1] :
( member(sK4(union(null_class,X0),X1),X0)
| subclass(union(null_class,X0),X1) )
| ~ spl8_6
| ~ spl8_185 ),
inference(resolution,[],[f2501,f296]) ).
fof(f14919,plain,
( spl8_415
| ~ spl8_6
| ~ spl8_185 ),
inference(avatar_split_clause,[],[f2579,f2500,f295,f14917]) ).
fof(f2579,plain,
( ! [X0,X1] :
( member(sK4(union(X0,null_class),X1),X0)
| subclass(union(X0,null_class),X1) )
| ~ spl8_6
| ~ spl8_185 ),
inference(resolution,[],[f2501,f296]) ).
fof(f14915,plain,
( spl8_414
| ~ spl8_33
| ~ spl8_184 ),
inference(avatar_split_clause,[],[f2541,f2496,f419,f14913]) ).
fof(f2541,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0)) )
| ~ spl8_33
| ~ spl8_184 ),
inference(duplicate_literal_removal,[],[f2515]) ).
fof(f2515,plain,
( ! [X0,X1] :
( ~ member(sK4(X0,intersection(X1,X0)),X1)
| subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0)) )
| ~ spl8_33
| ~ spl8_184 ),
inference(resolution,[],[f2497,f420]) ).
fof(f14911,plain,
( spl8_413
| ~ spl8_106
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2283,f2243,f997,f14909]) ).
fof(f14909,plain,
( spl8_413
<=> ! [X0,X1] :
( ~ subclass(sK4(complement(X0),power_class(X1)),X1)
| subclass(complement(X0),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_413])]) ).
fof(f2283,plain,
( ! [X0,X1] :
( ~ subclass(sK4(complement(X0),power_class(X1)),X1)
| subclass(complement(X0),power_class(X1)) )
| ~ spl8_106
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2268]) ).
fof(f2268,plain,
( ! [X0,X1] :
( ~ subclass(sK4(complement(X0),power_class(X1)),X1)
| subclass(complement(X0),power_class(X1))
| subclass(complement(X0),power_class(X1)) )
| ~ spl8_106
| ~ spl8_176 ),
inference(resolution,[],[f2244,f998]) ).
fof(f14907,plain,
( spl8_412
| ~ spl8_107
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2282,f2243,f1001,f14905]) ).
fof(f14905,plain,
( spl8_412
<=> ! [X0,X1] :
( ~ subclass(sK4(domain_of(X0),power_class(X1)),X1)
| subclass(domain_of(X0),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_412])]) ).
fof(f2282,plain,
( ! [X0,X1] :
( ~ subclass(sK4(domain_of(X0),power_class(X1)),X1)
| subclass(domain_of(X0),power_class(X1)) )
| ~ spl8_107
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2269]) ).
fof(f2269,plain,
( ! [X0,X1] :
( ~ subclass(sK4(domain_of(X0),power_class(X1)),X1)
| subclass(domain_of(X0),power_class(X1))
| subclass(domain_of(X0),power_class(X1)) )
| ~ spl8_107
| ~ spl8_176 ),
inference(resolution,[],[f2244,f1002]) ).
fof(f14903,plain,
( spl8_411
| ~ spl8_109
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2281,f2243,f1009,f14901]) ).
fof(f14901,plain,
( spl8_411
<=> ! [X0,X1] :
( ~ subclass(sK4(power_class(X0),power_class(X1)),X1)
| subclass(power_class(X0),power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_411])]) ).
fof(f2281,plain,
( ! [X0,X1] :
( ~ subclass(sK4(power_class(X0),power_class(X1)),X1)
| subclass(power_class(X0),power_class(X1)) )
| ~ spl8_109
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2270]) ).
fof(f2270,plain,
( ! [X0,X1] :
( ~ subclass(sK4(power_class(X0),power_class(X1)),X1)
| subclass(power_class(X0),power_class(X1))
| subclass(power_class(X0),power_class(X1)) )
| ~ spl8_109
| ~ spl8_176 ),
inference(resolution,[],[f2244,f1010]) ).
fof(f14899,plain,
( spl8_410
| ~ spl8_106
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2267,f2239,f997,f14897]) ).
fof(f14897,plain,
( spl8_410
<=> ! [X0,X1] :
( member(sK4(complement(X0),complement(X1)),X1)
| subclass(complement(X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_410])]) ).
fof(f2267,plain,
( ! [X0,X1] :
( member(sK4(complement(X0),complement(X1)),X1)
| subclass(complement(X0),complement(X1)) )
| ~ spl8_106
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2251]) ).
fof(f2251,plain,
( ! [X0,X1] :
( member(sK4(complement(X0),complement(X1)),X1)
| subclass(complement(X0),complement(X1))
| subclass(complement(X0),complement(X1)) )
| ~ spl8_106
| ~ spl8_175 ),
inference(resolution,[],[f2240,f998]) ).
fof(f14895,plain,
( spl8_409
| ~ spl8_107
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2266,f2239,f1001,f14893]) ).
fof(f14893,plain,
( spl8_409
<=> ! [X0,X1] :
( member(sK4(domain_of(X0),complement(X1)),X1)
| subclass(domain_of(X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_409])]) ).
fof(f2266,plain,
( ! [X0,X1] :
( member(sK4(domain_of(X0),complement(X1)),X1)
| subclass(domain_of(X0),complement(X1)) )
| ~ spl8_107
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2252]) ).
fof(f2252,plain,
( ! [X0,X1] :
( member(sK4(domain_of(X0),complement(X1)),X1)
| subclass(domain_of(X0),complement(X1))
| subclass(domain_of(X0),complement(X1)) )
| ~ spl8_107
| ~ spl8_175 ),
inference(resolution,[],[f2240,f1002]) ).
fof(f14891,plain,
( spl8_408
| ~ spl8_109
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2265,f2239,f1009,f14889]) ).
fof(f14889,plain,
( spl8_408
<=> ! [X0,X1] :
( member(sK4(power_class(X0),complement(X1)),X1)
| subclass(power_class(X0),complement(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_408])]) ).
fof(f2265,plain,
( ! [X0,X1] :
( member(sK4(power_class(X0),complement(X1)),X1)
| subclass(power_class(X0),complement(X1)) )
| ~ spl8_109
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2253]) ).
fof(f2253,plain,
( ! [X0,X1] :
( member(sK4(power_class(X0),complement(X1)),X1)
| subclass(power_class(X0),complement(X1))
| subclass(power_class(X0),complement(X1)) )
| ~ spl8_109
| ~ spl8_175 ),
inference(resolution,[],[f2240,f1010]) ).
fof(f14887,plain,
( spl8_407
| ~ spl8_8
| ~ spl8_172 ),
inference(avatar_split_clause,[],[f2229,f2105,f303,f14884]) ).
fof(f14884,plain,
( spl8_407
<=> sK7 = first(unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK7,sK7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_407])]) ).
fof(f303,plain,
( spl8_8
<=> member(sK7,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f2105,plain,
( spl8_172
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7,sK7)))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_172])]) ).
fof(f2229,plain,
( sK7 = first(unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK7,sK7))))
| ~ spl8_8
| ~ spl8_172 ),
inference(resolution,[],[f2106,f305]) ).
fof(f305,plain,
( member(sK7,universal_class)
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f2106,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7,sK7)))) = X0 )
| ~ spl8_172 ),
inference(avatar_component_clause,[],[f2105]) ).
fof(f14882,plain,
( spl8_406
| ~ spl8_30
| ~ spl8_172 ),
inference(avatar_split_clause,[],[f2197,f2105,f406,f14879]) ).
fof(f14879,plain,
( spl8_406
<=> null_class = first(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK7,sK7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_406])]) ).
fof(f2197,plain,
( null_class = first(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK7,sK7))))
| ~ spl8_30
| ~ spl8_172 ),
inference(resolution,[],[f2106,f408]) ).
fof(f14877,plain,
( spl8_405
| ~ spl8_8
| ~ spl8_171 ),
inference(avatar_split_clause,[],[f2194,f2101,f303,f14874]) ).
fof(f14874,plain,
( spl8_405
<=> sK7 = second(unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK7,sK7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_405])]) ).
fof(f2101,plain,
( spl8_171
<=> ! [X0] :
( sK7 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7,sK7))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_171])]) ).
fof(f2194,plain,
( sK7 = second(unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK7,sK7))))
| ~ spl8_8
| ~ spl8_171 ),
inference(resolution,[],[f2102,f305]) ).
fof(f2102,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| sK7 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7,sK7)))) )
| ~ spl8_171 ),
inference(avatar_component_clause,[],[f2101]) ).
fof(f14872,plain,
( spl8_404
| ~ spl8_30
| ~ spl8_171 ),
inference(avatar_split_clause,[],[f2162,f2101,f406,f14869]) ).
fof(f14869,plain,
( spl8_404
<=> sK7 = second(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK7,sK7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_404])]) ).
fof(f2162,plain,
( sK7 = second(unordered_pair(unordered_pair(null_class,null_class),unordered_pair(null_class,unordered_pair(sK7,sK7))))
| ~ spl8_30
| ~ spl8_171 ),
inference(resolution,[],[f2102,f408]) ).
fof(f14867,plain,
( spl8_403
| ~ spl8_8
| ~ spl8_169 ),
inference(avatar_split_clause,[],[f2159,f2091,f303,f14865]) ).
fof(f14865,plain,
( spl8_403
<=> ! [X0,X1] :
( ~ member(universal_class,X0)
| member(sK7,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_403])]) ).
fof(f2159,plain,
( ! [X0,X1] :
( ~ member(universal_class,X0)
| member(sK7,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) )
| ~ spl8_8
| ~ spl8_169 ),
inference(resolution,[],[f2092,f305]) ).
fof(f14669,plain,
( ~ spl8_5
| ~ spl8_269 ),
inference(avatar_contradiction_clause,[],[f14668]) ).
fof(f14668,plain,
( $false
| ~ spl8_5
| ~ spl8_269 ),
inference(resolution,[],[f7447,f292]) ).
fof(f292,plain,
( inductive(sK7)
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f290,plain,
( spl8_5
<=> inductive(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f7447,plain,
( ! [X0] : ~ inductive(X0)
| ~ spl8_269 ),
inference(avatar_component_clause,[],[f7446]) ).
fof(f7446,plain,
( spl8_269
<=> ! [X0] : ~ inductive(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_269])]) ).
fof(f14667,plain,
( spl8_402
| ~ spl8_30
| ~ spl8_169 ),
inference(avatar_split_clause,[],[f2128,f2091,f406,f14665]) ).
fof(f14665,plain,
( spl8_402
<=> ! [X0,X1] :
( ~ member(universal_class,X0)
| member(null_class,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_402])]) ).
fof(f2128,plain,
( ! [X0,X1] :
( ~ member(universal_class,X0)
| member(null_class,sum_class(intersection(X0,X1)))
| ~ member(universal_class,X1) )
| ~ spl8_30
| ~ spl8_169 ),
inference(resolution,[],[f2092,f408]) ).
fof(f14663,plain,
( spl8_401
| ~ spl8_12
| ~ spl8_163 ),
inference(avatar_split_clause,[],[f1981,f1882,f322,f14661]) ).
fof(f14661,plain,
( spl8_401
<=> ! [X0,X1] :
( member(null_class,sum_class(X0))
| ~ member(X1,sum_class(X0))
| ~ inductive(sK5(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_401])]) ).
fof(f1981,plain,
( ! [X0,X1] :
( member(null_class,sum_class(X0))
| ~ member(X1,sum_class(X0))
| ~ inductive(sK5(X1,X0)) )
| ~ spl8_12
| ~ spl8_163 ),
inference(resolution,[],[f1883,f323]) ).
fof(f14659,plain,
( spl8_400
| ~ spl8_27
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1377,f1255,f384,f14657]) ).
fof(f14657,plain,
( spl8_400
<=> ! [X2,X0,X1] :
( ~ subclass(X0,power_class(X1))
| subclass(X0,X2)
| subclass(sK4(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_400])]) ).
fof(f1377,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,power_class(X1))
| subclass(X0,X2)
| subclass(sK4(X0,X2),X1) )
| ~ spl8_27
| ~ spl8_130 ),
inference(resolution,[],[f1256,f385]) ).
fof(f14655,plain,
( spl8_399
| ~ spl8_25
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1372,f1255,f376,f14653]) ).
fof(f14653,plain,
( spl8_399
<=> ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(sK4(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_399])]) ).
fof(f1372,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,complement(X1))
| subclass(X0,X2)
| ~ member(sK4(X0,X2),X1) )
| ~ spl8_25
| ~ spl8_130 ),
inference(resolution,[],[f1256,f377]) ).
fof(f14651,plain,
( spl8_398
| ~ spl8_20
| ~ spl8_129 ),
inference(avatar_split_clause,[],[f1356,f1251,f355,f14649]) ).
fof(f14649,plain,
( spl8_398
<=> ! [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,[spl8_398])]) ).
fof(f1251,plain,
( spl8_129
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X0,X2),X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_129])]) ).
fof(f1356,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X0,X1)) )
| ~ spl8_20
| ~ spl8_129 ),
inference(resolution,[],[f1252,f356]) ).
fof(f1252,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X2),X1)
| member(X0,X1)
| ~ member(X0,universal_class) )
| ~ spl8_129 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f14647,plain,
( spl8_397
| ~ spl8_20
| ~ spl8_128 ),
inference(avatar_split_clause,[],[f1353,f1247,f355,f14645]) ).
fof(f14645,plain,
( spl8_397
<=> ! [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,[spl8_397])]) ).
fof(f1247,plain,
( spl8_128
<=> ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X2,X0),X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_128])]) ).
fof(f1353,plain,
( ! [X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,universal_class)
| ~ function(unordered_pair(X1,X0)) )
| ~ spl8_20
| ~ spl8_128 ),
inference(resolution,[],[f1248,f356]) ).
fof(f1248,plain,
( ! [X2,X0,X1] :
( ~ subclass(unordered_pair(X2,X0),X1)
| member(X0,X1)
| ~ member(X0,universal_class) )
| ~ spl8_128 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f14641,plain,
( spl8_396
| ~ spl8_20
| ~ spl8_127 ),
inference(avatar_split_clause,[],[f1350,f1243,f355,f14639]) ).
fof(f14639,plain,
( spl8_396
<=> ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_396])]) ).
fof(f1243,plain,
( spl8_127
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_127])]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X1,X2)) )
| ~ spl8_20
| ~ spl8_127 ),
inference(resolution,[],[f1244,f356]) ).
fof(f1244,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(union(X2,X3),X1)
| member(X0,X1)
| ~ member(X0,X2) )
| ~ spl8_127 ),
inference(avatar_component_clause,[],[f1243]) ).
fof(f14637,plain,
( spl8_395
| ~ spl8_20
| ~ spl8_125 ),
inference(avatar_split_clause,[],[f1347,f1235,f355,f14635]) ).
fof(f14635,plain,
( spl8_395
<=> ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_395])]) ).
fof(f1235,plain,
( spl8_125
<=> ! [X0,X3,X2,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_125])]) ).
fof(f1347,plain,
( ! [X2,X0,X1] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| ~ function(union(X2,X1)) )
| ~ spl8_20
| ~ spl8_125 ),
inference(resolution,[],[f1236,f356]) ).
fof(f1236,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(union(X2,X3),X1)
| member(X0,X1)
| ~ member(X0,X3) )
| ~ spl8_125 ),
inference(avatar_component_clause,[],[f1235]) ).
fof(f14633,plain,
( spl8_394
| ~ spl8_35
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f1213,f1056,f427,f14631]) ).
fof(f14631,plain,
( spl8_394
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK3(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_394])]) ).
fof(f1213,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK3(X2),X0) )
| ~ spl8_35
| ~ spl8_120 ),
inference(resolution,[],[f1057,f428]) ).
fof(f14629,plain,
( spl8_393
| ~ spl8_36
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f1212,f1056,f431,f14627]) ).
fof(f14627,plain,
( spl8_393
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK3(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_393])]) ).
fof(f1212,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,identity_relation)
| member(sK3(X2),X1) )
| ~ spl8_36
| ~ spl8_120 ),
inference(resolution,[],[f1057,f432]) ).
fof(f14625,plain,
( spl8_392
| ~ spl8_35
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1190,f1052,f427,f14623]) ).
fof(f14623,plain,
( spl8_392
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK2(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_392])]) ).
fof(f1190,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK2(X0),X1) )
| ~ spl8_35
| ~ spl8_119 ),
inference(resolution,[],[f1053,f428]) ).
fof(f14621,plain,
( spl8_391
| ~ spl8_36
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1189,f1052,f431,f14619]) ).
fof(f14619,plain,
( spl8_391
<=> ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK2(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_391])]) ).
fof(f1189,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,intersection(X1,X2))
| null_class = X0
| member(sK2(X0),X2) )
| ~ spl8_36
| ~ spl8_119 ),
inference(resolution,[],[f1053,f432]) ).
fof(f14617,plain,
( spl8_390
| ~ spl8_35
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1166,f1043,f427,f14615]) ).
fof(f14615,plain,
( spl8_390
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK2(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_390])]) ).
fof(f1166,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK2(X2),X0) )
| ~ spl8_35
| ~ spl8_117 ),
inference(resolution,[],[f1044,f428]) ).
fof(f14613,plain,
( spl8_389
| ~ spl8_36
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1165,f1043,f431,f14611]) ).
fof(f14611,plain,
( spl8_389
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK2(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_389])]) ).
fof(f1165,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| null_class = X2
| member(sK2(X2),X1) )
| ~ spl8_36
| ~ spl8_117 ),
inference(resolution,[],[f1044,f432]) ).
fof(f14609,plain,
( spl8_388
| ~ spl8_35
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1143,f1039,f427,f14607]) ).
fof(f14607,plain,
( spl8_388
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_388])]) ).
fof(f1143,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X0) )
| ~ spl8_35
| ~ spl8_116 ),
inference(resolution,[],[f1040,f428]) ).
fof(f14605,plain,
( spl8_387
| ~ spl8_36
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1142,f1039,f431,f14603]) ).
fof(f14603,plain,
( spl8_387
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_387])]) ).
fof(f1142,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(power_class(X2),X1) )
| ~ spl8_36
| ~ spl8_116 ),
inference(resolution,[],[f1040,f432]) ).
fof(f14587,plain,
( spl8_386
| ~ spl8_35
| ~ spl8_115 ),
inference(avatar_split_clause,[],[f1120,f1035,f427,f14585]) ).
fof(f14585,plain,
( spl8_386
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_386])]) ).
fof(f1120,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X0) )
| ~ spl8_35
| ~ spl8_115 ),
inference(resolution,[],[f1036,f428]) ).
fof(f14583,plain,
( spl8_385
| ~ spl8_36
| ~ spl8_115 ),
inference(avatar_split_clause,[],[f1119,f1035,f431,f14581]) ).
fof(f14581,plain,
( spl8_385
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_385])]) ).
fof(f1119,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| ~ member(X2,universal_class)
| member(sum_class(X2),X1) )
| ~ spl8_36
| ~ spl8_115 ),
inference(resolution,[],[f1036,f432]) ).
fof(f14579,plain,
( spl8_384
| ~ spl8_16
| ~ spl8_114 ),
inference(avatar_split_clause,[],[f1101,f1031,f339,f14577]) ).
fof(f14577,plain,
( spl8_384
<=> ! [X0] :
( ~ member(sK2(sK2(X0)),X0)
| null_class = X0
| null_class = sK2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_384])]) ).
fof(f1101,plain,
( ! [X0] :
( ~ member(sK2(sK2(X0)),X0)
| null_class = X0
| null_class = sK2(X0) )
| ~ spl8_16
| ~ spl8_114 ),
inference(resolution,[],[f1032,f340]) ).
fof(f14575,plain,
( spl8_383
| ~ spl8_99
| ~ spl8_114 ),
inference(avatar_split_clause,[],[f1098,f1031,f896,f14573]) ).
fof(f14573,plain,
( spl8_383
<=> ! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,sK2(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_383])]) ).
fof(f1098,plain,
( ! [X2,X0,X1] :
( ~ member(unordered_pair(X0,X1),X2)
| null_class = X2
| ~ subclass(universal_class,sK2(X2)) )
| ~ spl8_99
| ~ spl8_114 ),
inference(resolution,[],[f1032,f897]) ).
fof(f14571,plain,
( spl8_382
| ~ spl8_100
| ~ spl8_108 ),
inference(avatar_split_clause,[],[f1089,f1005,f900,f14569]) ).
fof(f14569,plain,
( spl8_382
<=> ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(null_class,X0)
| ~ inductive(sK4(power_class(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_382])]) ).
fof(f1089,plain,
( ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(null_class,X0)
| ~ inductive(sK4(power_class(X0),X1)) )
| ~ spl8_100
| ~ spl8_108 ),
inference(resolution,[],[f1006,f901]) ).
fof(f14567,plain,
( spl8_381
| ~ spl8_95
| ~ spl8_105 ),
inference(avatar_split_clause,[],[f1072,f993,f872,f14565]) ).
fof(f14565,plain,
( spl8_381
<=> ! [X0] :
( subclass(complement(sum_class(universal_class)),X0)
| ~ member(sK4(complement(sum_class(universal_class)),X0),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_381])]) ).
fof(f1072,plain,
( ! [X0] :
( subclass(complement(sum_class(universal_class)),X0)
| ~ member(sK4(complement(sum_class(universal_class)),X0),sK7) )
| ~ spl8_95
| ~ spl8_105 ),
inference(resolution,[],[f994,f873]) ).
fof(f14563,plain,
( spl8_380
| ~ spl8_16
| ~ spl8_104 ),
inference(avatar_split_clause,[],[f989,f969,f339,f14561]) ).
fof(f14561,plain,
( spl8_380
<=> ! [X0,X1] :
( member(sK2(unordered_pair(X0,X1)),sum_class(universal_class))
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_380])]) ).
fof(f989,plain,
( ! [X0,X1] :
( member(sK2(unordered_pair(X0,X1)),sum_class(universal_class))
| unordered_pair(X0,X1) = null_class )
| ~ spl8_16
| ~ spl8_104 ),
inference(resolution,[],[f970,f340]) ).
fof(f14559,plain,
( spl8_379
| ~ spl8_50
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f908,f896,f544,f14557]) ).
fof(f14557,plain,
( spl8_379
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,X0)
| member(X1,sum_class(X0))
| ~ member(X1,unordered_pair(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_379])]) ).
fof(f908,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| member(X1,sum_class(X0))
| ~ member(X1,unordered_pair(X2,X3)) )
| ~ spl8_50
| ~ spl8_99 ),
inference(resolution,[],[f897,f545]) ).
fof(f14551,plain,
( ~ spl8_378
| ~ spl8_224
| ~ spl8_348 ),
inference(avatar_split_clause,[],[f13884,f13876,f3743,f14548]) ).
fof(f14548,plain,
( spl8_378
<=> subclass(universal_class,sK2(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_378])]) ).
fof(f13876,plain,
( spl8_348
<=> ! [X2,X3] : ~ subclass(universal_class,unordered_pair(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_348])]) ).
fof(f13884,plain,
( ~ subclass(universal_class,sK2(identity_relation))
| ~ spl8_224
| ~ spl8_348 ),
inference(superposition,[],[f13877,f3745]) ).
fof(f13877,plain,
( ! [X2,X3] : ~ subclass(universal_class,unordered_pair(X2,X3))
| ~ spl8_348 ),
inference(avatar_component_clause,[],[f13876]) ).
fof(f14250,plain,
( spl8_377
| ~ spl8_7
| ~ spl8_342 ),
inference(avatar_split_clause,[],[f13848,f13734,f299,f14247]) ).
fof(f299,plain,
( spl8_7
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f13734,plain,
( spl8_342
<=> ! [X0] :
( ~ subclass(sK4(universal_class,power_class(X0)),X0)
| subclass(universal_class,power_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_342])]) ).
fof(f13848,plain,
( subclass(universal_class,power_class(universal_class))
| ~ spl8_7
| ~ spl8_342 ),
inference(resolution,[],[f13735,f300]) ).
fof(f300,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f13735,plain,
( ! [X0] :
( ~ subclass(sK4(universal_class,power_class(X0)),X0)
| subclass(universal_class,power_class(X0)) )
| ~ spl8_342 ),
inference(avatar_component_clause,[],[f13734]) ).
fof(f14101,plain,
( spl8_376
| ~ spl8_6
| ~ spl8_341 ),
inference(avatar_split_clause,[],[f13818,f13730,f295,f14098]) ).
fof(f13730,plain,
( spl8_341
<=> ! [X0] :
( member(sK4(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_341])]) ).
fof(f13818,plain,
( subclass(universal_class,complement(null_class))
| ~ spl8_6
| ~ spl8_341 ),
inference(resolution,[],[f13731,f296]) ).
fof(f13731,plain,
( ! [X0] :
( member(sK4(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl8_341 ),
inference(avatar_component_clause,[],[f13730]) ).
fof(f14023,plain,
( spl8_375
| ~ spl8_13
| ~ spl8_241 ),
inference(avatar_split_clause,[],[f7795,f4563,f326,f14021]) ).
fof(f14021,plain,
( spl8_375
<=> ! [X0,X1] :
( member(sK2(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = identity_relation ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_375])]) ).
fof(f4563,plain,
( spl8_241
<=> ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| sK2(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK2(cross_product(X0,X1))),first(sK2(cross_product(X0,X1)))),unordered_pair(first(sK2(cross_product(X0,X1))),unordered_pair(second(sK2(cross_product(X0,X1))),second(sK2(cross_product(X0,X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_241])]) ).
fof(f7795,plain,
( ! [X0,X1] :
( member(sK2(cross_product(X0,X1)),universal_class)
| cross_product(X0,X1) = identity_relation )
| ~ spl8_13
| ~ spl8_241 ),
inference(superposition,[],[f327,f4564]) ).
fof(f4564,plain,
( ! [X0,X1] :
( sK2(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK2(cross_product(X0,X1))),first(sK2(cross_product(X0,X1)))),unordered_pair(first(sK2(cross_product(X0,X1))),unordered_pair(second(sK2(cross_product(X0,X1))),second(sK2(cross_product(X0,X1))))))
| cross_product(X0,X1) = identity_relation )
| ~ spl8_241 ),
inference(avatar_component_clause,[],[f4563]) ).
fof(f14019,plain,
( spl8_374
| ~ spl8_68
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f3962,f3743,f671,f14017]) ).
fof(f14017,plain,
( spl8_374
<=> ! [X0,X1] :
( ~ member(sK2(identity_relation),cross_product(X0,X1))
| member(sK3(sK2(identity_relation)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_374])]) ).
fof(f3962,plain,
( ! [X0,X1] :
( ~ member(sK2(identity_relation),cross_product(X0,X1))
| member(sK3(sK2(identity_relation)),X0) )
| ~ spl8_68
| ~ spl8_224 ),
inference(superposition,[],[f672,f3745]) ).
fof(f14015,plain,
( spl8_373
| ~ spl8_67
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f3961,f3743,f667,f14013]) ).
fof(f14013,plain,
( spl8_373
<=> ! [X0,X1] :
( ~ member(sK2(identity_relation),cross_product(X0,X1))
| member(sK3(sK2(identity_relation)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_373])]) ).
fof(f3961,plain,
( ! [X0,X1] :
( ~ member(sK2(identity_relation),cross_product(X0,X1))
| member(sK3(sK2(identity_relation)),X1) )
| ~ spl8_67
| ~ spl8_224 ),
inference(superposition,[],[f668,f3745]) ).
fof(f14011,plain,
( ~ spl8_329
| spl8_357
| ~ spl8_62
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f3978,f3743,f642,f13914,f13570]) ).
fof(f13570,plain,
( spl8_329
<=> member(sK3(sK2(identity_relation)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_329])]) ).
fof(f13914,plain,
( spl8_357
<=> member(sK2(identity_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_357])]) ).
fof(f642,plain,
( spl8_62
<=> ! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
fof(f3978,plain,
( member(sK2(identity_relation),identity_relation)
| ~ member(sK3(sK2(identity_relation)),universal_class)
| ~ spl8_62
| ~ spl8_224 ),
inference(superposition,[],[f643,f3745]) ).
fof(f643,plain,
( ! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) )
| ~ spl8_62 ),
inference(avatar_component_clause,[],[f642]) ).
fof(f13980,plain,
( spl8_329
| spl8_372
| ~ spl8_66
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f3960,f3743,f663,f13978,f13570]) ).
fof(f13978,plain,
( spl8_372
<=> ! [X0,X1] : ~ member(sK2(identity_relation),compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_372])]) ).
fof(f663,plain,
( spl8_66
<=> ! [X0,X3,X2,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
fof(f3960,plain,
( ! [X0,X1] :
( ~ member(sK2(identity_relation),compose(X0,X1))
| member(sK3(sK2(identity_relation)),universal_class) )
| ~ spl8_66
| ~ spl8_224 ),
inference(superposition,[],[f664,f3745]) ).
fof(f664,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| member(X2,universal_class) )
| ~ spl8_66 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f13976,plain,
( spl8_371
| ~ spl8_67
| ~ spl8_180 ),
inference(avatar_split_clause,[],[f2419,f2293,f667,f13974]) ).
fof(f13974,plain,
( spl8_371
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_371])]) ).
fof(f2419,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X2) )
| ~ spl8_67
| ~ spl8_180 ),
inference(resolution,[],[f2294,f668]) ).
fof(f13972,plain,
( spl8_370
| ~ spl8_68
| ~ spl8_180 ),
inference(avatar_split_clause,[],[f2418,f2293,f671,f13970]) ).
fof(f13970,plain,
( spl8_370
<=> ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_370])]) ).
fof(f2418,plain,
( ! [X2,X0,X1] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,cross_product(X1,X2))
| member(X0,X1) )
| ~ spl8_68
| ~ spl8_180 ),
inference(resolution,[],[f2294,f672]) ).
fof(f13968,plain,
( spl8_369
| ~ spl8_178 ),
inference(avatar_split_clause,[],[f2360,f2285,f13966]) ).
fof(f13966,plain,
( spl8_369
<=> ! [X0] :
( member(sK2(union(X0,X0)),X0)
| null_class = union(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_369])]) ).
fof(f2285,plain,
( spl8_178
<=> ! [X0,X1] :
( member(sK2(union(X0,X1)),X0)
| member(sK2(union(X0,X1)),X1)
| null_class = union(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_178])]) ).
fof(f2360,plain,
( ! [X0] :
( member(sK2(union(X0,X0)),X0)
| null_class = union(X0,X0) )
| ~ spl8_178 ),
inference(factoring,[],[f2286]) ).
fof(f2286,plain,
( ! [X0,X1] :
( member(sK2(union(X0,X1)),X1)
| member(sK2(union(X0,X1)),X0)
| null_class = union(X0,X1) )
| ~ spl8_178 ),
inference(avatar_component_clause,[],[f2285]) ).
fof(f13964,plain,
( spl8_368
| ~ spl8_33
| ~ spl8_332 ),
inference(avatar_split_clause,[],[f13748,f13672,f419,f13961]) ).
fof(f13961,plain,
( spl8_368
<=> subclass(sK7,sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_368])]) ).
fof(f13672,plain,
( spl8_332
<=> ! [X0] :
( ~ member(sK4(X0,sum_class(universal_class)),sK7)
| subclass(X0,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_332])]) ).
fof(f13748,plain,
( subclass(sK7,sum_class(universal_class))
| ~ spl8_33
| ~ spl8_332 ),
inference(duplicate_literal_removal,[],[f13737]) ).
fof(f13737,plain,
( subclass(sK7,sum_class(universal_class))
| subclass(sK7,sum_class(universal_class))
| ~ spl8_33
| ~ spl8_332 ),
inference(resolution,[],[f13673,f420]) ).
fof(f13673,plain,
( ! [X0] :
( ~ member(sK4(X0,sum_class(universal_class)),sK7)
| subclass(X0,sum_class(universal_class)) )
| ~ spl8_332 ),
inference(avatar_component_clause,[],[f13672]) ).
fof(f13959,plain,
( spl8_367
| ~ spl8_6
| ~ spl8_178 ),
inference(avatar_split_clause,[],[f2345,f2285,f295,f13957]) ).
fof(f13957,plain,
( spl8_367
<=> ! [X0] :
( member(sK2(union(null_class,X0)),X0)
| null_class = union(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_367])]) ).
fof(f2345,plain,
( ! [X0] :
( member(sK2(union(null_class,X0)),X0)
| null_class = union(null_class,X0) )
| ~ spl8_6
| ~ spl8_178 ),
inference(resolution,[],[f2286,f296]) ).
fof(f13955,plain,
( spl8_366
| ~ spl8_6
| ~ spl8_178 ),
inference(avatar_split_clause,[],[f2313,f2285,f295,f13953]) ).
fof(f2313,plain,
( ! [X0] :
( member(sK2(union(X0,null_class)),X0)
| null_class = union(X0,null_class) )
| ~ spl8_6
| ~ spl8_178 ),
inference(resolution,[],[f2286,f296]) ).
fof(f13951,plain,
( spl8_365
| ~ spl8_8
| ~ spl8_167 ),
inference(avatar_split_clause,[],[f2085,f2009,f303,f13949]) ).
fof(f13949,plain,
( spl8_365
<=> ! [X0,X1] :
( ~ member(X0,sK7)
| ~ subclass(sK7,X1)
| member(X0,sum_class(power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_365])]) ).
fof(f2085,plain,
( ! [X0,X1] :
( ~ member(X0,sK7)
| ~ subclass(sK7,X1)
| member(X0,sum_class(power_class(X1))) )
| ~ spl8_8
| ~ spl8_167 ),
inference(resolution,[],[f2010,f305]) ).
fof(f13947,plain,
( spl8_364
| ~ spl8_8
| ~ spl8_166 ),
inference(avatar_split_clause,[],[f2050,f2005,f303,f13945]) ).
fof(f13945,plain,
( spl8_364
<=> ! [X0,X1] :
( ~ member(X0,sK7)
| member(sK7,X1)
| member(X0,sum_class(complement(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_364])]) ).
fof(f2050,plain,
( ! [X0,X1] :
( ~ member(X0,sK7)
| member(sK7,X1)
| member(X0,sum_class(complement(X1))) )
| ~ spl8_8
| ~ spl8_166 ),
inference(resolution,[],[f2006,f305]) ).
fof(f13943,plain,
( spl8_363
| ~ spl8_12
| ~ spl8_155 ),
inference(avatar_split_clause,[],[f1812,f1548,f322,f13941]) ).
fof(f13941,plain,
( spl8_363
<=> ! [X0,X1] :
( member(null_class,sum_class(X0))
| subclass(X0,X1)
| ~ inductive(sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_363])]) ).
fof(f1812,plain,
( ! [X0,X1] :
( member(null_class,sum_class(X0))
| subclass(X0,X1)
| ~ inductive(sK4(X0,X1)) )
| ~ spl8_12
| ~ spl8_155 ),
inference(resolution,[],[f1549,f323]) ).
fof(f13938,plain,
( spl8_362
| ~ spl8_13
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1776,f1544,f326,f13936]) ).
fof(f13936,plain,
( spl8_362
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(universal_class,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_362])]) ).
fof(f1776,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(universal_class,X3))) )
| ~ spl8_13
| ~ spl8_154 ),
inference(resolution,[],[f1545,f327]) ).
fof(f13933,plain,
( spl8_361
| ~ spl8_13
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1728,f1540,f326,f13931]) ).
fof(f13931,plain,
( spl8_361
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_361])]) ).
fof(f1728,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,sum_class(union(X3,universal_class))) )
| ~ spl8_13
| ~ spl8_153 ),
inference(resolution,[],[f1541,f327]) ).
fof(f13929,plain,
( spl8_360
| ~ spl8_27
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f1221,f1056,f384,f13927]) ).
fof(f13927,plain,
( spl8_360
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,identity_relation)
| subclass(sK3(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_360])]) ).
fof(f1221,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,identity_relation)
| subclass(sK3(X1),X0) )
| ~ spl8_27
| ~ spl8_120 ),
inference(resolution,[],[f1057,f385]) ).
fof(f13925,plain,
( spl8_359
| ~ spl8_25
| ~ spl8_120 ),
inference(avatar_split_clause,[],[f1214,f1056,f376,f13923]) ).
fof(f13923,plain,
( spl8_359
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,identity_relation)
| ~ member(sK3(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_359])]) ).
fof(f1214,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,identity_relation)
| ~ member(sK3(X1),X0) )
| ~ spl8_25
| ~ spl8_120 ),
inference(resolution,[],[f1057,f377]) ).
fof(f13921,plain,
( spl8_358
| ~ spl8_27
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1198,f1052,f384,f13919]) ).
fof(f13919,plain,
( spl8_358
<=> ! [X0,X1] :
( ~ subclass(X0,power_class(X1))
| null_class = X0
| subclass(sK2(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_358])]) ).
fof(f1198,plain,
( ! [X0,X1] :
( ~ subclass(X0,power_class(X1))
| null_class = X0
| subclass(sK2(X0),X1) )
| ~ spl8_27
| ~ spl8_119 ),
inference(resolution,[],[f1053,f385]) ).
fof(f13917,plain,
( ~ spl8_357
| ~ spl8_22
| spl8_329 ),
inference(avatar_split_clause,[],[f13580,f13570,f364,f13914]) ).
fof(f364,plain,
( spl8_22
<=> ! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
fof(f13580,plain,
( ~ member(sK2(identity_relation),identity_relation)
| ~ spl8_22
| spl8_329 ),
inference(resolution,[],[f13571,f365]) ).
fof(f365,plain,
( ! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) )
| ~ spl8_22 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f13571,plain,
( ~ member(sK3(sK2(identity_relation)),universal_class)
| spl8_329 ),
inference(avatar_component_clause,[],[f13570]) ).
fof(f13912,plain,
( spl8_356
| ~ spl8_25
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1191,f1052,f376,f13910]) ).
fof(f13910,plain,
( spl8_356
<=> ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(sK2(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_356])]) ).
fof(f1191,plain,
( ! [X0,X1] :
( ~ subclass(X0,complement(X1))
| null_class = X0
| ~ member(sK2(X0),X1) )
| ~ spl8_25
| ~ spl8_119 ),
inference(resolution,[],[f1053,f377]) ).
fof(f13908,plain,
( spl8_355
| ~ spl8_27
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1174,f1043,f384,f13906]) ).
fof(f13906,plain,
( spl8_355
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| null_class = X1
| subclass(sK2(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_355])]) ).
fof(f1174,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| null_class = X1
| subclass(sK2(X1),X0) )
| ~ spl8_27
| ~ spl8_117 ),
inference(resolution,[],[f1044,f385]) ).
fof(f13904,plain,
( spl8_354
| ~ spl8_25
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1167,f1043,f376,f13902]) ).
fof(f13902,plain,
( spl8_354
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| null_class = X1
| ~ member(sK2(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_354])]) ).
fof(f1167,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| null_class = X1
| ~ member(sK2(X1),X0) )
| ~ spl8_25
| ~ spl8_117 ),
inference(resolution,[],[f1044,f377]) ).
fof(f13900,plain,
( spl8_353
| ~ spl8_27
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1151,f1039,f384,f13898]) ).
fof(f13898,plain,
( spl8_353
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(power_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_353])]) ).
fof(f1151,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(power_class(X1),X0) )
| ~ spl8_27
| ~ spl8_116 ),
inference(resolution,[],[f1040,f385]) ).
fof(f13896,plain,
( spl8_352
| ~ spl8_25
| ~ spl8_116 ),
inference(avatar_split_clause,[],[f1144,f1039,f376,f13894]) ).
fof(f13894,plain,
( spl8_352
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_352])]) ).
fof(f1144,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(power_class(X1),X0) )
| ~ spl8_25
| ~ spl8_116 ),
inference(resolution,[],[f1040,f377]) ).
fof(f13892,plain,
( spl8_351
| ~ spl8_27
| ~ spl8_115 ),
inference(avatar_split_clause,[],[f1128,f1035,f384,f13890]) ).
fof(f13890,plain,
( spl8_351
<=> ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(sum_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_351])]) ).
fof(f1128,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(X1,universal_class)
| subclass(sum_class(X1),X0) )
| ~ spl8_27
| ~ spl8_115 ),
inference(resolution,[],[f1036,f385]) ).
fof(f13888,plain,
( spl8_350
| ~ spl8_25
| ~ spl8_115 ),
inference(avatar_split_clause,[],[f1121,f1035,f376,f13886]) ).
fof(f13886,plain,
( spl8_350
<=> ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_350])]) ).
fof(f1121,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(X1,universal_class)
| ~ member(sum_class(X1),X0) )
| ~ spl8_25
| ~ spl8_115 ),
inference(resolution,[],[f1036,f377]) ).
fof(f13881,plain,
( spl8_348
| spl8_349
| ~ spl8_99
| ~ spl8_104 ),
inference(avatar_split_clause,[],[f986,f969,f896,f13879,f13876]) ).
fof(f986,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(X0,X1),sum_class(universal_class))
| ~ subclass(universal_class,unordered_pair(X2,X3)) )
| ~ spl8_99
| ~ spl8_104 ),
inference(resolution,[],[f970,f897]) ).
fof(f13874,plain,
( spl8_347
| ~ spl8_100
| ~ spl8_103 ),
inference(avatar_split_clause,[],[f981,f965,f900,f13872]) ).
fof(f13872,plain,
( spl8_347
<=> ! [X0] :
( null_class = power_class(X0)
| member(null_class,X0)
| ~ inductive(sK2(power_class(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_347])]) ).
fof(f981,plain,
( ! [X0] :
( null_class = power_class(X0)
| member(null_class,X0)
| ~ inductive(sK2(power_class(X0))) )
| ~ spl8_100
| ~ spl8_103 ),
inference(resolution,[],[f966,f901]) ).
fof(f13868,plain,
( ~ spl8_345
| spl8_346
| ~ spl8_95
| ~ spl8_101 ),
inference(avatar_split_clause,[],[f978,f956,f872,f13865,f13861]) ).
fof(f13861,plain,
( spl8_345
<=> member(sK2(complement(sum_class(universal_class))),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_345])]) ).
fof(f13865,plain,
( spl8_346
<=> null_class = complement(sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_346])]) ).
fof(f978,plain,
( null_class = complement(sum_class(universal_class))
| ~ member(sK2(complement(sum_class(universal_class))),sK7)
| ~ spl8_95
| ~ spl8_101 ),
inference(resolution,[],[f957,f873]) ).
fof(f13859,plain,
( spl8_344
| ~ spl8_45
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f909,f896,f488,f13857]) ).
fof(f13857,plain,
( spl8_344
<=> ! [X0,X3,X2,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X3)
| ~ subclass(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_344])]) ).
fof(f909,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| member(unordered_pair(X1,X2),X3)
| ~ subclass(X0,X3) )
| ~ spl8_45
| ~ spl8_99 ),
inference(resolution,[],[f897,f489]) ).
fof(f13855,plain,
( spl8_343
| ~ spl8_50
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f876,f872,f544,f13853]) ).
fof(f13853,plain,
( spl8_343
<=> ! [X0,X1] :
( ~ member(X0,sK7)
| member(X1,sum_class(sum_class(universal_class)))
| ~ member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_343])]) ).
fof(f876,plain,
( ! [X0,X1] :
( ~ member(X0,sK7)
| member(X1,sum_class(sum_class(universal_class)))
| ~ member(X1,X0) )
| ~ spl8_50
| ~ spl8_95 ),
inference(resolution,[],[f873,f545]) ).
fof(f13736,plain,
( spl8_342
| ~ spl8_33
| ~ spl8_176 ),
inference(avatar_split_clause,[],[f2280,f2243,f419,f13734]) ).
fof(f2280,plain,
( ! [X0] :
( ~ subclass(sK4(universal_class,power_class(X0)),X0)
| subclass(universal_class,power_class(X0)) )
| ~ spl8_33
| ~ spl8_176 ),
inference(duplicate_literal_removal,[],[f2271]) ).
fof(f2271,plain,
( ! [X0] :
( ~ subclass(sK4(universal_class,power_class(X0)),X0)
| subclass(universal_class,power_class(X0))
| subclass(universal_class,power_class(X0)) )
| ~ spl8_33
| ~ spl8_176 ),
inference(resolution,[],[f2244,f420]) ).
fof(f13732,plain,
( spl8_341
| ~ spl8_33
| ~ spl8_175 ),
inference(avatar_split_clause,[],[f2264,f2239,f419,f13730]) ).
fof(f2264,plain,
( ! [X0] :
( member(sK4(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) )
| ~ spl8_33
| ~ spl8_175 ),
inference(duplicate_literal_removal,[],[f2254]) ).
fof(f2254,plain,
( ! [X0] :
( member(sK4(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0))
| subclass(universal_class,complement(X0)) )
| ~ spl8_33
| ~ spl8_175 ),
inference(resolution,[],[f2240,f420]) ).
fof(f13728,plain,
( spl8_340
| ~ spl8_12
| ~ spl8_139 ),
inference(avatar_split_clause,[],[f1456,f1294,f322,f13726]) ).
fof(f13726,plain,
( spl8_340
<=> ! [X0] :
( member(null_class,sum_class(X0))
| null_class = X0
| ~ inductive(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_340])]) ).
fof(f1456,plain,
( ! [X0] :
( member(null_class,sum_class(X0))
| null_class = X0
| ~ inductive(sK2(X0)) )
| ~ spl8_12
| ~ spl8_139 ),
inference(resolution,[],[f1295,f323]) ).
fof(f13712,plain,
( spl8_339
| spl8_307
| ~ spl8_12
| ~ spl8_136 ),
inference(avatar_split_clause,[],[f1412,f1279,f322,f13354,f13710]) ).
fof(f13710,plain,
( spl8_339
<=> ! [X0] :
( ~ member(X0,universal_class)
| ~ inductive(sum_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_339])]) ).
fof(f1412,plain,
( ! [X0] :
( member(null_class,sum_class(universal_class))
| ~ member(X0,universal_class)
| ~ inductive(sum_class(X0)) )
| ~ spl8_12
| ~ spl8_136 ),
inference(resolution,[],[f1280,f323]) ).
fof(f13699,plain,
( spl8_338
| spl8_337
| ~ spl8_32
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f950,f900,f415,f13691,f13697]) ).
fof(f13697,plain,
( spl8_338
<=> ! [X0] : ~ inductive(flip(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_338])]) ).
fof(f13691,plain,
( spl8_337
<=> member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_337])]) ).
fof(f415,plain,
( spl8_32
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
fof(f950,plain,
( ! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X0)) )
| ~ spl8_32
| ~ spl8_100 ),
inference(resolution,[],[f901,f416]) ).
fof(f416,plain,
( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f415]) ).
fof(f13694,plain,
( spl8_336
| spl8_337
| ~ spl8_31
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f949,f900,f411,f13691,f13688]) ).
fof(f13688,plain,
( spl8_336
<=> ! [X0] : ~ inductive(rotate(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_336])]) ).
fof(f411,plain,
( spl8_31
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
fof(f949,plain,
( ! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X0)) )
| ~ spl8_31
| ~ spl8_100 ),
inference(resolution,[],[f901,f412]) ).
fof(f412,plain,
( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f411]) ).
fof(f13686,plain,
( spl8_335
| ~ spl8_35
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f922,f896,f427,f13684]) ).
fof(f13684,plain,
( spl8_335
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_335])]) ).
fof(f922,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) )
| ~ spl8_35
| ~ spl8_99 ),
inference(resolution,[],[f897,f428]) ).
fof(f13682,plain,
( spl8_334
| ~ spl8_36
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f921,f896,f431,f13680]) ).
fof(f13680,plain,
( spl8_334
<=> ! [X2,X0,X1,X3] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_334])]) ).
fof(f921,plain,
( ! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) )
| ~ spl8_36
| ~ spl8_99 ),
inference(resolution,[],[f897,f432]) ).
fof(f13678,plain,
( spl8_333
| ~ spl8_45
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f877,f872,f488,f13676]) ).
fof(f13676,plain,
( spl8_333
<=> ! [X0,X1] :
( ~ member(X0,sK7)
| member(X0,X1)
| ~ subclass(sum_class(universal_class),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_333])]) ).
fof(f877,plain,
( ! [X0,X1] :
( ~ member(X0,sK7)
| member(X0,X1)
| ~ subclass(sum_class(universal_class),X1) )
| ~ spl8_45
| ~ spl8_95 ),
inference(resolution,[],[f873,f489]) ).
fof(f13674,plain,
( spl8_332
| ~ spl8_34
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f875,f872,f423,f13672]) ).
fof(f875,plain,
( ! [X0] :
( ~ member(sK4(X0,sum_class(universal_class)),sK7)
| subclass(X0,sum_class(universal_class)) )
| ~ spl8_34
| ~ spl8_95 ),
inference(resolution,[],[f873,f424]) ).
fof(f13586,plain,
( spl8_329
| ~ spl8_331
| ~ spl8_60
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f4244,f3743,f634,f13583,f13570]) ).
fof(f13583,plain,
( spl8_331
<=> member(sK2(identity_relation),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_331])]) ).
fof(f634,plain,
( spl8_60
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
fof(f4244,plain,
( ~ member(sK2(identity_relation),successor_relation)
| member(sK3(sK2(identity_relation)),universal_class)
| ~ spl8_60
| ~ spl8_224 ),
inference(superposition,[],[f635,f3745]) ).
fof(f635,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| member(X1,universal_class) )
| ~ spl8_60 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f13577,plain,
( spl8_329
| ~ spl8_330
| ~ spl8_59
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f3957,f3743,f630,f13574,f13570]) ).
fof(f13574,plain,
( spl8_330
<=> member(sK2(identity_relation),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_330])]) ).
fof(f630,plain,
( spl8_59
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
fof(f3957,plain,
( ~ member(sK2(identity_relation),element_relation)
| member(sK3(sK2(identity_relation)),universal_class)
| ~ spl8_59
| ~ spl8_224 ),
inference(superposition,[],[f631,f3745]) ).
fof(f631,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X1,universal_class) )
| ~ spl8_59 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f13568,plain,
( ~ spl8_327
| spl8_328
| ~ spl8_6
| ~ spl8_194 ),
inference(avatar_split_clause,[],[f2990,f2725,f295,f13566,f13562]) ).
fof(f13562,plain,
( spl8_327
<=> subclass(element_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_327])]) ).
fof(f13566,plain,
( spl8_328
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_328])]) ).
fof(f2990,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| ~ member(X1,X0)
| ~ subclass(element_relation,null_class) )
| ~ spl8_6
| ~ spl8_194 ),
inference(resolution,[],[f2726,f296]) ).
fof(f13559,plain,
( ~ spl8_325
| spl8_326
| ~ spl8_58
| ~ spl8_180 ),
inference(avatar_split_clause,[],[f2424,f2293,f620,f13557,f13553]) ).
fof(f13553,plain,
( spl8_325
<=> subclass(identity_relation,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_325])]) ).
fof(f13557,plain,
( spl8_326
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_326])]) ).
fof(f620,plain,
( spl8_58
<=> ! [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,[spl8_58])]) ).
fof(f2424,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,element_relation)
| member(X0,X0) )
| ~ spl8_58
| ~ spl8_180 ),
inference(resolution,[],[f2294,f621]) ).
fof(f621,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X0,X1) )
| ~ spl8_58 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f13550,plain,
( spl8_324
| ~ spl8_8
| ~ spl8_154 ),
inference(avatar_split_clause,[],[f1810,f1544,f303,f13548]) ).
fof(f13548,plain,
( spl8_324
<=> ! [X0,X1] :
( ~ member(X0,sK7)
| member(X0,sum_class(union(universal_class,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_324])]) ).
fof(f1810,plain,
( ! [X0,X1] :
( ~ member(X0,sK7)
| member(X0,sum_class(union(universal_class,X1))) )
| ~ spl8_8
| ~ spl8_154 ),
inference(resolution,[],[f1545,f305]) ).
fof(f13545,plain,
( spl8_323
| ~ spl8_8
| ~ spl8_153 ),
inference(avatar_split_clause,[],[f1762,f1540,f303,f13543]) ).
fof(f13543,plain,
( spl8_323
<=> ! [X0,X1] :
( ~ member(X0,sK7)
| member(X0,sum_class(union(X1,universal_class))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_323])]) ).
fof(f1762,plain,
( ! [X0,X1] :
( ~ member(X0,sK7)
| member(X0,sum_class(union(X1,universal_class))) )
| ~ spl8_8
| ~ spl8_153 ),
inference(resolution,[],[f1541,f305]) ).
fof(f13541,plain,
( ~ spl8_322
| ~ spl8_4
| ~ spl8_317 ),
inference(avatar_split_clause,[],[f13507,f13490,f285,f13538]) ).
fof(f13538,plain,
( spl8_322
<=> inductive(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_322])]) ).
fof(f285,plain,
( spl8_4
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f13490,plain,
( spl8_317
<=> ! [X0] :
( ~ inductive(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_317])]) ).
fof(f13507,plain,
( ~ inductive(sK6)
| ~ spl8_4
| ~ spl8_317 ),
inference(resolution,[],[f13491,f287]) ).
fof(f287,plain,
( function(sK6)
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f13491,plain,
( ! [X0] :
( ~ function(X0)
| ~ inductive(X0) )
| ~ spl8_317 ),
inference(avatar_component_clause,[],[f13490]) ).
fof(f13536,plain,
( spl8_321
| ~ spl8_131
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1695,f1516,f1259,f13534]) ).
fof(f13534,plain,
( spl8_321
<=> ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ subclass(complement(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_321])]) ).
fof(f1695,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ subclass(complement(X1),X1) )
| ~ spl8_131
| ~ spl8_150 ),
inference(duplicate_literal_removal,[],[f1672]) ).
fof(f1672,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ subclass(complement(X1),X1)
| ~ member(X0,sum_class(complement(X1))) )
| ~ spl8_131
| ~ spl8_150 ),
inference(resolution,[],[f1517,f1260]) ).
fof(f13532,plain,
( spl8_320
| ~ spl8_12
| ~ spl8_114 ),
inference(avatar_split_clause,[],[f1099,f1031,f322,f13530]) ).
fof(f13530,plain,
( spl8_320
<=> ! [X0] :
( ~ member(null_class,X0)
| null_class = X0
| ~ inductive(sK2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_320])]) ).
fof(f1099,plain,
( ! [X0] :
( ~ member(null_class,X0)
| null_class = X0
| ~ inductive(sK2(X0)) )
| ~ spl8_12
| ~ spl8_114 ),
inference(resolution,[],[f1032,f323]) ).
fof(f13511,plain,
( spl8_319
| spl8_213
| ~ spl8_23
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f952,f900,f368,f3488,f13509]) ).
fof(f13509,plain,
( spl8_319
<=> ! [X0,X1] : ~ inductive(compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_319])]) ).
fof(f3488,plain,
( spl8_213
<=> member(null_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_213])]) ).
fof(f368,plain,
( spl8_23
<=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
fof(f952,plain,
( ! [X0,X1] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(compose(X0,X1)) )
| ~ spl8_23
| ~ spl8_100 ),
inference(resolution,[],[f901,f369]) ).
fof(f369,plain,
( ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class))
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f13505,plain,
( spl8_318
| ~ spl8_45
| ~ spl8_213 ),
inference(avatar_split_clause,[],[f13494,f3488,f488,f13503]) ).
fof(f13503,plain,
( spl8_318
<=> ! [X0] :
( member(null_class,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_318])]) ).
fof(f13494,plain,
( ! [X0] :
( member(null_class,X0)
| ~ subclass(cross_product(universal_class,universal_class),X0) )
| ~ spl8_45
| ~ spl8_213 ),
inference(resolution,[],[f3489,f489]) ).
fof(f3489,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ spl8_213 ),
inference(avatar_component_clause,[],[f3488]) ).
fof(f13492,plain,
( spl8_317
| spl8_213
| ~ spl8_20
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f945,f900,f355,f3488,f13490]) ).
fof(f945,plain,
( ! [X0] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(X0)
| ~ function(X0) )
| ~ spl8_20
| ~ spl8_100 ),
inference(resolution,[],[f901,f356]) ).
fof(f13488,plain,
( ~ spl8_316
| ~ spl8_12
| spl8_307 ),
inference(avatar_split_clause,[],[f13361,f13354,f322,f13485]) ).
fof(f13485,plain,
( spl8_316
<=> inductive(sum_class(universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_316])]) ).
fof(f13361,plain,
( ~ inductive(sum_class(universal_class))
| ~ spl8_12
| spl8_307 ),
inference(resolution,[],[f13355,f323]) ).
fof(f13355,plain,
( ~ member(null_class,sum_class(universal_class))
| spl8_307 ),
inference(avatar_component_clause,[],[f13354]) ).
fof(f13483,plain,
( spl8_315
| ~ spl8_27
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f937,f896,f384,f13481]) ).
fof(f13481,plain,
( spl8_315
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| subclass(unordered_pair(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_315])]) ).
fof(f937,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,power_class(X0))
| subclass(unordered_pair(X1,X2),X0) )
| ~ spl8_27
| ~ spl8_99 ),
inference(resolution,[],[f897,f385]) ).
fof(f13479,plain,
( spl8_314
| ~ spl8_25
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f923,f896,f376,f13477]) ).
fof(f923,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) )
| ~ spl8_25
| ~ spl8_99 ),
inference(resolution,[],[f897,f377]) ).
fof(f13388,plain,
( spl8_313
| ~ spl8_134
| ~ spl8_149 ),
inference(avatar_split_clause,[],[f1671,f1512,f1271,f13386]) ).
fof(f13386,plain,
( spl8_313
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum_class(power_class(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_313])]) ).
fof(f1671,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl8_134
| ~ spl8_149 ),
inference(duplicate_literal_removal,[],[f1667]) ).
fof(f1667,plain,
( ! [X0,X1] :
( member(X0,X1)
| ~ member(X0,sum_class(power_class(X1)))
| ~ member(X0,sum_class(power_class(X1))) )
| ~ spl8_134
| ~ spl8_149 ),
inference(resolution,[],[f1513,f1272]) ).
fof(f13384,plain,
( ~ spl8_312
| ~ spl8_224
| ~ spl8_306 ),
inference(avatar_split_clause,[],[f13360,f13351,f3743,f13381]) ).
fof(f13381,plain,
( spl8_312
<=> inductive(sK2(identity_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_312])]) ).
fof(f13351,plain,
( spl8_306
<=> ! [X0,X1] : ~ inductive(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_306])]) ).
fof(f13360,plain,
( ~ inductive(sK2(identity_relation))
| ~ spl8_224
| ~ spl8_306 ),
inference(superposition,[],[f13352,f3745]) ).
fof(f13352,plain,
( ! [X0,X1] : ~ inductive(unordered_pair(X0,X1))
| ~ spl8_306 ),
inference(avatar_component_clause,[],[f13351]) ).
fof(f13379,plain,
( spl8_311
| ~ spl8_130
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1644,f1500,f1255,f13377]) ).
fof(f13377,plain,
( spl8_311
<=> ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_311])]) ).
fof(f1644,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X2) )
| ~ spl8_130
| ~ spl8_146 ),
inference(duplicate_literal_removal,[],[f1632]) ).
fof(f1632,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X2)
| subclass(X0,union(X1,X2)) )
| ~ spl8_130
| ~ spl8_146 ),
inference(resolution,[],[f1501,f1256]) ).
fof(f13375,plain,
( spl8_310
| ~ spl8_130
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1623,f1496,f1255,f13373]) ).
fof(f13373,plain,
( spl8_310
<=> ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_310])]) ).
fof(f1623,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X1) )
| ~ spl8_130
| ~ spl8_145 ),
inference(duplicate_literal_removal,[],[f1611]) ).
fof(f1611,plain,
( ! [X2,X0,X1] :
( subclass(X0,union(X1,X2))
| ~ subclass(X0,X1)
| subclass(X0,union(X1,X2)) )
| ~ spl8_130
| ~ spl8_145 ),
inference(resolution,[],[f1497,f1256]) ).
fof(f13371,plain,
( spl8_309
| ~ spl8_105
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1381,f1255,f993,f13369]) ).
fof(f13369,plain,
( spl8_309
<=> ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_309])]) ).
fof(f1381,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) )
| ~ spl8_105
| ~ spl8_130 ),
inference(duplicate_literal_removal,[],[f1361]) ).
fof(f1361,plain,
( ! [X0,X1] :
( ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1)
| subclass(complement(X0),X1) )
| ~ spl8_105
| ~ spl8_130 ),
inference(resolution,[],[f1256,f994]) ).
fof(f13367,plain,
( spl8_308
| ~ spl8_101
| ~ spl8_119 ),
inference(avatar_split_clause,[],[f1202,f1052,f956,f13365]) ).
fof(f13365,plain,
( spl8_308
<=> ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_308])]) ).
fof(f1202,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class )
| ~ spl8_101
| ~ spl8_119 ),
inference(duplicate_literal_removal,[],[f1180]) ).
fof(f1180,plain,
( ! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class )
| ~ spl8_101
| ~ spl8_119 ),
inference(resolution,[],[f1053,f957]) ).
fof(f13357,plain,
( spl8_306
| spl8_307
| ~ spl8_12
| ~ spl8_104 ),
inference(avatar_split_clause,[],[f987,f969,f322,f13354,f13351]) ).
fof(f987,plain,
( ! [X0,X1] :
( member(null_class,sum_class(universal_class))
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl8_12
| ~ spl8_104 ),
inference(resolution,[],[f970,f323]) ).
fof(f13261,plain,
( spl8_305
| ~ spl8_12
| ~ spl8_298 ),
inference(avatar_split_clause,[],[f11031,f7724,f322,f13259]) ).
fof(f13259,plain,
( spl8_305
<=> ! [X0] :
( ~ subclass(X0,null_class)
| ~ inductive(sum_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_305])]) ).
fof(f7724,plain,
( spl8_298
<=> ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_298])]) ).
fof(f11031,plain,
( ! [X0] :
( ~ subclass(X0,null_class)
| ~ inductive(sum_class(X0)) )
| ~ spl8_12
| ~ spl8_298 ),
inference(resolution,[],[f7725,f323]) ).
fof(f7725,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,null_class) )
| ~ spl8_298 ),
inference(avatar_component_clause,[],[f7724]) ).
fof(f11121,plain,
( spl8_250
| ~ spl8_272 ),
inference(avatar_contradiction_clause,[],[f11093]) ).
fof(f11093,plain,
( $false
| spl8_250
| ~ spl8_272 ),
inference(resolution,[],[f7474,f6786]) ).
fof(f7474,plain,
( ! [X0] : member(X0,universal_class)
| ~ spl8_272 ),
inference(avatar_component_clause,[],[f7473]) ).
fof(f7473,plain,
( spl8_272
<=> ! [X0] : member(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_272])]) ).
fof(f11120,plain,
( spl8_233
| ~ spl8_272 ),
inference(avatar_contradiction_clause,[],[f11095]) ).
fof(f11095,plain,
( $false
| spl8_233
| ~ spl8_272 ),
inference(resolution,[],[f7474,f4212]) ).
fof(f11119,plain,
( spl8_1
| ~ spl8_272 ),
inference(avatar_contradiction_clause,[],[f11096]) ).
fof(f11096,plain,
( $false
| spl8_1
| ~ spl8_272 ),
inference(resolution,[],[f7474,f272]) ).
fof(f11118,plain,
( spl8_2
| ~ spl8_272 ),
inference(avatar_contradiction_clause,[],[f11097]) ).
fof(f11097,plain,
( $false
| spl8_2
| ~ spl8_272 ),
inference(resolution,[],[f7474,f277]) ).
fof(f11073,plain,
( spl8_272
| spl8_304
| ~ spl8_66
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f940,f896,f663,f11071,f7473]) ).
fof(f11071,plain,
( spl8_304
<=> ! [X0,X1] : ~ subclass(universal_class,compose(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_304])]) ).
fof(f940,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,compose(X0,X1))
| member(X2,universal_class) )
| ~ spl8_66
| ~ spl8_99 ),
inference(resolution,[],[f897,f664]) ).
fof(f11069,plain,
( spl8_303
| ~ spl8_67
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f915,f896,f667,f11067]) ).
fof(f11067,plain,
( spl8_303
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_303])]) ).
fof(f915,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X1) )
| ~ spl8_67
| ~ spl8_99 ),
inference(resolution,[],[f897,f668]) ).
fof(f11065,plain,
( spl8_302
| ~ spl8_68
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f914,f896,f671,f11063]) ).
fof(f11063,plain,
( spl8_302
<=> ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_302])]) ).
fof(f914,plain,
( ! [X2,X0,X1] :
( ~ subclass(universal_class,cross_product(X0,X1))
| member(X2,X0) )
| ~ spl8_68
| ~ spl8_99 ),
inference(resolution,[],[f897,f672]) ).
fof(f10979,plain,
( spl8_301
| ~ spl8_233
| spl8_223
| ~ spl8_76
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f4776,f765,f744,f3739,f4211,f10976]) ).
fof(f10976,plain,
( spl8_301
<=> sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))) = unordered_pair(unordered_pair(sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),unordered_pair(sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),unordered_pair(sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_301])]) ).
fof(f3739,plain,
( spl8_223
<=> null_class = identity_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl8_223])]) ).
fof(f744,plain,
( spl8_76
<=> ! [X0] :
( unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),unordered_pair(sK3(X0),sK3(X0)))) = X0
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).
fof(f765,plain,
( spl8_79
<=> ! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).
fof(f4776,plain,
( null_class = identity_relation
| ~ member(identity_relation,universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))) = unordered_pair(unordered_pair(sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class))))))),unordered_pair(sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),unordered_pair(sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))),sK3(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(identity_relation,identity_relation),universal_class)),universal_class)))))))))
| ~ spl8_76
| ~ spl8_79 ),
inference(resolution,[],[f766,f745]) ).
fof(f745,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),unordered_pair(sK3(X0),sK3(X0)))) = X0 )
| ~ spl8_76 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f766,plain,
( ! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) )
| ~ spl8_79 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f7916,plain,
( ~ spl8_13
| ~ spl8_283 ),
inference(avatar_contradiction_clause,[],[f7885]) ).
fof(f7885,plain,
( $false
| ~ spl8_13
| ~ spl8_283 ),
inference(resolution,[],[f7566,f327]) ).
fof(f7566,plain,
( ! [X0] : ~ member(X0,universal_class)
| ~ spl8_283 ),
inference(avatar_component_clause,[],[f7565]) ).
fof(f7565,plain,
( spl8_283
<=> ! [X0] : ~ member(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_283])]) ).
fof(f7915,plain,
( ~ spl8_30
| ~ spl8_283 ),
inference(avatar_contradiction_clause,[],[f7887]) ).
fof(f7887,plain,
( $false
| ~ spl8_30
| ~ spl8_283 ),
inference(resolution,[],[f7566,f408]) ).
fof(f7914,plain,
( ~ spl8_233
| ~ spl8_283 ),
inference(avatar_contradiction_clause,[],[f7889]) ).
fof(f7889,plain,
( $false
| ~ spl8_233
| ~ spl8_283 ),
inference(resolution,[],[f7566,f4213]) ).
fof(f4213,plain,
( member(identity_relation,universal_class)
| ~ spl8_233 ),
inference(avatar_component_clause,[],[f4211]) ).
fof(f7913,plain,
( ~ spl8_228
| ~ spl8_283 ),
inference(avatar_contradiction_clause,[],[f7898]) ).
fof(f7898,plain,
( $false
| ~ spl8_228
| ~ spl8_283 ),
inference(resolution,[],[f7566,f4007]) ).
fof(f4007,plain,
( member(sK2(identity_relation),universal_class)
| ~ spl8_228 ),
inference(avatar_component_clause,[],[f4005]) ).
fof(f4005,plain,
( spl8_228
<=> member(sK2(identity_relation),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_228])]) ).
fof(f7912,plain,
( ~ spl8_8
| ~ spl8_283 ),
inference(avatar_contradiction_clause,[],[f7911]) ).
fof(f7911,plain,
( $false
| ~ spl8_8
| ~ spl8_283 ),
inference(resolution,[],[f7566,f305]) ).
fof(f7884,plain,
( spl8_283
| ~ spl8_62
| ~ spl8_225 ),
inference(avatar_split_clause,[],[f4517,f3763,f642,f7565]) ).
fof(f3763,plain,
( spl8_225
<=> ! [X0] : ~ member(X0,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_225])]) ).
fof(f4517,plain,
( ! [X0] : ~ member(X0,universal_class)
| ~ spl8_62
| ~ spl8_225 ),
inference(resolution,[],[f3764,f643]) ).
fof(f3764,plain,
( ! [X0] : ~ member(X0,identity_relation)
| ~ spl8_225 ),
inference(avatar_component_clause,[],[f3763]) ).
fof(f7818,plain,
( spl8_300
| ~ spl8_12
| ~ spl8_223 ),
inference(avatar_split_clause,[],[f3748,f3739,f322,f7816]) ).
fof(f7816,plain,
( spl8_300
<=> ! [X0] :
( member(identity_relation,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_300])]) ).
fof(f3748,plain,
( ! [X0] :
( member(identity_relation,X0)
| ~ inductive(X0) )
| ~ spl8_12
| ~ spl8_223 ),
inference(superposition,[],[f323,f3741]) ).
fof(f3741,plain,
( null_class = identity_relation
| ~ spl8_223 ),
inference(avatar_component_clause,[],[f3739]) ).
fof(f7730,plain,
( spl8_299
| ~ spl8_99
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f3983,f3743,f896,f7728]) ).
fof(f7728,plain,
( spl8_299
<=> ! [X0] :
( member(sK2(identity_relation),X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_299])]) ).
fof(f3983,plain,
( ! [X0] :
( member(sK2(identity_relation),X0)
| ~ subclass(universal_class,X0) )
| ~ spl8_99
| ~ spl8_224 ),
inference(superposition,[],[f897,f3745]) ).
fof(f7726,plain,
( spl8_298
| ~ spl8_6
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1683,f1516,f295,f7724]) ).
fof(f1683,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(X1))
| ~ subclass(X1,null_class) )
| ~ spl8_6
| ~ spl8_150 ),
inference(resolution,[],[f1517,f296]) ).
fof(f7721,plain,
( spl8_297
| ~ spl8_145
| ~ spl8_147 ),
inference(avatar_split_clause,[],[f1657,f1504,f1496,f7719]) ).
fof(f7719,plain,
( spl8_297
<=> ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(universal_class,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_297])]) ).
fof(f1657,plain,
( ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(universal_class,X2))
| ~ spl8_145
| ~ spl8_147 ),
inference(duplicate_literal_removal,[],[f1652]) ).
fof(f1652,plain,
( ! [X2,X0,X1] :
( subclass(unordered_pair(X0,X1),union(universal_class,X2))
| subclass(unordered_pair(X0,X1),union(universal_class,X2)) )
| ~ spl8_145
| ~ spl8_147 ),
inference(resolution,[],[f1505,f1497]) ).
fof(f7716,plain,
( spl8_296
| ~ spl8_146
| ~ spl8_147 ),
inference(avatar_split_clause,[],[f1656,f1504,f1500,f7714]) ).
fof(f7714,plain,
( spl8_296
<=> ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(X2,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_296])]) ).
fof(f1656,plain,
( ! [X2,X0,X1] : subclass(unordered_pair(X0,X1),union(X2,universal_class))
| ~ spl8_146
| ~ spl8_147 ),
inference(duplicate_literal_removal,[],[f1655]) ).
fof(f1655,plain,
( ! [X2,X0,X1] :
( subclass(unordered_pair(X0,X1),union(X2,universal_class))
| subclass(unordered_pair(X0,X1),union(X2,universal_class)) )
| ~ spl8_146
| ~ spl8_147 ),
inference(resolution,[],[f1505,f1501]) ).
fof(f7712,plain,
( spl8_295
| ~ spl8_143
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1643,f1500,f1488,f7710]) ).
fof(f7710,plain,
( spl8_295
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_295])]) ).
fof(f1643,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X0))
| ~ spl8_143
| ~ spl8_146 ),
inference(duplicate_literal_removal,[],[f1633]) ).
fof(f1633,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X2,X0))
| subclass(intersection(X0,X1),union(X2,X0)) )
| ~ spl8_143
| ~ spl8_146 ),
inference(resolution,[],[f1501,f1489]) ).
fof(f7708,plain,
( spl8_294
| ~ spl8_144
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1642,f1500,f1492,f7706]) ).
fof(f7706,plain,
( spl8_294
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_294])]) ).
fof(f1642,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X2,X1))
| ~ spl8_144
| ~ spl8_146 ),
inference(duplicate_literal_removal,[],[f1634]) ).
fof(f1634,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X2,X1))
| subclass(intersection(X0,X1),union(X2,X1)) )
| ~ spl8_144
| ~ spl8_146 ),
inference(resolution,[],[f1501,f1493]) ).
fof(f7704,plain,
( spl8_293
| ~ spl8_143
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1622,f1496,f1488,f7702]) ).
fof(f7702,plain,
( spl8_293
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_293])]) ).
fof(f1622,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X0,X2))
| ~ spl8_143
| ~ spl8_145 ),
inference(duplicate_literal_removal,[],[f1612]) ).
fof(f1612,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X0,X2))
| subclass(intersection(X0,X1),union(X0,X2)) )
| ~ spl8_143
| ~ spl8_145 ),
inference(resolution,[],[f1497,f1489]) ).
fof(f7700,plain,
( spl8_292
| ~ spl8_144
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1621,f1496,f1492,f7698]) ).
fof(f7698,plain,
( spl8_292
<=> ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_292])]) ).
fof(f1621,plain,
( ! [X2,X0,X1] : subclass(intersection(X0,X1),union(X1,X2))
| ~ spl8_144
| ~ spl8_145 ),
inference(duplicate_literal_removal,[],[f1613]) ).
fof(f1613,plain,
( ! [X2,X0,X1] :
( subclass(intersection(X0,X1),union(X1,X2))
| subclass(intersection(X0,X1),union(X1,X2)) )
| ~ spl8_144
| ~ spl8_145 ),
inference(resolution,[],[f1497,f1493]) ).
fof(f7696,plain,
( spl8_291
| ~ spl8_101
| ~ spl8_117 ),
inference(avatar_split_clause,[],[f1178,f1043,f956,f7694]) ).
fof(f7694,plain,
( spl8_291
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_291])]) ).
fof(f1178,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| complement(X0) = null_class )
| ~ spl8_101
| ~ spl8_117 ),
inference(duplicate_literal_removal,[],[f1156]) ).
fof(f1156,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| complement(X0) = null_class
| complement(X0) = null_class )
| ~ spl8_101
| ~ spl8_117 ),
inference(resolution,[],[f1044,f957]) ).
fof(f7692,plain,
( spl8_290
| ~ spl8_91
| ~ spl8_211 ),
inference(avatar_split_clause,[],[f6326,f3451,f850,f7690]) ).
fof(f7690,plain,
( spl8_290
<=> ! [X0] : universal_class = union(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_290])]) ).
fof(f3451,plain,
( spl8_211
<=> ! [X0,X1] : subclass(X0,union(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_211])]) ).
fof(f6326,plain,
( ! [X0] : universal_class = union(X0,universal_class)
| ~ spl8_91
| ~ spl8_211 ),
inference(resolution,[],[f3452,f851]) ).
fof(f3452,plain,
( ! [X0,X1] : subclass(X0,union(X1,X0))
| ~ spl8_211 ),
inference(avatar_component_clause,[],[f3451]) ).
fof(f7688,plain,
( spl8_289
| ~ spl8_40
| ~ spl8_104 ),
inference(avatar_split_clause,[],[f984,f969,f447,f7686]) ).
fof(f7686,plain,
( spl8_289
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_289])]) ).
fof(f984,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,universal_class) )
| ~ spl8_40
| ~ spl8_104 ),
inference(resolution,[],[f970,f448]) ).
fof(f7684,plain,
( ~ spl8_288
| spl8_213
| ~ spl8_11
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f951,f900,f317,f3488,f7681]) ).
fof(f7681,plain,
( spl8_288
<=> inductive(successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_288])]) ).
fof(f317,plain,
( spl8_11
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f951,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation)
| ~ spl8_11
| ~ spl8_100 ),
inference(resolution,[],[f901,f319]) ).
fof(f319,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f7679,plain,
( ~ spl8_287
| spl8_213
| ~ spl8_10
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f946,f900,f312,f3488,f7676]) ).
fof(f7676,plain,
( spl8_287
<=> inductive(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_287])]) ).
fof(f312,plain,
( spl8_10
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f946,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(element_relation)
| ~ spl8_10
| ~ spl8_100 ),
inference(resolution,[],[f901,f314]) ).
fof(f314,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f7674,plain,
( ~ spl8_285
| spl8_286
| ~ spl8_20
| ~ spl8_91 ),
inference(avatar_split_clause,[],[f859,f850,f355,f7671,f7667]) ).
fof(f7667,plain,
( spl8_285
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_285])]) ).
fof(f7671,plain,
( spl8_286
<=> universal_class = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_286])]) ).
fof(f859,plain,
( universal_class = cross_product(universal_class,universal_class)
| ~ function(universal_class)
| ~ spl8_20
| ~ spl8_91 ),
inference(resolution,[],[f851,f356]) ).
fof(f7572,plain,
( spl8_284
| ~ spl8_92
| ~ spl8_211 ),
inference(avatar_split_clause,[],[f6325,f3451,f854,f7570]) ).
fof(f7570,plain,
( spl8_284
<=> ! [X0] : member(sK7,union(X0,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_284])]) ).
fof(f6325,plain,
( ! [X0] : member(sK7,union(X0,universal_class))
| ~ spl8_92
| ~ spl8_211 ),
inference(resolution,[],[f3452,f855]) ).
fof(f7567,plain,
( ~ spl8_282
| spl8_283
| ~ spl8_6
| ~ spl8_180 ),
inference(avatar_split_clause,[],[f2428,f2293,f295,f7565,f7561]) ).
fof(f7561,plain,
( spl8_282
<=> subclass(identity_relation,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_282])]) ).
fof(f2428,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| ~ subclass(identity_relation,null_class) )
| ~ spl8_6
| ~ spl8_180 ),
inference(resolution,[],[f2294,f296]) ).
fof(f7558,plain,
( spl8_281
| ~ spl8_106
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1647,f1500,f997,f7556]) ).
fof(f7556,plain,
( spl8_281
<=> ! [X0,X1] : subclass(complement(X0),union(X1,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_281])]) ).
fof(f1647,plain,
( ! [X0,X1] : subclass(complement(X0),union(X1,universal_class))
| ~ spl8_106
| ~ spl8_146 ),
inference(duplicate_literal_removal,[],[f1629]) ).
fof(f1629,plain,
( ! [X0,X1] :
( subclass(complement(X0),union(X1,universal_class))
| subclass(complement(X0),union(X1,universal_class)) )
| ~ spl8_106
| ~ spl8_146 ),
inference(resolution,[],[f1501,f998]) ).
fof(f7553,plain,
( spl8_280
| ~ spl8_107
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1646,f1500,f1001,f7551]) ).
fof(f7551,plain,
( spl8_280
<=> ! [X0,X1] : subclass(domain_of(X0),union(X1,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_280])]) ).
fof(f1646,plain,
( ! [X0,X1] : subclass(domain_of(X0),union(X1,universal_class))
| ~ spl8_107
| ~ spl8_146 ),
inference(duplicate_literal_removal,[],[f1630]) ).
fof(f1630,plain,
( ! [X0,X1] :
( subclass(domain_of(X0),union(X1,universal_class))
| subclass(domain_of(X0),union(X1,universal_class)) )
| ~ spl8_107
| ~ spl8_146 ),
inference(resolution,[],[f1501,f1002]) ).
fof(f7548,plain,
( spl8_279
| ~ spl8_109
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1645,f1500,f1009,f7546]) ).
fof(f7546,plain,
( spl8_279
<=> ! [X0,X1] : subclass(power_class(X0),union(X1,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_279])]) ).
fof(f1645,plain,
( ! [X0,X1] : subclass(power_class(X0),union(X1,universal_class))
| ~ spl8_109
| ~ spl8_146 ),
inference(duplicate_literal_removal,[],[f1631]) ).
fof(f1631,plain,
( ! [X0,X1] :
( subclass(power_class(X0),union(X1,universal_class))
| subclass(power_class(X0),union(X1,universal_class)) )
| ~ spl8_109
| ~ spl8_146 ),
inference(resolution,[],[f1501,f1010]) ).
fof(f7543,plain,
( spl8_278
| ~ spl8_106
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1626,f1496,f997,f7541]) ).
fof(f7541,plain,
( spl8_278
<=> ! [X0,X1] : subclass(complement(X0),union(universal_class,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_278])]) ).
fof(f1626,plain,
( ! [X0,X1] : subclass(complement(X0),union(universal_class,X1))
| ~ spl8_106
| ~ spl8_145 ),
inference(duplicate_literal_removal,[],[f1608]) ).
fof(f1608,plain,
( ! [X0,X1] :
( subclass(complement(X0),union(universal_class,X1))
| subclass(complement(X0),union(universal_class,X1)) )
| ~ spl8_106
| ~ spl8_145 ),
inference(resolution,[],[f1497,f998]) ).
fof(f7538,plain,
( spl8_277
| ~ spl8_107
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1625,f1496,f1001,f7536]) ).
fof(f7536,plain,
( spl8_277
<=> ! [X0,X1] : subclass(domain_of(X0),union(universal_class,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_277])]) ).
fof(f1625,plain,
( ! [X0,X1] : subclass(domain_of(X0),union(universal_class,X1))
| ~ spl8_107
| ~ spl8_145 ),
inference(duplicate_literal_removal,[],[f1609]) ).
fof(f1609,plain,
( ! [X0,X1] :
( subclass(domain_of(X0),union(universal_class,X1))
| subclass(domain_of(X0),union(universal_class,X1)) )
| ~ spl8_107
| ~ spl8_145 ),
inference(resolution,[],[f1497,f1002]) ).
fof(f7533,plain,
( spl8_276
| ~ spl8_109
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1624,f1496,f1009,f7531]) ).
fof(f7531,plain,
( spl8_276
<=> ! [X0,X1] : subclass(power_class(X0),union(universal_class,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_276])]) ).
fof(f1624,plain,
( ! [X0,X1] : subclass(power_class(X0),union(universal_class,X1))
| ~ spl8_109
| ~ spl8_145 ),
inference(duplicate_literal_removal,[],[f1610]) ).
fof(f1610,plain,
( ! [X0,X1] :
( subclass(power_class(X0),union(universal_class,X1))
| subclass(power_class(X0),union(universal_class,X1)) )
| ~ spl8_109
| ~ spl8_145 ),
inference(resolution,[],[f1497,f1010]) ).
fof(f7529,plain,
( spl8_275
| ~ spl8_6
| ~ spl8_130 ),
inference(avatar_split_clause,[],[f1373,f1255,f295,f7527]) ).
fof(f7527,plain,
( spl8_275
<=> ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_275])]) ).
fof(f1373,plain,
( ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) )
| ~ spl8_6
| ~ spl8_130 ),
inference(resolution,[],[f1256,f296]) ).
fof(f7497,plain,
( spl8_30
| ~ spl8_91
| ~ spl8_211
| ~ spl8_264 ),
inference(avatar_split_clause,[],[f7449,f7337,f3451,f850,f406]) ).
fof(f7337,plain,
( spl8_264
<=> ! [X0] : member(null_class,union(X0,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_264])]) ).
fof(f7449,plain,
( member(null_class,universal_class)
| ~ spl8_91
| ~ spl8_211
| ~ spl8_264 ),
inference(forward_demodulation,[],[f7338,f6326]) ).
fof(f7338,plain,
( ! [X0] : member(null_class,union(X0,universal_class))
| ~ spl8_264 ),
inference(avatar_component_clause,[],[f7337]) ).
fof(f7496,plain,
( spl8_274
| ~ spl8_7
| ~ spl8_125 ),
inference(avatar_split_clause,[],[f1345,f1235,f299,f7494]) ).
fof(f1345,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) )
| ~ spl8_7
| ~ spl8_125 ),
inference(resolution,[],[f1236,f300]) ).
fof(f7479,plain,
( spl8_272
| ~ spl8_273
| ~ spl8_61
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f934,f896,f638,f7476,f7473]) ).
fof(f7476,plain,
( spl8_273
<=> subclass(universal_class,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_273])]) ).
fof(f638,plain,
( spl8_61
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
fof(f934,plain,
( ! [X0] :
( ~ subclass(universal_class,successor_relation)
| member(X0,universal_class) )
| ~ spl8_61
| ~ spl8_99 ),
inference(resolution,[],[f897,f639]) ).
fof(f639,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| member(X0,universal_class) )
| ~ spl8_61 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f7471,plain,
( spl8_270
| ~ spl8_271
| ~ spl8_58
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f920,f896,f620,f7468,f7465]) ).
fof(f7465,plain,
( spl8_270
<=> ! [X0,X1] : member(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_270])]) ).
fof(f7468,plain,
( spl8_271
<=> subclass(universal_class,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_271])]) ).
fof(f920,plain,
( ! [X0,X1] :
( ~ subclass(universal_class,element_relation)
| member(X0,X1) )
| ~ spl8_58
| ~ spl8_99 ),
inference(resolution,[],[f897,f621]) ).
fof(f7448,plain,
( spl8_269
| spl8_30
| ~ spl8_7
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f943,f900,f299,f406,f7446]) ).
fof(f943,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(X0) )
| ~ spl8_7
| ~ spl8_100 ),
inference(resolution,[],[f901,f300]) ).
fof(f7431,plain,
( spl8_30
| ~ spl8_91
| ~ spl8_206
| ~ spl8_245 ),
inference(avatar_split_clause,[],[f6628,f6625,f3193,f850,f406]) ).
fof(f3193,plain,
( spl8_206
<=> ! [X0,X1] : subclass(X0,union(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_206])]) ).
fof(f6625,plain,
( spl8_245
<=> ! [X0] : member(null_class,union(universal_class,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_245])]) ).
fof(f6628,plain,
( member(null_class,universal_class)
| ~ spl8_91
| ~ spl8_206
| ~ spl8_245 ),
inference(forward_demodulation,[],[f6626,f6037]) ).
fof(f6037,plain,
( ! [X0] : universal_class = union(universal_class,X0)
| ~ spl8_91
| ~ spl8_206 ),
inference(resolution,[],[f3194,f851]) ).
fof(f3194,plain,
( ! [X0,X1] : subclass(X0,union(X0,X1))
| ~ spl8_206 ),
inference(avatar_component_clause,[],[f3193]) ).
fof(f6626,plain,
( ! [X0] : member(null_class,union(universal_class,X0))
| ~ spl8_245 ),
inference(avatar_component_clause,[],[f6625]) ).
fof(f7430,plain,
( spl8_268
| ~ spl8_79
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f815,f810,f765,f7428]) ).
fof(f7428,plain,
( spl8_268
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),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(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),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(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_268])]) ).
fof(f810,plain,
( spl8_83
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
fof(f815,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),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(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),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(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))
| ~ member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),universal_class) )
| ~ spl8_79
| ~ spl8_83 ),
inference(resolution,[],[f811,f766]) ).
fof(f811,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X2,universal_class) )
| ~ spl8_83 ),
inference(avatar_component_clause,[],[f810]) ).
fof(f7426,plain,
( spl8_267
| ~ spl8_78
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f779,f765,f761,f7424]) ).
fof(f7424,plain,
( spl8_267
<=> ! [X0,X1] :
( cross_product(X0,X1) = null_class
| ~ member(cross_product(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))),unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),unordered_pair(second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_267])]) ).
fof(f761,plain,
( spl8_78
<=> ! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
fof(f779,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = null_class
| ~ member(cross_product(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))) = unordered_pair(unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))),unordered_pair(first(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),unordered_pair(second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))),second(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))) )
| ~ spl8_78
| ~ spl8_79 ),
inference(resolution,[],[f766,f762]) ).
fof(f762,plain,
( ! [X2,X0,X1] :
( ~ member(X2,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2 )
| ~ spl8_78 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f7359,plain,
( spl8_266
| ~ spl8_77
| ~ spl8_89 ),
inference(avatar_split_clause,[],[f844,f840,f748,f7357]) ).
fof(f7357,plain,
( spl8_266
<=> ! [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))),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))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_266])]) ).
fof(f748,plain,
( spl8_77
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).
fof(f840,plain,
( spl8_89
<=> ! [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(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(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(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_89])]) ).
fof(f844,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))),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))),flip(X3))
| ~ member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl8_77
| ~ spl8_89 ),
inference(resolution,[],[f841,f749]) ).
fof(f749,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
| ~ spl8_77 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f841,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))),cross_product(cross_product(universal_class,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(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(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)) )
| ~ spl8_89 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f7355,plain,
( spl8_265
| ~ spl8_77
| ~ spl8_88 ),
inference(avatar_split_clause,[],[f843,f836,f748,f7353]) ).
fof(f7353,plain,
( spl8_265
<=> ! [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))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X3))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_265])]) ).
fof(f836,plain,
( spl8_88
<=> ! [X0,X3,X2,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))),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(X1,X1))),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(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_88])]) ).
fof(f843,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))),X3)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),unordered_pair(X1,X1))),rotate(X3))
| ~ member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),cross_product(universal_class,universal_class)) )
| ~ spl8_77
| ~ spl8_88 ),
inference(resolution,[],[f837,f749]) ).
fof(f837,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))),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(X1,X1))),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))),rotate(X0)) )
| ~ spl8_88 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f7339,plain,
( spl8_264
| ~ spl8_97
| ~ spl8_211 ),
inference(avatar_split_clause,[],[f6324,f3451,f883,f7337]) ).
fof(f6324,plain,
( ! [X0] : member(null_class,union(X0,universal_class))
| ~ spl8_97
| ~ spl8_211 ),
inference(resolution,[],[f3452,f884]) ).
fof(f7335,plain,
( spl8_263
| ~ spl8_47
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f818,f810,f496,f7333]) ).
fof(f7333,plain,
( spl8_263
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK5(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_263])]) ).
fof(f818,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK5(X1,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X2,X3))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))) )
| ~ spl8_47
| ~ spl8_83 ),
inference(resolution,[],[f811,f497]) ).
fof(f7320,plain,
( spl8_262
| ~ spl8_33
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f817,f810,f419,f7318]) ).
fof(f7318,plain,
( spl8_262
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(X0,universal_class)
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_262])]) ).
fof(f817,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3),sK4(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3)))),compose(X1,X2))
| ~ member(X0,universal_class)
| subclass(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))),X3) )
| ~ spl8_33
| ~ spl8_83 ),
inference(resolution,[],[f811,f420]) ).
fof(f7305,plain,
( spl8_261
| ~ spl8_16
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f816,f810,f339,f7303]) ).
fof(f7303,plain,
( spl8_261
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK2(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_261])]) ).
fof(f816,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))),sK2(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))))))),compose(X1,X2))
| ~ member(X0,universal_class)
| null_class = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class)))) )
| ~ spl8_16
| ~ spl8_83 ),
inference(resolution,[],[f811,f340]) ).
fof(f7228,plain,
( spl8_260
| ~ spl8_77
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f768,f761,f748,f7226]) ).
fof(f7226,plain,
( spl8_260
<=> ! [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,[spl8_260])]) ).
fof(f768,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) )
| ~ spl8_77
| ~ spl8_78 ),
inference(resolution,[],[f762,f749]) ).
fof(f7151,plain,
( spl8_259
| ~ spl8_62
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f751,f744,f642,f7149]) ).
fof(f7149,plain,
( spl8_259
<=> ! [X0] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))) = unordered_pair(unordered_pair(sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))))),unordered_pair(sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),unordered_pair(sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_259])]) ).
fof(f751,plain,
( ! [X0] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))) = unordered_pair(unordered_pair(sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))))),unordered_pair(sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),unordered_pair(sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))),sK3(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))))))
| ~ member(X0,universal_class) )
| ~ spl8_62
| ~ spl8_76 ),
inference(resolution,[],[f745,f643]) ).
fof(f6946,plain,
( spl8_258
| ~ spl8_91
| ~ spl8_206 ),
inference(avatar_split_clause,[],[f6037,f3193,f850,f6944]) ).
fof(f6944,plain,
( spl8_258
<=> ! [X0] : universal_class = union(universal_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_258])]) ).
fof(f6935,plain,
( spl8_257
| ~ spl8_52
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f786,f765,f578,f6933]) ).
fof(f6933,plain,
( spl8_257
<=> ! [X0,X1] :
( null_class = union(X0,X1)
| ~ member(union(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X0)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_257])]) ).
fof(f786,plain,
( ! [X0,X1] :
( null_class = union(X0,X1)
| ~ member(union(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X0)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(union(X0,X1),union(X0,X1)),universal_class)),universal_class))))),X1) )
| ~ spl8_52
| ~ spl8_79 ),
inference(resolution,[],[f766,f579]) ).
fof(f6931,plain,
( spl8_256
| ~ spl8_54
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f777,f765,f586,f6929]) ).
fof(f6929,plain,
( spl8_256
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X0
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_256])]) ).
fof(f586,plain,
( spl8_54
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
fof(f777,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X0
| sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))) = X1 )
| ~ spl8_54
| ~ spl8_79 ),
inference(resolution,[],[f766,f587]) ).
fof(f587,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 )
| ~ spl8_54 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f6851,plain,
( spl8_255
| ~ spl8_65
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f813,f810,f659,f6849]) ).
fof(f6849,plain,
( spl8_255
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X0,universal_class)
| null_class = intersection(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_255])]) ).
fof(f659,plain,
( spl8_65
<=> ! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
fof(f813,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
| ~ member(X0,universal_class)
| null_class = intersection(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(X3,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))),cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) )
| ~ spl8_65
| ~ spl8_83 ),
inference(resolution,[],[f811,f660]) ).
fof(f660,plain,
( ! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) )
| ~ spl8_65 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f6847,plain,
( spl8_254
| ~ spl8_71
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f720,f706,f689,f6845]) ).
fof(f6845,plain,
( spl8_254
<=> ! [X2,X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class))))))))
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_254])]) ).
fof(f689,plain,
( spl8_71
<=> ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
fof(f706,plain,
( spl8_73
<=> ! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
fof(f720,plain,
( ! [X2,X0,X1] :
( domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class))))))))
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) )
| ~ spl8_71
| ~ spl8_73 ),
inference(resolution,[],[f707,f690]) ).
fof(f690,plain,
( ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) )
| ~ spl8_71 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f707,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X0,universal_class) )
| ~ spl8_73 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f6811,plain,
( spl8_253
| ~ spl8_47
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f772,f761,f496,f6809]) ).
fof(f6809,plain,
( spl8_253
<=> ! [X2,X0,X1] :
( sK5(X0,cross_product(X1,X2)) = unordered_pair(unordered_pair(first(sK5(X0,cross_product(X1,X2))),first(sK5(X0,cross_product(X1,X2)))),unordered_pair(first(sK5(X0,cross_product(X1,X2))),unordered_pair(second(sK5(X0,cross_product(X1,X2))),second(sK5(X0,cross_product(X1,X2))))))
| ~ member(X0,sum_class(cross_product(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_253])]) ).
fof(f772,plain,
( ! [X2,X0,X1] :
( sK5(X0,cross_product(X1,X2)) = unordered_pair(unordered_pair(first(sK5(X0,cross_product(X1,X2))),first(sK5(X0,cross_product(X1,X2)))),unordered_pair(first(sK5(X0,cross_product(X1,X2))),unordered_pair(second(sK5(X0,cross_product(X1,X2))),second(sK5(X0,cross_product(X1,X2))))))
| ~ member(X0,sum_class(cross_product(X1,X2))) )
| ~ spl8_47
| ~ spl8_78 ),
inference(resolution,[],[f762,f497]) ).
fof(f6795,plain,
( spl8_252
| ~ spl8_92
| ~ spl8_206 ),
inference(avatar_split_clause,[],[f6036,f3193,f854,f6793]) ).
fof(f6793,plain,
( spl8_252
<=> ! [X0] : member(sK7,union(universal_class,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_252])]) ).
fof(f6036,plain,
( ! [X0] : member(sK7,union(universal_class,X0))
| ~ spl8_92
| ~ spl8_206 ),
inference(resolution,[],[f3194,f855]) ).
fof(f6791,plain,
( spl8_249
| ~ spl8_250
| spl8_251
| ~ spl8_74
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f775,f765,f710,f6788,f6784,f6781]) ).
fof(f6781,plain,
( spl8_249
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_249])]) ).
fof(f6788,plain,
( spl8_251
<=> universal_class = null_class ),
introduced(avatar_definition,[new_symbols(naming,[spl8_251])]) ).
fof(f710,plain,
( spl8_74
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
fof(f775,plain,
( ! [X0] :
( universal_class = null_class
| ~ member(universal_class,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))),sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(universal_class,universal_class),universal_class)),universal_class))))))))) = X0
| ~ member(X0,universal_class) )
| ~ spl8_74
| ~ spl8_79 ),
inference(resolution,[],[f766,f711]) ).
fof(f711,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X0,universal_class) )
| ~ spl8_74 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f6779,plain,
( spl8_248
| ~ spl8_33
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f771,f761,f419,f6777]) ).
fof(f6777,plain,
( spl8_248
<=> ! [X2,X0,X1] :
( sK4(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(sK4(cross_product(X0,X1),X2)),first(sK4(cross_product(X0,X1),X2))),unordered_pair(first(sK4(cross_product(X0,X1),X2)),unordered_pair(second(sK4(cross_product(X0,X1),X2)),second(sK4(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_248])]) ).
fof(f771,plain,
( ! [X2,X0,X1] :
( sK4(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(sK4(cross_product(X0,X1),X2)),first(sK4(cross_product(X0,X1),X2))),unordered_pair(first(sK4(cross_product(X0,X1),X2)),unordered_pair(second(sK4(cross_product(X0,X1),X2)),second(sK4(cross_product(X0,X1),X2)))))
| subclass(cross_product(X0,X1),X2) )
| ~ spl8_33
| ~ spl8_78 ),
inference(resolution,[],[f762,f420]) ).
fof(f6670,plain,
( spl8_247
| ~ spl8_12
| ~ spl8_83 ),
inference(avatar_split_clause,[],[f814,f810,f322,f6668]) ).
fof(f6668,plain,
( spl8_247
<=> ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
| ~ member(X0,universal_class)
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_247])]) ).
fof(f814,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
| ~ member(X0,universal_class)
| ~ inductive(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class)),universal_class))))) )
| ~ spl8_12
| ~ spl8_83 ),
inference(resolution,[],[f811,f323]) ).
fof(f6666,plain,
( spl8_246
| ~ spl8_71
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f734,f710,f689,f6664]) ).
fof(f6664,plain,
( spl8_246
<=> ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))))))) = X0
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_246])]) ).
fof(f734,plain,
( ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X2,universal_class)),universal_class)))))))) = X0
| ~ member(X0,universal_class)
| ~ function(X1)
| ~ member(X2,universal_class) )
| ~ spl8_71
| ~ spl8_74 ),
inference(resolution,[],[f711,f690]) ).
fof(f6627,plain,
( spl8_245
| ~ spl8_97
| ~ spl8_206 ),
inference(avatar_split_clause,[],[f6035,f3193,f883,f6625]) ).
fof(f6035,plain,
( ! [X0] : member(null_class,union(universal_class,X0))
| ~ spl8_97
| ~ spl8_206 ),
inference(resolution,[],[f3194,f884]) ).
fof(f6623,plain,
( spl8_244
| ~ spl8_50
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f803,f797,f544,f6621]) ).
fof(f6621,plain,
( spl8_244
<=> ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(X1,sum_class(successor_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_244])]) ).
fof(f797,plain,
( spl8_81
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).
fof(f803,plain,
( ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(X1,sum_class(successor_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0)))))) )
| ~ spl8_50
| ~ spl8_81 ),
inference(resolution,[],[f798,f545]) ).
fof(f798,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) )
| ~ spl8_81 ),
inference(avatar_component_clause,[],[f797]) ).
fof(f6517,plain,
( spl8_243
| ~ spl8_45
| ~ spl8_81 ),
inference(avatar_split_clause,[],[f804,f797,f488,f6515]) ).
fof(f804,plain,
( ! [X0,X1] :
( ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),X1)
| ~ subclass(successor_relation,X1) )
| ~ spl8_45
| ~ spl8_81 ),
inference(resolution,[],[f798,f489]) ).
fof(f6513,plain,
( spl8_242
| ~ spl8_47
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f755,f744,f496,f6511]) ).
fof(f6511,plain,
( spl8_242
<=> ! [X0] :
( sK5(X0,identity_relation) = unordered_pair(unordered_pair(sK3(sK5(X0,identity_relation)),sK3(sK5(X0,identity_relation))),unordered_pair(sK3(sK5(X0,identity_relation)),unordered_pair(sK3(sK5(X0,identity_relation)),sK3(sK5(X0,identity_relation)))))
| ~ member(X0,sum_class(identity_relation)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_242])]) ).
fof(f755,plain,
( ! [X0] :
( sK5(X0,identity_relation) = unordered_pair(unordered_pair(sK3(sK5(X0,identity_relation)),sK3(sK5(X0,identity_relation))),unordered_pair(sK3(sK5(X0,identity_relation)),unordered_pair(sK3(sK5(X0,identity_relation)),sK3(sK5(X0,identity_relation)))))
| ~ member(X0,sum_class(identity_relation)) )
| ~ spl8_47
| ~ spl8_76 ),
inference(resolution,[],[f745,f497]) ).
fof(f5007,plain,
( spl8_30
| ~ spl8_7
| ~ spl8_97 ),
inference(avatar_split_clause,[],[f1282,f883,f299,f406]) ).
fof(f1282,plain,
( member(null_class,universal_class)
| ~ spl8_7
| ~ spl8_97 ),
inference(resolution,[],[f884,f300]) ).
fof(f4565,plain,
( spl8_241
| ~ spl8_16
| ~ spl8_225
| ~ spl8_240 ),
inference(avatar_split_clause,[],[f4561,f4558,f3763,f339,f4563]) ).
fof(f4558,plain,
( spl8_240
<=> ! [X0,X1] :
( sK2(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK2(cross_product(X0,X1))),first(sK2(cross_product(X0,X1)))),unordered_pair(first(sK2(cross_product(X0,X1))),unordered_pair(second(sK2(cross_product(X0,X1))),second(sK2(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_240])]) ).
fof(f4561,plain,
( ! [X0,X1] :
( cross_product(X0,X1) = identity_relation
| sK2(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK2(cross_product(X0,X1))),first(sK2(cross_product(X0,X1)))),unordered_pair(first(sK2(cross_product(X0,X1))),unordered_pair(second(sK2(cross_product(X0,X1))),second(sK2(cross_product(X0,X1)))))) )
| ~ spl8_16
| ~ spl8_225
| ~ spl8_240 ),
inference(forward_demodulation,[],[f4559,f4529]) ).
fof(f4529,plain,
( null_class = identity_relation
| ~ spl8_16
| ~ spl8_225 ),
inference(resolution,[],[f3764,f340]) ).
fof(f4559,plain,
( ! [X0,X1] :
( sK2(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK2(cross_product(X0,X1))),first(sK2(cross_product(X0,X1)))),unordered_pair(first(sK2(cross_product(X0,X1))),unordered_pair(second(sK2(cross_product(X0,X1))),second(sK2(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class )
| ~ spl8_240 ),
inference(avatar_component_clause,[],[f4558]) ).
fof(f4560,plain,
( spl8_240
| ~ spl8_16
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f770,f761,f339,f4558]) ).
fof(f770,plain,
( ! [X0,X1] :
( sK2(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(sK2(cross_product(X0,X1))),first(sK2(cross_product(X0,X1)))),unordered_pair(first(sK2(cross_product(X0,X1))),unordered_pair(second(sK2(cross_product(X0,X1))),second(sK2(cross_product(X0,X1))))))
| cross_product(X0,X1) = null_class )
| ~ spl8_16
| ~ spl8_78 ),
inference(resolution,[],[f762,f340]) ).
fof(f4511,plain,
( spl8_239
| ~ spl8_33
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f754,f744,f419,f4509]) ).
fof(f4509,plain,
( spl8_239
<=> ! [X0] :
( sK4(identity_relation,X0) = unordered_pair(unordered_pair(sK3(sK4(identity_relation,X0)),sK3(sK4(identity_relation,X0))),unordered_pair(sK3(sK4(identity_relation,X0)),unordered_pair(sK3(sK4(identity_relation,X0)),sK3(sK4(identity_relation,X0)))))
| subclass(identity_relation,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_239])]) ).
fof(f754,plain,
( ! [X0] :
( sK4(identity_relation,X0) = unordered_pair(unordered_pair(sK3(sK4(identity_relation,X0)),sK3(sK4(identity_relation,X0))),unordered_pair(sK3(sK4(identity_relation,X0)),unordered_pair(sK3(sK4(identity_relation,X0)),sK3(sK4(identity_relation,X0)))))
| subclass(identity_relation,X0) )
| ~ spl8_33
| ~ spl8_76 ),
inference(resolution,[],[f745,f420]) ).
fof(f4374,plain,
( spl8_238
| ~ spl8_35
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f781,f765,f427,f4372]) ).
fof(f4372,plain,
( spl8_238
<=> ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_238])]) ).
fof(f781,plain,
( ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X0) )
| ~ spl8_35
| ~ spl8_79 ),
inference(resolution,[],[f766,f428]) ).
fof(f4370,plain,
( spl8_237
| ~ spl8_36
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f780,f765,f431,f4368]) ).
fof(f4368,plain,
( spl8_237
<=> ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_237])]) ).
fof(f780,plain,
( ! [X0,X1] :
( intersection(X0,X1) = null_class
| ~ member(intersection(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))),X1) )
| ~ spl8_36
| ~ spl8_79 ),
inference(resolution,[],[f766,f432]) ).
fof(f4366,plain,
( spl8_236
| ~ spl8_39
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f778,f765,f443,f4364]) ).
fof(f4364,plain,
( spl8_236
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_236])]) ).
fof(f443,plain,
( spl8_39
<=> ! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
fof(f778,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = null_class
| ~ member(unordered_pair(X0,X1),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))),universal_class) )
| ~ spl8_39
| ~ spl8_79 ),
inference(resolution,[],[f766,f444]) ).
fof(f444,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) )
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f443]) ).
fof(f4359,plain,
( ~ spl8_80
| ~ spl8_12
| spl8_30 ),
inference(avatar_split_clause,[],[f886,f406,f322,f792]) ).
fof(f886,plain,
( ~ inductive(universal_class)
| ~ spl8_12
| spl8_30 ),
inference(resolution,[],[f407,f323]) ).
fof(f407,plain,
( ~ member(null_class,universal_class)
| spl8_30 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f4358,plain,
( spl8_235
| ~ spl8_43
| ~ spl8_57 ),
inference(avatar_split_clause,[],[f645,f616,f480,f4356]) ).
fof(f4356,plain,
( spl8_235
<=> ! [X0] :
( ~ inductive(X0)
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_235])]) ).
fof(f616,plain,
( spl8_57
<=> ! [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,[spl8_57])]) ).
fof(f645,plain,
( ! [X0] :
( ~ inductive(X0)
| domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0
| ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class))))) )
| ~ spl8_43
| ~ spl8_57 ),
inference(resolution,[],[f617,f481]) ).
fof(f617,plain,
( ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) )
| ~ spl8_57 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f4240,plain,
( spl8_234
| ~ spl8_223
| ~ spl8_229 ),
inference(avatar_split_clause,[],[f4032,f4029,f3739,f4238]) ).
fof(f4238,plain,
( spl8_234
<=> ! [X0] :
( complement(X0) = identity_relation
| ~ member(complement(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_234])]) ).
fof(f4029,plain,
( spl8_229
<=> ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_229])]) ).
fof(f4032,plain,
( ! [X0] :
( complement(X0) = identity_relation
| ~ member(complement(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),universal_class) )
| ~ spl8_223
| ~ spl8_229 ),
inference(forward_demodulation,[],[f4030,f3741]) ).
fof(f4030,plain,
( ! [X0] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),universal_class)
| ~ member(complement(X0),universal_class)
| complement(X0) = null_class )
| ~ spl8_229 ),
inference(avatar_component_clause,[],[f4029]) ).
fof(f4214,plain,
( spl8_233
| ~ spl8_30
| ~ spl8_223 ),
inference(avatar_split_clause,[],[f3750,f3739,f406,f4211]) ).
fof(f3750,plain,
( member(identity_relation,universal_class)
| ~ spl8_30
| ~ spl8_223 ),
inference(superposition,[],[f408,f3741]) ).
fof(f4046,plain,
( spl8_232
| ~ spl8_26
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f789,f765,f380,f4044]) ).
fof(f4044,plain,
( spl8_232
<=> ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_232])]) ).
fof(f380,plain,
( spl8_26
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
fof(f789,plain,
( ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),universal_class) )
| ~ spl8_26
| ~ spl8_79 ),
inference(resolution,[],[f766,f381]) ).
fof(f381,plain,
( ! [X0,X1] :
( ~ member(X0,power_class(X1))
| member(X0,universal_class) )
| ~ spl8_26 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f4041,plain,
( spl8_231
| ~ spl8_27
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f788,f765,f384,f4039]) ).
fof(f4039,plain,
( spl8_231
<=> ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| subclass(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_231])]) ).
fof(f788,plain,
( ! [X0] :
( null_class = power_class(X0)
| ~ member(power_class(X0),universal_class)
| subclass(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(power_class(X0),power_class(X0)),universal_class)),universal_class))))),X0) )
| ~ spl8_27
| ~ spl8_79 ),
inference(resolution,[],[f766,f385]) ).
fof(f4036,plain,
( spl8_230
| ~ spl8_28
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f785,f765,f388,f4034]) ).
fof(f4034,plain,
( spl8_230
<=> ! [X0] :
( null_class = domain_of(X0)
| ~ member(domain_of(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(domain_of(X0),domain_of(X0)),universal_class)),universal_class))))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_230])]) ).
fof(f388,plain,
( spl8_28
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
fof(f785,plain,
( ! [X0] :
( null_class = domain_of(X0)
| ~ member(domain_of(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(domain_of(X0),domain_of(X0)),universal_class)),universal_class))))),universal_class) )
| ~ spl8_28
| ~ spl8_79 ),
inference(resolution,[],[f766,f389]) ).
fof(f389,plain,
( ! [X0,X1] :
( ~ member(X1,domain_of(X0))
| member(X1,universal_class) )
| ~ spl8_28 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f4031,plain,
( spl8_229
| ~ spl8_24
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f783,f765,f372,f4029]) ).
fof(f372,plain,
( spl8_24
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
fof(f783,plain,
( ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),universal_class) )
| ~ spl8_24
| ~ spl8_79 ),
inference(resolution,[],[f766,f373]) ).
fof(f373,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| member(X1,universal_class) )
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f4008,plain,
( spl8_228
| ~ spl8_13
| ~ spl8_224 ),
inference(avatar_split_clause,[],[f3979,f3743,f326,f4005]) ).
fof(f3979,plain,
( member(sK2(identity_relation),universal_class)
| ~ spl8_13
| ~ spl8_224 ),
inference(superposition,[],[f327,f3745]) ).
fof(f4003,plain,
( spl8_227
| ~ spl8_25
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f782,f765,f376,f4001]) ).
fof(f4001,plain,
( spl8_227
<=> ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_227])]) ).
fof(f782,plain,
( ! [X0] :
( complement(X0) = null_class
| ~ member(complement(X0),universal_class)
| ~ member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))),X0) )
| ~ spl8_25
| ~ spl8_79 ),
inference(resolution,[],[f766,f377]) ).
fof(f3999,plain,
( spl8_226
| ~ spl8_50
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f773,f765,f544,f3997]) ).
fof(f3997,plain,
( spl8_226
<=> ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(X1,sum_class(X0))
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_226])]) ).
fof(f773,plain,
( ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(X1,sum_class(X0))
| ~ member(X1,sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))))) )
| ~ spl8_50
| ~ spl8_79 ),
inference(resolution,[],[f766,f545]) ).
fof(f3765,plain,
( spl8_225
| ~ spl8_6
| ~ spl8_223 ),
inference(avatar_split_clause,[],[f3747,f3739,f295,f3763]) ).
fof(f3747,plain,
( ! [X0] : ~ member(X0,identity_relation)
| ~ spl8_6
| ~ spl8_223 ),
inference(superposition,[],[f296,f3741]) ).
fof(f3746,plain,
( spl8_223
| spl8_224
| ~ spl8_16
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f753,f744,f339,f3743,f3739]) ).
fof(f753,plain,
( sK2(identity_relation) = unordered_pair(unordered_pair(sK3(sK2(identity_relation)),sK3(sK2(identity_relation))),unordered_pair(sK3(sK2(identity_relation)),unordered_pair(sK3(sK2(identity_relation)),sK3(sK2(identity_relation)))))
| null_class = identity_relation
| ~ spl8_16
| ~ spl8_76 ),
inference(resolution,[],[f745,f340]) ).
fof(f3737,plain,
( spl8_222
| ~ spl8_47
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f727,f706,f496,f3735]) ).
fof(f3735,plain,
( spl8_222
<=> ! [X0,X1] :
( sK5(X1,universal_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1,universal_class),sK5(X1,universal_class)))))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_222])]) ).
fof(f727,plain,
( ! [X0,X1] :
( sK5(X1,universal_class) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1,universal_class),sK5(X1,universal_class)))))
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) )
| ~ spl8_47
| ~ spl8_73 ),
inference(resolution,[],[f707,f497]) ).
fof(f3733,plain,
( spl8_221
| ~ spl8_34
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f676,f659,f423,f3731]) ).
fof(f3731,plain,
( spl8_221
<=> ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(sK4(X1,domain_of(X0)),sK4(X1,domain_of(X0))),universal_class))
| ~ member(sK4(X1,domain_of(X0)),universal_class)
| subclass(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_221])]) ).
fof(f676,plain,
( ! [X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(sK4(X1,domain_of(X0)),sK4(X1,domain_of(X0))),universal_class))
| ~ member(sK4(X1,domain_of(X0)),universal_class)
| subclass(X1,domain_of(X0)) )
| ~ spl8_34
| ~ spl8_65 ),
inference(resolution,[],[f660,f424]) ).
fof(f3632,plain,
( spl8_220
| ~ spl8_45
| ~ spl8_79 ),
inference(avatar_split_clause,[],[f774,f765,f488,f3630]) ).
fof(f3630,plain,
( spl8_220
<=> ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))),X1)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_220])]) ).
fof(f774,plain,
( ! [X0,X1] :
( null_class = X0
| ~ member(X0,universal_class)
| member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))),X1)
| ~ subclass(X0,X1) )
| ~ spl8_45
| ~ spl8_79 ),
inference(resolution,[],[f766,f489]) ).
fof(f3628,plain,
( spl8_219
| ~ spl8_33
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f726,f706,f419,f3626]) ).
fof(f3626,plain,
( spl8_219
<=> ! [X0,X1] :
( sK4(universal_class,X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(universal_class,X1),sK4(universal_class,X1)))))
| ~ member(X0,universal_class)
| subclass(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_219])]) ).
fof(f726,plain,
( ! [X0,X1] :
( sK4(universal_class,X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(universal_class,X1),sK4(universal_class,X1)))))
| ~ member(X0,universal_class)
| subclass(universal_class,X1) )
| ~ spl8_33
| ~ spl8_73 ),
inference(resolution,[],[f707,f420]) ).
fof(f3559,plain,
( spl8_218
| ~ spl8_50
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f758,f748,f544,f3557]) ).
fof(f3557,plain,
( spl8_218
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(X4,sum_class(cross_product(X3,X1)))
| ~ member(X4,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_218])]) ).
fof(f758,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(X4,sum_class(cross_product(X3,X1)))
| ~ member(X4,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0)))) )
| ~ spl8_50
| ~ spl8_77 ),
inference(resolution,[],[f749,f545]) ).
fof(f3555,plain,
( spl8_217
| ~ spl8_47
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f741,f710,f496,f3553]) ).
fof(f3553,plain,
( spl8_217
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1,universal_class),sK5(X1,universal_class))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_217])]) ).
fof(f741,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK5(X1,universal_class),sK5(X1,universal_class))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,sum_class(universal_class)) )
| ~ spl8_47
| ~ spl8_74 ),
inference(resolution,[],[f711,f497]) ).
fof(f3504,plain,
( spl8_216
| ~ spl8_45
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f759,f748,f488,f3502]) ).
fof(f3502,plain,
( spl8_216
<=> ! [X4,X0,X3,X2,X1] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4)
| ~ subclass(cross_product(X3,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_216])]) ).
fof(f759,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X0,X1)
| ~ member(X2,X3)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4)
| ~ subclass(cross_product(X3,X1),X4) )
| ~ spl8_45
| ~ spl8_77 ),
inference(resolution,[],[f749,f489]) ).
fof(f3500,plain,
( spl8_215
| ~ spl8_33
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f740,f710,f419,f3498]) ).
fof(f3498,plain,
( spl8_215
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(universal_class,X1),sK4(universal_class,X1))))) = X0
| ~ member(X0,universal_class)
| subclass(universal_class,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_215])]) ).
fof(f740,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK4(universal_class,X1),sK4(universal_class,X1))))) = X0
| ~ member(X0,universal_class)
| subclass(universal_class,X1) )
| ~ spl8_33
| ~ spl8_74 ),
inference(resolution,[],[f711,f420]) ).
fof(f3495,plain,
( ~ spl8_212
| ~ spl8_213
| spl8_214
| ~ spl8_20
| ~ spl8_70 ),
inference(avatar_split_clause,[],[f698,f685,f355,f3492,f3488,f3484]) ).
fof(f3484,plain,
( spl8_212
<=> 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,[spl8_212])]) ).
fof(f3492,plain,
( spl8_214
<=> inductive(cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_214])]) ).
fof(f685,plain,
( spl8_70
<=> ! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
fof(f698,plain,
( inductive(cross_product(universal_class,universal_class))
| ~ member(null_class,cross_product(universal_class,universal_class))
| ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
| ~ spl8_20
| ~ spl8_70 ),
inference(resolution,[],[f686,f356]) ).
fof(f686,plain,
( ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) )
| ~ spl8_70 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f3453,plain,
( spl8_211
| ~ spl8_33
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1648,f1500,f419,f3451]) ).
fof(f1648,plain,
( ! [X0,X1] : subclass(X0,union(X1,X0))
| ~ spl8_33
| ~ spl8_146 ),
inference(duplicate_literal_removal,[],[f1628]) ).
fof(f1628,plain,
( ! [X0,X1] :
( subclass(X0,union(X1,X0))
| subclass(X0,union(X1,X0)) )
| ~ spl8_33
| ~ spl8_146 ),
inference(resolution,[],[f1501,f420]) ).
fof(f3211,plain,
( spl8_210
| ~ spl8_22
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f725,f706,f364,f3209]) ).
fof(f3209,plain,
( spl8_210
<=> ! [X0,X1] :
( sK3(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK3(X1),sK3(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_210])]) ).
fof(f725,plain,
( ! [X0,X1] :
( sK3(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK3(X1),sK3(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) )
| ~ spl8_22
| ~ spl8_73 ),
inference(resolution,[],[f707,f365]) ).
fof(f3207,plain,
( spl8_209
| ~ spl8_15
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f723,f706,f335,f3205]) ).
fof(f3205,plain,
( spl8_209
<=> ! [X0,X1] :
( sK2(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2(X1),sK2(X1)))))
| ~ member(X0,universal_class)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_209])]) ).
fof(f723,plain,
( ! [X0,X1] :
( sK2(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2(X1),sK2(X1)))))
| ~ member(X0,universal_class)
| null_class = X1 )
| ~ spl8_15
| ~ spl8_73 ),
inference(resolution,[],[f707,f336]) ).
fof(f3203,plain,
( spl8_208
| ~ spl8_18
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f722,f706,f347,f3201]) ).
fof(f3201,plain,
( spl8_208
<=> ! [X0,X1] :
( power_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_208])]) ).
fof(f347,plain,
( spl8_18
<=> ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
fof(f722,plain,
( ! [X0,X1] :
( power_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl8_18
| ~ spl8_73 ),
inference(resolution,[],[f707,f348]) ).
fof(f348,plain,
( ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f3199,plain,
( spl8_207
| ~ spl8_19
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f721,f706,f351,f3197]) ).
fof(f351,plain,
( spl8_19
<=> ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
fof(f721,plain,
( ! [X0,X1] :
( sum_class(X1) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1)))))
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl8_19
| ~ spl8_73 ),
inference(resolution,[],[f707,f352]) ).
fof(f352,plain,
( ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) )
| ~ spl8_19 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f3195,plain,
( spl8_206
| ~ spl8_33
| ~ spl8_145 ),
inference(avatar_split_clause,[],[f1627,f1496,f419,f3193]) ).
fof(f1627,plain,
( ! [X0,X1] : subclass(X0,union(X0,X1))
| ~ spl8_33
| ~ spl8_145 ),
inference(duplicate_literal_removal,[],[f1607]) ).
fof(f1607,plain,
( ! [X0,X1] :
( subclass(X0,union(X0,X1))
| subclass(X0,union(X0,X1)) )
| ~ spl8_33
| ~ spl8_145 ),
inference(resolution,[],[f1497,f420]) ).
fof(f3191,plain,
( spl8_205
| ~ spl8_13
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f717,f706,f326,f3189]) ).
fof(f3189,plain,
( spl8_205
<=> ! [X2,X0,X1] :
( unordered_pair(X1,X2) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_205])]) ).
fof(f717,plain,
( ! [X2,X0,X1] :
( unordered_pair(X1,X2) = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2)))))
| ~ member(X0,universal_class) )
| ~ spl8_13
| ~ spl8_73 ),
inference(resolution,[],[f707,f327]) ).
fof(f3187,plain,
( spl8_204
| ~ spl8_50
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f703,f693,f544,f3185]) ).
fof(f3185,plain,
( spl8_204
<=> ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X2,sum_class(element_relation))
| ~ member(X2,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_204])]) ).
fof(f693,plain,
( spl8_72
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
fof(f703,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(X2,sum_class(element_relation))
| ~ member(X2,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) )
| ~ spl8_50
| ~ spl8_72 ),
inference(resolution,[],[f694,f545]) ).
fof(f694,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) )
| ~ spl8_72 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f3183,plain,
( spl8_203
| ~ spl8_50
| ~ spl8_71 ),
inference(avatar_split_clause,[],[f699,f689,f544,f3181]) ).
fof(f3181,plain,
( spl8_203
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_203])]) ).
fof(f699,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(X2,sum_class(universal_class))
| ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class))))) )
| ~ spl8_50
| ~ spl8_71 ),
inference(resolution,[],[f690,f545]) ).
fof(f2864,plain,
( spl8_202
| ~ spl8_34
| ~ spl8_144 ),
inference(avatar_split_clause,[],[f1603,f1492,f423,f2862]) ).
fof(f2862,plain,
( spl8_202
<=> ! [X0,X1] : subclass(intersection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_202])]) ).
fof(f1603,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X1)
| ~ spl8_34
| ~ spl8_144 ),
inference(duplicate_literal_removal,[],[f1579]) ).
fof(f1579,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) )
| ~ spl8_34
| ~ spl8_144 ),
inference(resolution,[],[f1493,f424]) ).
fof(f2755,plain,
( spl8_200
| spl8_201
| ~ spl8_12
| ~ spl8_78 ),
inference(avatar_split_clause,[],[f769,f761,f322,f2752,f2749]) ).
fof(f2749,plain,
( spl8_200
<=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_200])]) ).
fof(f2752,plain,
( spl8_201
<=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_201])]) ).
fof(f769,plain,
( ! [X0,X1] :
( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
| ~ inductive(cross_product(X0,X1)) )
| ~ spl8_12
| ~ spl8_78 ),
inference(resolution,[],[f762,f323]) ).
fof(f2747,plain,
( spl8_199
| ~ spl8_22
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f739,f710,f364,f2745]) ).
fof(f2745,plain,
( spl8_199
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK3(X1),sK3(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_199])]) ).
fof(f739,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK3(X1),sK3(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,identity_relation) )
| ~ spl8_22
| ~ spl8_74 ),
inference(resolution,[],[f711,f365]) ).
fof(f2743,plain,
( spl8_198
| ~ spl8_15
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f737,f710,f335,f2741]) ).
fof(f2741,plain,
( spl8_198
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2(X1),sK2(X1))))) = X0
| ~ member(X0,universal_class)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_198])]) ).
fof(f737,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK2(X1),sK2(X1))))) = X0
| ~ member(X0,universal_class)
| null_class = X1 )
| ~ spl8_15
| ~ spl8_74 ),
inference(resolution,[],[f711,f336]) ).
fof(f2739,plain,
( spl8_197
| ~ spl8_18
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f736,f710,f347,f2737]) ).
fof(f2737,plain,
( spl8_197
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_197])]) ).
fof(f736,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(power_class(X1),power_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl8_18
| ~ spl8_74 ),
inference(resolution,[],[f711,f348]) ).
fof(f2735,plain,
( spl8_196
| ~ spl8_19
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f735,f710,f351,f2733]) ).
fof(f735,plain,
( ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sum_class(X1),sum_class(X1))))) = X0
| ~ member(X0,universal_class)
| ~ member(X1,universal_class) )
| ~ spl8_19
| ~ spl8_74 ),
inference(resolution,[],[f711,f352]) ).
fof(f2731,plain,
( spl8_195
| ~ spl8_34
| ~ spl8_143 ),
inference(avatar_split_clause,[],[f1575,f1488,f423,f2729]) ).
fof(f2729,plain,
( spl8_195
<=> ! [X0,X1] : subclass(intersection(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_195])]) ).
fof(f1575,plain,
( ! [X0,X1] : subclass(intersection(X0,X1),X0)
| ~ spl8_34
| ~ spl8_143 ),
inference(duplicate_literal_removal,[],[f1551]) ).
fof(f1551,plain,
( ! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) )
| ~ spl8_34
| ~ spl8_143 ),
inference(resolution,[],[f1489,f424]) ).
fof(f2727,plain,
( spl8_194
| ~ spl8_45
| ~ spl8_72 ),
inference(avatar_split_clause,[],[f704,f693,f488,f2725]) ).
fof(f704,plain,
( ! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X1,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),X2)
| ~ subclass(element_relation,X2) )
| ~ spl8_45
| ~ spl8_72 ),
inference(resolution,[],[f694,f489]) ).
fof(f2723,plain,
( spl8_193
| ~ spl8_45
| ~ spl8_71 ),
inference(avatar_split_clause,[],[f700,f689,f488,f2721]) ).
fof(f2721,plain,
( spl8_193
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_193])]) ).
fof(f700,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ member(X1,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_45
| ~ spl8_71 ),
inference(resolution,[],[f690,f489]) ).
fof(f2719,plain,
( spl8_192
| ~ spl8_50
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f677,f659,f544,f2717]) ).
fof(f2717,plain,
( spl8_192
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X2,sum_class(domain_of(X0)))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_192])]) ).
fof(f677,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X2,sum_class(domain_of(X0)))
| ~ member(X2,X1) )
| ~ spl8_50
| ~ spl8_65 ),
inference(resolution,[],[f660,f545]) ).
fof(f2715,plain,
( spl8_191
| ~ spl8_43
| ~ spl8_55 ),
inference(avatar_split_clause,[],[f610,f590,f480,f2713]) ).
fof(f2713,plain,
( spl8_191
<=> ! [X0] :
( ~ function(X0)
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class))))
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_191])]) ).
fof(f610,plain,
( ! [X0] :
( ~ function(X0)
| identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class))))
| ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class))))) )
| ~ spl8_43
| ~ spl8_55 ),
inference(resolution,[],[f591,f481]) ).
fof(f2711,plain,
( spl8_190
| ~ spl8_47
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f609,f586,f496,f2709]) ).
fof(f2709,plain,
( spl8_190
<=> ! [X2,X0,X1] :
( sK5(X0,unordered_pair(X1,X2)) = X1
| sK5(X0,unordered_pair(X1,X2)) = X2
| ~ member(X0,sum_class(unordered_pair(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_190])]) ).
fof(f609,plain,
( ! [X2,X0,X1] :
( sK5(X0,unordered_pair(X1,X2)) = X1
| sK5(X0,unordered_pair(X1,X2)) = X2
| ~ member(X0,sum_class(unordered_pair(X1,X2))) )
| ~ spl8_47
| ~ spl8_54 ),
inference(resolution,[],[f587,f497]) ).
fof(f2707,plain,
( spl8_189
| ~ spl8_47
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f603,f578,f496,f2705]) ).
fof(f603,plain,
( ! [X2,X0,X1] :
( member(sK5(X0,union(X1,X2)),X1)
| member(sK5(X0,union(X1,X2)),X2)
| ~ member(X0,sum_class(union(X1,X2))) )
| ~ spl8_47
| ~ spl8_52 ),
inference(resolution,[],[f579,f497]) ).
fof(f2514,plain,
( spl8_188
| ~ spl8_13
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f731,f710,f326,f2512]) ).
fof(f2512,plain,
( spl8_188
<=> ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2))))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_188])]) ).
fof(f731,plain,
( ! [X2,X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X2))))) = X0
| ~ member(X0,universal_class) )
| ~ spl8_13
| ~ spl8_74 ),
inference(resolution,[],[f711,f327]) ).
fof(f2510,plain,
( spl8_187
| ~ spl8_45
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f678,f659,f488,f2508]) ).
fof(f2508,plain,
( spl8_187
<=> ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X1,X2)
| ~ subclass(domain_of(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_187])]) ).
fof(f678,plain,
( ! [X2,X0,X1] :
( null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class)
| member(X1,X2)
| ~ subclass(domain_of(X0),X2) )
| ~ spl8_45
| ~ spl8_65 ),
inference(resolution,[],[f660,f489]) ).
fof(f2506,plain,
( spl8_186
| ~ spl8_33
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f608,f586,f419,f2504]) ).
fof(f2504,plain,
( spl8_186
<=> ! [X2,X0,X1] :
( sK4(unordered_pair(X0,X1),X2) = X0
| sK4(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_186])]) ).
fof(f608,plain,
( ! [X2,X0,X1] :
( sK4(unordered_pair(X0,X1),X2) = X0
| sK4(unordered_pair(X0,X1),X2) = X1
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl8_33
| ~ spl8_54 ),
inference(resolution,[],[f587,f420]) ).
fof(f2502,plain,
( spl8_185
| ~ spl8_33
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f602,f578,f419,f2500]) ).
fof(f602,plain,
( ! [X2,X0,X1] :
( member(sK4(union(X0,X1),X2),X0)
| member(sK4(union(X0,X1),X2),X1)
| subclass(union(X0,X1),X2) )
| ~ spl8_33
| ~ spl8_52 ),
inference(resolution,[],[f579,f420]) ).
fof(f2498,plain,
( spl8_184
| ~ spl8_34
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f595,f574,f423,f2496]) ).
fof(f574,plain,
( spl8_51
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
fof(f595,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,intersection(X1,X2)),X2)
| ~ member(sK4(X0,intersection(X1,X2)),X1)
| subclass(X0,intersection(X1,X2)) )
| ~ spl8_34
| ~ spl8_51 ),
inference(resolution,[],[f575,f424]) ).
fof(f575,plain,
( ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ spl8_51 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f2470,plain,
( ~ spl8_182
| spl8_183
| ~ spl8_12
| ~ spl8_76 ),
inference(avatar_split_clause,[],[f752,f744,f322,f2467,f2463]) ).
fof(f2463,plain,
( spl8_182
<=> inductive(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_182])]) ).
fof(f2467,plain,
( spl8_183
<=> null_class = unordered_pair(unordered_pair(sK3(null_class),sK3(null_class)),unordered_pair(sK3(null_class),unordered_pair(sK3(null_class),sK3(null_class)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_183])]) ).
fof(f752,plain,
( null_class = unordered_pair(unordered_pair(sK3(null_class),sK3(null_class)),unordered_pair(sK3(null_class),unordered_pair(sK3(null_class),sK3(null_class))))
| ~ inductive(identity_relation)
| ~ spl8_12
| ~ spl8_76 ),
inference(resolution,[],[f745,f323]) ).
fof(f2457,plain,
( spl8_181
| ~ spl8_50
| ~ spl8_62 ),
inference(avatar_split_clause,[],[f646,f642,f544,f2455]) ).
fof(f646,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X1,sum_class(identity_relation))
| ~ member(X1,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0)))) )
| ~ spl8_50
| ~ spl8_62 ),
inference(resolution,[],[f643,f545]) ).
fof(f2295,plain,
( spl8_180
| ~ spl8_45
| ~ spl8_62 ),
inference(avatar_split_clause,[],[f647,f642,f488,f2293]) ).
fof(f647,plain,
( ! [X0,X1] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X0,X0))),X1)
| ~ subclass(identity_relation,X1) )
| ~ spl8_45
| ~ spl8_62 ),
inference(resolution,[],[f643,f489]) ).
fof(f2291,plain,
( spl8_179
| ~ spl8_16
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f607,f586,f339,f2289]) ).
fof(f607,plain,
( ! [X0,X1] :
( sK2(unordered_pair(X0,X1)) = X0
| sK2(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class )
| ~ spl8_16
| ~ spl8_54 ),
inference(resolution,[],[f587,f340]) ).
fof(f2287,plain,
( spl8_178
| ~ spl8_16
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f601,f578,f339,f2285]) ).
fof(f601,plain,
( ! [X0,X1] :
( member(sK2(union(X0,X1)),X0)
| member(sK2(union(X0,X1)),X1)
| null_class = union(X0,X1) )
| ~ spl8_16
| ~ spl8_52 ),
inference(resolution,[],[f579,f340]) ).
fof(f2250,plain,
( spl8_177
| ~ spl8_16
| ~ spl8_156 ),
inference(avatar_split_clause,[],[f1846,f1664,f339,f2247]) ).
fof(f2247,plain,
( spl8_177
<=> null_class = domain_of(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_177])]) ).
fof(f1664,plain,
( spl8_156
<=> ! [X0] : ~ member(X0,domain_of(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_156])]) ).
fof(f1846,plain,
( null_class = domain_of(null_class)
| ~ spl8_16
| ~ spl8_156 ),
inference(resolution,[],[f1665,f340]) ).
fof(f1665,plain,
( ! [X0] : ~ member(X0,domain_of(null_class))
| ~ spl8_156 ),
inference(avatar_component_clause,[],[f1664]) ).
fof(f2245,plain,
( spl8_176
| ~ spl8_34
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f553,f540,f423,f2243]) ).
fof(f540,plain,
( spl8_49
<=> ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
fof(f553,plain,
( ! [X0,X1] :
( ~ subclass(sK4(X0,power_class(X1)),X1)
| ~ member(sK4(X0,power_class(X1)),universal_class)
| subclass(X0,power_class(X1)) )
| ~ spl8_34
| ~ spl8_49 ),
inference(resolution,[],[f541,f424]) ).
fof(f541,plain,
( ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
| ~ spl8_49 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f2241,plain,
( spl8_175
| ~ spl8_34
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f549,f536,f423,f2239]) ).
fof(f536,plain,
( spl8_48
<=> ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
fof(f549,plain,
( ! [X0,X1] :
( member(sK4(X0,complement(X1)),X1)
| ~ member(sK4(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) )
| ~ spl8_34
| ~ spl8_48 ),
inference(resolution,[],[f537,f424]) ).
fof(f537,plain,
( ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
| ~ spl8_48 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f2237,plain,
( spl8_174
| ~ spl8_32
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f504,f480,f415,f2235]) ).
fof(f2235,plain,
( spl8_174
<=> ! [X0] :
( cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_174])]) ).
fof(f504,plain,
( ! [X0] :
( cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0)) )
| ~ spl8_32
| ~ spl8_43 ),
inference(resolution,[],[f481,f416]) ).
fof(f2233,plain,
( spl8_173
| ~ spl8_31
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f503,f480,f411,f2231]) ).
fof(f2231,plain,
( spl8_173
<=> ! [X0] :
( rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_173])]) ).
fof(f503,plain,
( ! [X0] :
( rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class)
| ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0)) )
| ~ spl8_31
| ~ spl8_43 ),
inference(resolution,[],[f481,f412]) ).
fof(f2107,plain,
( spl8_172
| ~ spl8_8
| ~ spl8_74 ),
inference(avatar_split_clause,[],[f742,f710,f303,f2105]) ).
fof(f742,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7,sK7)))) = X0
| ~ member(X0,universal_class) )
| ~ spl8_8
| ~ spl8_74 ),
inference(resolution,[],[f711,f305]) ).
fof(f2103,plain,
( spl8_171
| ~ spl8_8
| ~ spl8_73 ),
inference(avatar_split_clause,[],[f728,f706,f303,f2101]) ).
fof(f728,plain,
( ! [X0] :
( sK7 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK7,sK7))))
| ~ member(X0,universal_class) )
| ~ spl8_8
| ~ spl8_73 ),
inference(resolution,[],[f707,f305]) ).
fof(f2098,plain,
( ~ spl8_170
| ~ spl8_99
| ~ spl8_156 ),
inference(avatar_split_clause,[],[f1841,f1664,f896,f2095]) ).
fof(f2095,plain,
( spl8_170
<=> subclass(universal_class,domain_of(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_170])]) ).
fof(f1841,plain,
( ~ subclass(universal_class,domain_of(null_class))
| ~ spl8_99
| ~ spl8_156 ),
inference(resolution,[],[f1665,f897]) ).
fof(f2093,plain,
( spl8_169
| ~ spl8_50
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f596,f574,f544,f2091]) ).
fof(f596,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X3,sum_class(intersection(X2,X1)))
| ~ member(X3,X0) )
| ~ spl8_50
| ~ spl8_51 ),
inference(resolution,[],[f575,f545]) ).
fof(f2015,plain,
( spl8_168
| ~ spl8_45
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f597,f574,f488,f2013]) ).
fof(f597,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,X3)
| ~ subclass(intersection(X2,X1),X3) )
| ~ spl8_45
| ~ spl8_51 ),
inference(resolution,[],[f575,f489]) ).
fof(f2011,plain,
( spl8_167
| ~ spl8_49
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f560,f544,f540,f2009]) ).
fof(f560,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(power_class(X1)))
| ~ member(X0,X2)
| ~ subclass(X2,X1)
| ~ member(X2,universal_class) )
| ~ spl8_49
| ~ spl8_50 ),
inference(resolution,[],[f545,f541]) ).
fof(f2007,plain,
( spl8_166
| ~ spl8_48
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f557,f544,f536,f2005]) ).
fof(f557,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(complement(X1)))
| ~ member(X0,X2)
| member(X2,X1)
| ~ member(X2,universal_class) )
| ~ spl8_48
| ~ spl8_50 ),
inference(resolution,[],[f545,f537]) ).
fof(f2003,plain,
( spl8_165
| ~ spl8_23
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f506,f480,f368,f2001]) ).
fof(f2001,plain,
( spl8_165
<=> ! [X0,X1] :
( cross_product(universal_class,universal_class) = compose(X0,X1)
| ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_165])]) ).
fof(f506,plain,
( ! [X0,X1] :
( cross_product(universal_class,universal_class) = compose(X0,X1)
| ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1)) )
| ~ spl8_23
| ~ spl8_43 ),
inference(resolution,[],[f481,f369]) ).
fof(f1977,plain,
( ~ spl8_164
| ~ spl8_12
| ~ spl8_156 ),
inference(avatar_split_clause,[],[f1842,f1664,f322,f1974]) ).
fof(f1974,plain,
( spl8_164
<=> inductive(domain_of(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_164])]) ).
fof(f1842,plain,
( ~ inductive(domain_of(null_class))
| ~ spl8_12
| ~ spl8_156 ),
inference(resolution,[],[f1665,f323]) ).
fof(f1884,plain,
( spl8_163
| ~ spl8_47
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f571,f544,f496,f1882]) ).
fof(f571,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK5(X2,X1))
| ~ member(X2,sum_class(X1)) )
| ~ spl8_47
| ~ spl8_50 ),
inference(resolution,[],[f545,f497]) ).
fof(f1880,plain,
( spl8_162
| ~ spl8_46
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f561,f544,f492,f1878]) ).
fof(f1878,plain,
( spl8_162
<=> ! [X2,X0,X1] :
( member(X0,sum_class(sK5(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,sum_class(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_162])]) ).
fof(f561,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(sK5(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,sum_class(X2)) )
| ~ spl8_46
| ~ spl8_50 ),
inference(resolution,[],[f545,f493]) ).
fof(f1876,plain,
( spl8_161
| ~ spl8_45
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f554,f540,f488,f1874]) ).
fof(f554,plain,
( ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(power_class(X1),X2) )
| ~ spl8_45
| ~ spl8_49 ),
inference(resolution,[],[f541,f489]) ).
fof(f1872,plain,
( spl8_160
| ~ spl8_45
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f550,f536,f488,f1870]) ).
fof(f550,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| member(X0,X2)
| ~ subclass(complement(X1),X2) )
| ~ spl8_45
| ~ spl8_48 ),
inference(resolution,[],[f537,f489]) ).
fof(f1839,plain,
( spl8_159
| ~ spl8_35
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f528,f496,f427,f1837]) ).
fof(f528,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK5(X0,intersection(X1,X2)),X1) )
| ~ spl8_35
| ~ spl8_47 ),
inference(resolution,[],[f497,f428]) ).
fof(f1835,plain,
( spl8_158
| ~ spl8_36
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f527,f496,f431,f1833]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(intersection(X1,X2)))
| member(sK5(X0,intersection(X1,X2)),X2) )
| ~ spl8_36
| ~ spl8_47 ),
inference(resolution,[],[f497,f432]) ).
fof(f1831,plain,
( spl8_157
| ~ spl8_39
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f526,f496,f443,f1829]) ).
fof(f1829,plain,
( spl8_157
<=> ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| member(sK5(X0,unordered_pair(X1,X2)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_157])]) ).
fof(f526,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(unordered_pair(X1,X2)))
| member(sK5(X0,unordered_pair(X1,X2)),universal_class) )
| ~ spl8_39
| ~ spl8_47 ),
inference(resolution,[],[f497,f444]) ).
fof(f1666,plain,
( spl8_156
| ~ spl8_56
| ~ spl8_141 ),
inference(avatar_split_clause,[],[f1534,f1358,f612,f1664]) ).
fof(f612,plain,
( spl8_56
<=> ! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
fof(f1358,plain,
( spl8_141
<=> ! [X0] : null_class = intersection(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_141])]) ).
fof(f1534,plain,
( ! [X0] : ~ member(X0,domain_of(null_class))
| ~ spl8_56
| ~ spl8_141 ),
inference(trivial_inequality_removal,[],[f1531]) ).
fof(f1531,plain,
( ! [X0] :
( null_class != null_class
| ~ member(X0,domain_of(null_class)) )
| ~ spl8_56
| ~ spl8_141 ),
inference(superposition,[],[f613,f1359]) ).
fof(f1359,plain,
( ! [X0] : null_class = intersection(null_class,X0)
| ~ spl8_141 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f613,plain,
( ! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) )
| ~ spl8_56 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f1550,plain,
( spl8_155
| ~ spl8_33
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f570,f544,f419,f1548]) ).
fof(f570,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK4(X1,X2))
| subclass(X1,X2) )
| ~ spl8_33
| ~ spl8_50 ),
inference(resolution,[],[f545,f420]) ).
fof(f1546,plain,
( spl8_154
| ~ spl8_37
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f559,f544,f435,f1544]) ).
fof(f559,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X1) )
| ~ spl8_37
| ~ spl8_50 ),
inference(resolution,[],[f545,f436]) ).
fof(f1542,plain,
( spl8_153
| ~ spl8_38
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f558,f544,f439,f1540]) ).
fof(f558,plain,
( ! [X2,X3,X0,X1] :
( member(X0,sum_class(union(X1,X2)))
| ~ member(X0,X3)
| ~ member(X3,X2) )
| ~ spl8_38
| ~ spl8_50 ),
inference(resolution,[],[f545,f440]) ).
fof(f1538,plain,
( spl8_152
| ~ spl8_41
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f556,f544,f451,f1536]) ).
fof(f556,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
| ~ spl8_41
| ~ spl8_50 ),
inference(resolution,[],[f545,f452]) ).
fof(f1522,plain,
( spl8_151
| ~ spl8_40
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f555,f544,f447,f1520]) ).
fof(f555,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(unordered_pair(X1,X2)))
| ~ member(X0,X2)
| ~ member(X2,universal_class) )
| ~ spl8_40
| ~ spl8_50 ),
inference(resolution,[],[f545,f448]) ).
fof(f1518,plain,
( spl8_150
| ~ spl8_45
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f525,f496,f488,f1516]) ).
fof(f525,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(sK5(X0,X1),X2)
| ~ subclass(X1,X2) )
| ~ spl8_45
| ~ spl8_47 ),
inference(resolution,[],[f497,f489]) ).
fof(f1514,plain,
( spl8_149
| ~ spl8_45
| ~ spl8_46 ),
inference(avatar_split_clause,[],[f524,f492,f488,f1512]) ).
fof(f524,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sum_class(X1))
| member(X0,X2)
| ~ subclass(sK5(X0,X1),X2) )
| ~ spl8_45
| ~ spl8_46 ),
inference(resolution,[],[f493,f489]) ).
fof(f1510,plain,
( spl8_148
| ~ spl8_20
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f501,f480,f355,f1508]) ).
fof(f1508,plain,
( spl8_148
<=> ! [X0] :
( cross_product(universal_class,universal_class) = X0
| ~ subclass(cross_product(universal_class,universal_class),X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_148])]) ).
fof(f501,plain,
( ! [X0] :
( cross_product(universal_class,universal_class) = X0
| ~ subclass(cross_product(universal_class,universal_class),X0)
| ~ function(X0) )
| ~ spl8_20
| ~ spl8_43 ),
inference(resolution,[],[f481,f356]) ).
fof(f1506,plain,
( spl8_147
| ~ spl8_33
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f472,f443,f419,f1504]) ).
fof(f472,plain,
( ! [X2,X0,X1] :
( member(sK4(unordered_pair(X0,X1),X2),universal_class)
| subclass(unordered_pair(X0,X1),X2) )
| ~ spl8_33
| ~ spl8_39 ),
inference(resolution,[],[f444,f420]) ).
fof(f1502,plain,
( spl8_146
| ~ spl8_34
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f469,f439,f423,f1500]) ).
fof(f469,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X2)
| subclass(X0,union(X1,X2)) )
| ~ spl8_34
| ~ spl8_38 ),
inference(resolution,[],[f440,f424]) ).
fof(f1498,plain,
( spl8_145
| ~ spl8_34
| ~ spl8_37 ),
inference(avatar_split_clause,[],[f468,f435,f423,f1496]) ).
fof(f468,plain,
( ! [X2,X0,X1] :
( ~ member(sK4(X0,union(X1,X2)),X1)
| subclass(X0,union(X1,X2)) )
| ~ spl8_34
| ~ spl8_37 ),
inference(resolution,[],[f436,f424]) ).
fof(f1494,plain,
( spl8_144
| ~ spl8_33
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f467,f431,f419,f1492]) ).
fof(f467,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) )
| ~ spl8_33
| ~ spl8_36 ),
inference(resolution,[],[f432,f420]) ).
fof(f1490,plain,
( spl8_143
| ~ spl8_33
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f464,f427,f419,f1488]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( member(sK4(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) )
| ~ spl8_33
| ~ spl8_35 ),
inference(resolution,[],[f428,f420]) ).
fof(f1472,plain,
( spl8_142
| ~ spl8_6
| ~ spl8_124 ),
inference(avatar_split_clause,[],[f1335,f1231,f295,f1470]) ).
fof(f1470,plain,
( spl8_142
<=> ! [X0] : null_class = intersection(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_142])]) ).
fof(f1335,plain,
( ! [X0] : null_class = intersection(X0,null_class)
| ~ spl8_6
| ~ spl8_124 ),
inference(resolution,[],[f1232,f296]) ).
fof(f1360,plain,
( spl8_141
| ~ spl8_6
| ~ spl8_123 ),
inference(avatar_split_clause,[],[f1313,f1227,f295,f1358]) ).
fof(f1313,plain,
( ! [X0] : null_class = intersection(null_class,X0)
| ~ spl8_6
| ~ spl8_123 ),
inference(resolution,[],[f1228,f296]) ).
fof(f1300,plain,
( spl8_140
| ~ spl8_22
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f569,f544,f364,f1298]) ).
fof(f569,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK3(X1))
| ~ member(X1,identity_relation) )
| ~ spl8_22
| ~ spl8_50 ),
inference(resolution,[],[f545,f365]) ).
fof(f1296,plain,
( spl8_139
| ~ spl8_16
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f568,f544,f339,f1294]) ).
fof(f568,plain,
( ! [X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X0,sK2(X1))
| null_class = X1 )
| ~ spl8_16
| ~ spl8_50 ),
inference(resolution,[],[f545,f340]) ).
fof(f1292,plain,
( spl8_138
| ~ spl8_15
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f567,f544,f335,f1290]) ).
fof(f567,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK2(X1))
| null_class = X1 )
| ~ spl8_15
| ~ spl8_50 ),
inference(resolution,[],[f545,f336]) ).
fof(f1288,plain,
( spl8_137
| ~ spl8_18
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f566,f544,f347,f1286]) ).
fof(f566,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,power_class(X1))
| ~ member(X1,universal_class) )
| ~ spl8_18
| ~ spl8_50 ),
inference(resolution,[],[f545,f348]) ).
fof(f1281,plain,
( spl8_136
| ~ spl8_19
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f565,f544,f351,f1279]) ).
fof(f565,plain,
( ! [X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sum_class(X1))
| ~ member(X1,universal_class) )
| ~ spl8_19
| ~ spl8_50 ),
inference(resolution,[],[f545,f352]) ).
fof(f1277,plain,
( spl8_135
| ~ spl8_26
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f534,f496,f380,f1275]) ).
fof(f534,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| member(sK5(X0,power_class(X1)),universal_class) )
| ~ spl8_26
| ~ spl8_47 ),
inference(resolution,[],[f497,f381]) ).
fof(f1273,plain,
( spl8_134
| ~ spl8_27
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f533,f496,f384,f1271]) ).
fof(f533,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(power_class(X1)))
| subclass(sK5(X0,power_class(X1)),X1) )
| ~ spl8_27
| ~ spl8_47 ),
inference(resolution,[],[f497,f385]) ).
fof(f1269,plain,
( spl8_133
| ~ spl8_28
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f532,f496,f388,f1267]) ).
fof(f532,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(domain_of(X1)))
| member(sK5(X0,domain_of(X1)),universal_class) )
| ~ spl8_28
| ~ spl8_47 ),
inference(resolution,[],[f497,f389]) ).
fof(f1265,plain,
( spl8_132
| ~ spl8_24
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f530,f496,f372,f1263]) ).
fof(f530,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| member(sK5(X0,complement(X1)),universal_class) )
| ~ spl8_24
| ~ spl8_47 ),
inference(resolution,[],[f497,f373]) ).
fof(f1261,plain,
( spl8_131
| ~ spl8_25
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f529,f496,f376,f1259]) ).
fof(f529,plain,
( ! [X0,X1] :
( ~ member(X0,sum_class(complement(X1)))
| ~ member(sK5(X0,complement(X1)),X1) )
| ~ spl8_25
| ~ spl8_47 ),
inference(resolution,[],[f497,f377]) ).
fof(f1257,plain,
( spl8_130
| ~ spl8_33
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f521,f488,f419,f1255]) ).
fof(f521,plain,
( ! [X2,X0,X1] :
( member(sK4(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) )
| ~ spl8_33
| ~ spl8_45 ),
inference(resolution,[],[f489,f420]) ).
fof(f1253,plain,
( spl8_129
| ~ spl8_41
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f512,f488,f451,f1251]) ).
fof(f512,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X0,X2),X1)
| ~ member(X0,universal_class) )
| ~ spl8_41
| ~ spl8_45 ),
inference(resolution,[],[f489,f452]) ).
fof(f1249,plain,
( spl8_128
| ~ spl8_40
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f511,f488,f447,f1247]) ).
fof(f511,plain,
( ! [X2,X0,X1] :
( member(X0,X1)
| ~ subclass(unordered_pair(X2,X0),X1)
| ~ member(X0,universal_class) )
| ~ spl8_40
| ~ spl8_45 ),
inference(resolution,[],[f489,f448]) ).
fof(f1245,plain,
( spl8_127
| ~ spl8_37
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f510,f488,f435,f1243]) ).
fof(f510,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X2) )
| ~ spl8_37
| ~ spl8_45 ),
inference(resolution,[],[f489,f436]) ).
fof(f1241,plain,
( spl8_126
| ~ spl8_42
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f523,f480,f474,f1239]) ).
fof(f1239,plain,
( spl8_126
<=> ! [X0] :
( null_class = X0
| ~ subclass(X0,null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_126])]) ).
fof(f474,plain,
( spl8_42
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
fof(f523,plain,
( ! [X0] :
( null_class = X0
| ~ subclass(X0,null_class) )
| ~ spl8_42
| ~ spl8_43 ),
inference(resolution,[],[f475,f481]) ).
fof(f475,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl8_42 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f1237,plain,
( spl8_125
| ~ spl8_38
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f509,f488,f439,f1235]) ).
fof(f509,plain,
( ! [X2,X3,X0,X1] :
( member(X0,X1)
| ~ subclass(union(X2,X3),X1)
| ~ member(X0,X3) )
| ~ spl8_38
| ~ spl8_45 ),
inference(resolution,[],[f489,f440]) ).
fof(f1233,plain,
( spl8_124
| ~ spl8_16
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f466,f431,f339,f1231]) ).
fof(f466,plain,
( ! [X0,X1] :
( member(sK2(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class )
| ~ spl8_16
| ~ spl8_36 ),
inference(resolution,[],[f432,f340]) ).
fof(f1229,plain,
( spl8_123
| ~ spl8_16
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f463,f427,f339,f1227]) ).
fof(f463,plain,
( ! [X0,X1] :
( member(sK2(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class )
| ~ spl8_16
| ~ spl8_35 ),
inference(resolution,[],[f428,f340]) ).
fof(f1066,plain,
( spl8_122
| ~ spl8_12
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f606,f586,f322,f1064]) ).
fof(f1064,plain,
( spl8_122
<=> ! [X0,X1] :
( null_class = X0
| null_class = X1
| ~ inductive(unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_122])]) ).
fof(f606,plain,
( ! [X0,X1] :
( null_class = X0
| null_class = X1
| ~ inductive(unordered_pair(X0,X1)) )
| ~ spl8_12
| ~ spl8_54 ),
inference(resolution,[],[f587,f323]) ).
fof(f1062,plain,
( spl8_121
| ~ spl8_12
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f600,f578,f322,f1060]) ).
fof(f1060,plain,
( spl8_121
<=> ! [X0,X1] :
( member(null_class,X0)
| member(null_class,X1)
| ~ inductive(union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_121])]) ).
fof(f600,plain,
( ! [X0,X1] :
( member(null_class,X0)
| member(null_class,X1)
| ~ inductive(union(X0,X1)) )
| ~ spl8_12
| ~ spl8_52 ),
inference(resolution,[],[f579,f323]) ).
fof(f1058,plain,
( spl8_120
| ~ spl8_22
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f520,f488,f364,f1056]) ).
fof(f520,plain,
( ! [X0,X1] :
( member(sK3(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,identity_relation) )
| ~ spl8_22
| ~ spl8_45 ),
inference(resolution,[],[f489,f365]) ).
fof(f1054,plain,
( spl8_119
| ~ spl8_16
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f519,f488,f339,f1052]) ).
fof(f519,plain,
( ! [X0,X1] :
( member(sK2(X0),X1)
| ~ subclass(X0,X1)
| null_class = X0 )
| ~ spl8_16
| ~ spl8_45 ),
inference(resolution,[],[f489,f340]) ).
fof(f1050,plain,
( spl8_118
| ~ spl8_15
| ~ spl8_101 ),
inference(avatar_split_clause,[],[f980,f956,f335,f1047]) ).
fof(f1047,plain,
( spl8_118
<=> null_class = complement(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_118])]) ).
fof(f980,plain,
( null_class = complement(universal_class)
| ~ spl8_15
| ~ spl8_101 ),
inference(duplicate_literal_removal,[],[f972]) ).
fof(f972,plain,
( null_class = complement(universal_class)
| null_class = complement(universal_class)
| ~ spl8_15
| ~ spl8_101 ),
inference(resolution,[],[f957,f336]) ).
fof(f1045,plain,
( spl8_117
| ~ spl8_15
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f518,f488,f335,f1043]) ).
fof(f518,plain,
( ! [X0,X1] :
( member(sK2(X0),X1)
| ~ subclass(universal_class,X1)
| null_class = X0 )
| ~ spl8_15
| ~ spl8_45 ),
inference(resolution,[],[f489,f336]) ).
fof(f1041,plain,
( spl8_116
| ~ spl8_18
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f517,f488,f347,f1039]) ).
fof(f517,plain,
( ! [X0,X1] :
( member(power_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl8_18
| ~ spl8_45 ),
inference(resolution,[],[f489,f348]) ).
fof(f1037,plain,
( spl8_115
| ~ spl8_19
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f516,f488,f351,f1035]) ).
fof(f516,plain,
( ! [X0,X1] :
( member(sum_class(X0),X1)
| ~ subclass(universal_class,X1)
| ~ member(X0,universal_class) )
| ~ spl8_19
| ~ spl8_45 ),
inference(resolution,[],[f489,f352]) ).
fof(f1033,plain,
( spl8_114
| ~ spl8_17
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f508,f484,f343,f1031]) ).
fof(f343,plain,
( spl8_17
<=> ! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
fof(f484,plain,
( spl8_44
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
fof(f508,plain,
( ! [X0,X1] :
( ~ member(X0,sK2(X1))
| ~ member(X0,X1)
| null_class = X1 )
| ~ spl8_17
| ~ spl8_44 ),
inference(resolution,[],[f485,f344]) ).
fof(f344,plain,
( ! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 )
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f485,plain,
( ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ member(X2,X0)
| ~ member(X2,X1) )
| ~ spl8_44 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f1029,plain,
( ~ spl8_112
| spl8_113
| ~ spl8_11
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f505,f480,f317,f1026,f1022]) ).
fof(f1022,plain,
( spl8_112
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_112])]) ).
fof(f1026,plain,
( spl8_113
<=> cross_product(universal_class,universal_class) = successor_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl8_113])]) ).
fof(f505,plain,
( cross_product(universal_class,universal_class) = successor_relation
| ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| ~ spl8_11
| ~ spl8_43 ),
inference(resolution,[],[f481,f319]) ).
fof(f1020,plain,
( ~ spl8_110
| spl8_111
| ~ spl8_10
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f502,f480,f312,f1017,f1013]) ).
fof(f1013,plain,
( spl8_110
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_110])]) ).
fof(f1017,plain,
( spl8_111
<=> element_relation = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_111])]) ).
fof(f502,plain,
( element_relation = cross_product(universal_class,universal_class)
| ~ subclass(cross_product(universal_class,universal_class),element_relation)
| ~ spl8_10
| ~ spl8_43 ),
inference(resolution,[],[f481,f314]) ).
fof(f1011,plain,
( spl8_109
| ~ spl8_26
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f459,f419,f380,f1009]) ).
fof(f459,plain,
( ! [X0,X1] :
( subclass(power_class(X0),X1)
| member(sK4(power_class(X0),X1),universal_class) )
| ~ spl8_26
| ~ spl8_33 ),
inference(resolution,[],[f420,f381]) ).
fof(f1007,plain,
( spl8_108
| ~ spl8_27
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f458,f419,f384,f1005]) ).
fof(f458,plain,
( ! [X0,X1] :
( subclass(power_class(X0),X1)
| subclass(sK4(power_class(X0),X1),X0) )
| ~ spl8_27
| ~ spl8_33 ),
inference(resolution,[],[f420,f385]) ).
fof(f1003,plain,
( spl8_107
| ~ spl8_28
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f457,f419,f388,f1001]) ).
fof(f457,plain,
( ! [X0,X1] :
( subclass(domain_of(X0),X1)
| member(sK4(domain_of(X0),X1),universal_class) )
| ~ spl8_28
| ~ spl8_33 ),
inference(resolution,[],[f420,f389]) ).
fof(f999,plain,
( spl8_106
| ~ spl8_24
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f455,f419,f372,f997]) ).
fof(f455,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| member(sK4(complement(X0),X1),universal_class) )
| ~ spl8_24
| ~ spl8_33 ),
inference(resolution,[],[f420,f373]) ).
fof(f995,plain,
( spl8_105
| ~ spl8_25
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f454,f419,f376,f993]) ).
fof(f454,plain,
( ! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(sK4(complement(X0),X1),X0) )
| ~ spl8_25
| ~ spl8_33 ),
inference(resolution,[],[f420,f377]) ).
fof(f971,plain,
( spl8_104
| ~ spl8_13
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f562,f544,f326,f969]) ).
fof(f562,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,unordered_pair(X1,X2)) )
| ~ spl8_13
| ~ spl8_50 ),
inference(resolution,[],[f545,f327]) ).
fof(f967,plain,
( spl8_103
| ~ spl8_16
| ~ spl8_27 ),
inference(avatar_split_clause,[],[f399,f384,f339,f965]) ).
fof(f399,plain,
( ! [X0] :
( subclass(sK2(power_class(X0)),X0)
| null_class = power_class(X0) )
| ~ spl8_16
| ~ spl8_27 ),
inference(resolution,[],[f385,f340]) ).
fof(f963,plain,
( ~ spl8_102
| ~ spl8_6
| ~ spl8_99 ),
inference(avatar_split_clause,[],[f925,f896,f295,f960]) ).
fof(f960,plain,
( spl8_102
<=> subclass(universal_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).
fof(f925,plain,
( ~ subclass(universal_class,null_class)
| ~ spl8_6
| ~ spl8_99 ),
inference(resolution,[],[f897,f296]) ).
fof(f958,plain,
( spl8_101
| ~ spl8_16
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f395,f376,f339,f956]) ).
fof(f395,plain,
( ! [X0] :
( ~ member(sK2(complement(X0)),X0)
| complement(X0) = null_class )
| ~ spl8_16
| ~ spl8_25 ),
inference(resolution,[],[f377,f340]) ).
fof(f902,plain,
( spl8_100
| ~ spl8_12
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f514,f488,f322,f900]) ).
fof(f514,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ subclass(X1,X0)
| ~ inductive(X1) )
| ~ spl8_12
| ~ spl8_45 ),
inference(resolution,[],[f489,f323]) ).
fof(f898,plain,
( spl8_99
| ~ spl8_13
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f513,f488,f326,f896]) ).
fof(f513,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl8_13
| ~ spl8_45 ),
inference(resolution,[],[f489,f327]) ).
fof(f890,plain,
( spl8_98
| spl8_30
| ~ spl8_12
| ~ spl8_26 ),
inference(avatar_split_clause,[],[f396,f380,f322,f406,f888]) ).
fof(f396,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(power_class(X0)) )
| ~ spl8_12
| ~ spl8_26 ),
inference(resolution,[],[f381,f323]) ).
fof(f885,plain,
( spl8_97
| ~ spl8_30
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f515,f488,f406,f883]) ).
fof(f515,plain,
( ! [X0] :
( member(null_class,X0)
| ~ subclass(universal_class,X0) )
| ~ spl8_30
| ~ spl8_45 ),
inference(resolution,[],[f489,f408]) ).
fof(f881,plain,
( spl8_96
| ~ spl8_14
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f507,f480,f330,f879]) ).
fof(f330,plain,
( spl8_14
<=> ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
fof(f507,plain,
( ! [X0] :
( sK7 = X0
| ~ subclass(X0,sK7)
| ~ inductive(X0) )
| ~ spl8_14
| ~ spl8_43 ),
inference(resolution,[],[f481,f331]) ).
fof(f331,plain,
( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f874,plain,
( spl8_95
| ~ spl8_8
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f572,f544,f303,f872]) ).
fof(f572,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK7) )
| ~ spl8_8
| ~ spl8_50 ),
inference(resolution,[],[f545,f305]) ).
fof(f870,plain,
( spl8_94
| ~ spl8_12
| ~ spl8_36 ),
inference(avatar_split_clause,[],[f465,f431,f322,f868]) ).
fof(f868,plain,
( spl8_94
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_94])]) ).
fof(f465,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl8_12
| ~ spl8_36 ),
inference(resolution,[],[f432,f323]) ).
fof(f866,plain,
( spl8_93
| ~ spl8_12
| ~ spl8_35 ),
inference(avatar_split_clause,[],[f462,f427,f322,f864]) ).
fof(f864,plain,
( spl8_93
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_93])]) ).
fof(f462,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl8_12
| ~ spl8_35 ),
inference(resolution,[],[f428,f323]) ).
fof(f856,plain,
( spl8_92
| ~ spl8_8
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f522,f488,f303,f854]) ).
fof(f522,plain,
( ! [X0] :
( member(sK7,X0)
| ~ subclass(universal_class,X0) )
| ~ spl8_8
| ~ spl8_45 ),
inference(resolution,[],[f489,f305]) ).
fof(f852,plain,
( spl8_91
| ~ spl8_7
| ~ spl8_43 ),
inference(avatar_split_clause,[],[f499,f480,f299,f850]) ).
fof(f499,plain,
( ! [X0] :
( universal_class = X0
| ~ subclass(universal_class,X0) )
| ~ spl8_7
| ~ spl8_43 ),
inference(resolution,[],[f481,f300]) ).
fof(f848,plain,
( spl8_90
| ~ spl8_12
| ~ spl8_25 ),
inference(avatar_split_clause,[],[f394,f376,f322,f846]) ).
fof(f394,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl8_12
| ~ spl8_25 ),
inference(resolution,[],[f377,f323]) ).
fof(f842,plain,
spl8_89,
inference(avatar_split_clause,[],[f259,f840]) ).
fof(f259,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(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(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(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f220,f229,f229,f229,f229,f229,f229]) ).
fof(f229,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f167,f144,f144]) ).
fof(f144,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f167,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
<=> ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X2,X3,X6,X0] :
( member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X2),X6),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',flip_defn) ).
fof(f838,plain,
spl8_88,
inference(avatar_split_clause,[],[f256,f836]) ).
fof(f256,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))),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(X1,X1))),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(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f217,f229,f229,f229,f229,f229,f229]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X2,X3,X6] :
( member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X6),X2),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',rotate_defn) ).
fof(f834,plain,
spl8_87,
inference(avatar_split_clause,[],[f261,f832]) ).
fof(f832,plain,
( spl8_87
<=> ! [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(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).
fof(f261,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))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f218,f229,f229,f229,f229]) ).
fof(f218,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f830,plain,
spl8_86,
inference(avatar_split_clause,[],[f258,f828]) ).
fof(f828,plain,
( spl8_86
<=> ! [X0,X3,X2,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))),cross_product(cross_product(universal_class,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(X3,X3))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
fof(f258,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))),cross_product(cross_product(universal_class,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(X3,X3))),rotate(X0)) ),
inference(definition_unfolding,[],[f215,f229,f229,f229,f229]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f826,plain,
spl8_85,
inference(avatar_split_clause,[],[f260,f824]) ).
fof(f824,plain,
( spl8_85
<=> ! [X0,X3,X2,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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
fof(f260,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)) ),
inference(definition_unfolding,[],[f219,f229,f229,f229,f229]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f822,plain,
spl8_84,
inference(avatar_split_clause,[],[f257,f820]) ).
fof(f820,plain,
( spl8_84
<=> ! [X0,X3,X2,X1] :
( 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(X1,X1))),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))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( 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(X1,X1))),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))),rotate(X0)) ),
inference(definition_unfolding,[],[f216,f229,f229,f229,f229]) ).
fof(f216,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f812,plain,
spl8_83,
inference(avatar_split_clause,[],[f250,f810]) ).
fof(f250,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ),
inference(definition_unfolding,[],[f211,f229,f228,f228,f144]) ).
fof(f228,plain,
! [X0,X1] : image(X1,X0) = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f166,f227,f197]) ).
fof(f197,plain,
! [X2,X0,X1] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X5,X1] : restrict(X5,X0,X1) = intersection(X5,cross_product(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_defn) ).
fof(f227,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f143,f146]) ).
fof(f146,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1] : inverse(X1) = domain_of(flip(cross_product(X1,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_defn) ).
fof(f143,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X4] : range_of(X4) = domain_of(inverse(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).
fof(f166,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X0,X5] : image(X5,X0) = range_of(restrict(X5,X0,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_defn) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X2,X3),compose(X1,X0))
<=> ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X5,X7,X2,X3] :
( member(ordered_pair(X2,X3),compose(X7,X5))
<=> ( member(X3,image(X7,image(X5,singleton(X2))))
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn2) ).
fof(f808,plain,
spl8_82,
inference(avatar_split_clause,[],[f251,f806]) ).
fof(f806,plain,
( spl8_82
<=> ! [X0,X3,X2,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f210,f228,f228,f144,f229]) ).
fof(f210,plain,
! [X2,X3,X0,X1] :
( member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f799,plain,
spl8_81,
inference(avatar_split_clause,[],[f266,f797]) ).
fof(f266,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(equality_resolution,[],[f245]) ).
fof(f245,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| union(X0,unordered_pair(X0,X0)) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f196,f229,f226]) ).
fof(f226,plain,
! [X0] : successor(X0) = union(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f145,f144]) ).
fof(f145,plain,
! [X0] : successor(X0) = union(X0,singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] : successor(X0) = union(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_defn) ).
fof(f196,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
<=> ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn2) ).
fof(f795,plain,
( ~ spl8_30
| spl8_80
| ~ spl8_7
| ~ spl8_70 ),
inference(avatar_split_clause,[],[f697,f685,f299,f792,f406]) ).
fof(f697,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class)
| ~ spl8_7
| ~ spl8_70 ),
inference(resolution,[],[f686,f300]) ).
fof(f767,plain,
spl8_79,
inference(avatar_split_clause,[],[f262,f765]) ).
fof(f262,plain,
! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f222,f230]) ).
fof(f230,plain,
! [X0,X1] : apply(X0,X1) = sum_class(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f165,f228,f144]) ).
fof(f165,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X1] : apply(X8,X1) = sum_class(image(X8,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_defn) ).
fof(f222,plain,
! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f84,f132]) ).
fof(f132,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| null_class = X1 ) )
& function(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
? [X8] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X8,X1),X1)
| null_class = X1 ) )
& function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).
fof(f763,plain,
spl8_78,
inference(avatar_split_clause,[],[f249,f761]) ).
fof(f249,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f198,f229]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( member(X2,cross_product(X0,X1))
=> ordered_pair(first(X2),second(X2)) = X2 ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X4] :
( member(X4,cross_product(X0,X1))
=> ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product) ).
fof(f750,plain,
spl8_77,
inference(avatar_split_clause,[],[f253,f748]) ).
fof(f253,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(definition_unfolding,[],[f214,f229]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
<=> ( member(X3,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).
fof(f746,plain,
spl8_76,
inference(avatar_split_clause,[],[f236,f744]) ).
fof(f236,plain,
! [X0] :
( unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),unordered_pair(sK3(X0),sK3(X0)))) = X0
| ~ member(X0,identity_relation) ),
inference(definition_unfolding,[],[f161,f229]) ).
fof(f161,plain,
! [X0] :
( ordered_pair(sK3(X0),sK3(X0)) = X0
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ( ordered_pair(sK3(X0),sK3(X0)) = X0
& member(sK3(X0),universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f95,f96]) ).
fof(f96,plain,
! [X0] :
( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
=> ( ordered_pair(sK3(X0),sK3(X0)) = X0
& member(sK3(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(rectify,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( member(X0,identity_relation)
<=> ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X4] :
( member(X4,identity_relation)
<=> ? [X0] :
( ordered_pair(X0,X0) = X4
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
fof(f716,plain,
spl8_75,
inference(avatar_split_clause,[],[f246,f714]) ).
fof(f246,plain,
! [X0,X1] :
( union(X0,unordered_pair(X0,X0)) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f195,f226,f229]) ).
fof(f195,plain,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f117]) ).
fof(f712,plain,
spl8_74,
inference(avatar_split_clause,[],[f239,f710]) ).
fof(f239,plain,
! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f169,f229]) ).
fof(f169,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( member(X1,universal_class)
& member(X0,universal_class) )
=> ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_second) ).
fof(f708,plain,
spl8_73,
inference(avatar_split_clause,[],[f238,f706]) ).
fof(f238,plain,
! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f170,f229]) ).
fof(f170,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f79]) ).
fof(f695,plain,
spl8_72,
inference(avatar_split_clause,[],[f242,f693]) ).
fof(f242,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) ),
inference(definition_unfolding,[],[f192,f229]) ).
fof(f192,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
<=> ( member(X0,X1)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_defn) ).
fof(f691,plain,
spl8_71,
inference(avatar_split_clause,[],[f237,f689]) ).
fof(f237,plain,
! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f168,f228]) ).
fof(f168,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( function(X1)
& member(X0,universal_class) )
=> member(image(X1,X0),universal_class) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0,X8] :
( ( function(X8)
& member(X0,universal_class) )
=> member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
fof(f687,plain,
spl8_70,
inference(avatar_split_clause,[],[f231,f685]) ).
fof(f231,plain,
! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ),
inference(definition_unfolding,[],[f156,f228]) ).
fof(f156,plain,
! [X0] :
( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).
fof(f683,plain,
( spl8_69
| ~ spl8_16
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f624,f582,f339,f680]) ).
fof(f582,plain,
( spl8_53
<=> ! [X0] : ~ member(X0,sum_class(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
fof(f624,plain,
( null_class = sum_class(null_class)
| ~ spl8_16
| ~ spl8_53 ),
inference(resolution,[],[f583,f340]) ).
fof(f583,plain,
( ! [X0] : ~ member(X0,sum_class(null_class))
| ~ spl8_53 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f673,plain,
spl8_68,
inference(avatar_split_clause,[],[f255,f671]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f212,f229]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f669,plain,
spl8_67,
inference(avatar_split_clause,[],[f254,f667]) ).
fof(f254,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f213,f229]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f665,plain,
spl8_66,
inference(avatar_split_clause,[],[f252,f663]) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f209,f229]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f661,plain,
spl8_65,
inference(avatar_split_clause,[],[f240,f659]) ).
fof(f240,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f186,f197,f144]) ).
fof(f186,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) ) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X4] :
( member(X4,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X4),universal_class)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of) ).
fof(f657,plain,
spl8_64,
inference(avatar_split_clause,[],[f233,f655]) ).
fof(f655,plain,
( spl8_64
<=> ! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
fof(f233,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f159,f146]) ).
fof(f159,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( function(X0)
<=> ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X8] :
( function(X8)
<=> ( subclass(compose(X8,inverse(X8)),identity_relation)
& subclass(X8,cross_product(universal_class,universal_class)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_defn) ).
fof(f652,plain,
( ~ spl8_63
| ~ spl8_12
| ~ spl8_53 ),
inference(avatar_split_clause,[],[f623,f582,f322,f649]) ).
fof(f649,plain,
( spl8_63
<=> inductive(sum_class(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
fof(f623,plain,
( ~ inductive(sum_class(null_class))
| ~ spl8_12
| ~ spl8_53 ),
inference(resolution,[],[f583,f323]) ).
fof(f644,plain,
spl8_62,
inference(avatar_split_clause,[],[f263,f642]) ).
fof(f263,plain,
! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f235]) ).
fof(f235,plain,
! [X0,X1] :
( member(X0,identity_relation)
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))) != X0
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f162,f229]) ).
fof(f162,plain,
! [X0,X1] :
( member(X0,identity_relation)
| ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f97]) ).
fof(f640,plain,
spl8_61,
inference(avatar_split_clause,[],[f248,f638]) ).
fof(f248,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f193,f229]) ).
fof(f193,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f117]) ).
fof(f636,plain,
spl8_60,
inference(avatar_split_clause,[],[f247,f634]) ).
fof(f247,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f194,f229]) ).
fof(f194,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f117]) ).
fof(f632,plain,
spl8_59,
inference(avatar_split_clause,[],[f244,f630]) ).
fof(f244,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f190,f229]) ).
fof(f190,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f115]) ).
fof(f622,plain,
spl8_58,
inference(avatar_split_clause,[],[f243,f620]) ).
fof(f243,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,[],[f191,f229]) ).
fof(f191,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f115]) ).
fof(f618,plain,
spl8_57,
inference(avatar_split_clause,[],[f232,f616]) ).
fof(f232,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(definition_unfolding,[],[f155,f228]) ).
fof(f155,plain,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f614,plain,
spl8_56,
inference(avatar_split_clause,[],[f241,f612]) ).
fof(f241,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f185,f197,f144]) ).
fof(f185,plain,
! [X0,X1] :
( null_class != restrict(X0,singleton(X1),universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f592,plain,
spl8_55,
inference(avatar_split_clause,[],[f234,f590]) ).
fof(f234,plain,
! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(definition_unfolding,[],[f158,f146]) ).
fof(f158,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ function(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f588,plain,
spl8_54,
inference(avatar_split_clause,[],[f206,f586]) ).
fof(f206,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f584,plain,
( spl8_53
| ~ spl8_6
| ~ spl8_47 ),
inference(avatar_split_clause,[],[f531,f496,f295,f582]) ).
fof(f531,plain,
( ! [X0] : ~ member(X0,sum_class(null_class))
| ~ spl8_6
| ~ spl8_47 ),
inference(resolution,[],[f497,f296]) ).
fof(f580,plain,
spl8_52,
inference(avatar_split_clause,[],[f202,f578]) ).
fof(f202,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,union(X0,X1))
<=> ( member(X4,X1)
| member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f576,plain,
spl8_51,
inference(avatar_split_clause,[],[f201,f574]) ).
fof(f201,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
<=> ( member(X4,X1)
& member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f546,plain,
spl8_50,
inference(avatar_split_clause,[],[f189,f544]) ).
fof(f189,plain,
! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK5(X0,X1),X1)
& member(X0,sK5(X0,X1)) )
| ~ member(X0,sum_class(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f111,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
=> ( member(sK5(X0,X1),X1)
& member(X0,sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum_class(X1)) ) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum_class(X1)) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( member(X0,sum_class(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X2,X0] :
( member(X2,sum_class(X0))
<=> ? [X1] :
( member(X1,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_defn) ).
fof(f542,plain,
spl8_49,
inference(avatar_split_clause,[],[f183,f540]) ).
fof(f183,plain,
! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( member(X0,power_class(X1))
<=> ( subclass(X0,X1)
& member(X0,universal_class) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X2,X0] :
( member(X2,power_class(X0))
<=> ( subclass(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_defn) ).
fof(f538,plain,
spl8_48,
inference(avatar_split_clause,[],[f180,f536]) ).
fof(f180,plain,
! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X4] :
( member(X4,complement(X0))
<=> ( ~ member(X4,X0)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f498,plain,
spl8_47,
inference(avatar_split_clause,[],[f188,f496]) ).
fof(f188,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f494,plain,
spl8_46,
inference(avatar_split_clause,[],[f187,f492]) ).
fof(f187,plain,
! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f490,plain,
spl8_45,
inference(avatar_split_clause,[],[f175,f488]) ).
fof(f175,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f101,f102]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f486,plain,
spl8_44,
inference(avatar_split_clause,[],[f174,f484]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f482,plain,
spl8_43,
inference(avatar_split_clause,[],[f173,f480]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
fof(f476,plain,
( spl8_42
| ~ spl8_6
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f456,f419,f295,f474]) ).
fof(f456,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl8_6
| ~ spl8_33 ),
inference(resolution,[],[f420,f296]) ).
fof(f453,plain,
spl8_41,
inference(avatar_split_clause,[],[f268,f451]) ).
fof(f268,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f207]) ).
fof(f207,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f123]) ).
fof(f449,plain,
spl8_40,
inference(avatar_split_clause,[],[f267,f447]) ).
fof(f267,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f208]) ).
fof(f208,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f123]) ).
fof(f445,plain,
spl8_39,
inference(avatar_split_clause,[],[f205,f443]) ).
fof(f205,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f441,plain,
spl8_38,
inference(avatar_split_clause,[],[f204,f439]) ).
fof(f204,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f437,plain,
spl8_37,
inference(avatar_split_clause,[],[f203,f435]) ).
fof(f203,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f433,plain,
spl8_36,
inference(avatar_split_clause,[],[f200,f431]) ).
fof(f200,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f429,plain,
spl8_35,
inference(avatar_split_clause,[],[f199,f427]) ).
fof(f199,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f425,plain,
spl8_34,
inference(avatar_split_clause,[],[f177,f423]) ).
fof(f177,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f421,plain,
spl8_33,
inference(avatar_split_clause,[],[f176,f419]) ).
fof(f176,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f417,plain,
spl8_32,
inference(avatar_split_clause,[],[f148,f415]) ).
fof(f148,plain,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip) ).
fof(f413,plain,
spl8_31,
inference(avatar_split_clause,[],[f147,f411]) ).
fof(f147,plain,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate) ).
fof(f409,plain,
( spl8_29
| spl8_30
| ~ spl8_12
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f392,f372,f322,f406,f403]) ).
fof(f392,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(complement(X0)) )
| ~ spl8_12
| ~ spl8_24 ),
inference(resolution,[],[f373,f323]) ).
fof(f390,plain,
spl8_28,
inference(avatar_split_clause,[],[f184,f388]) ).
fof(f184,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f386,plain,
spl8_27,
inference(avatar_split_clause,[],[f182,f384]) ).
fof(f182,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f382,plain,
spl8_26,
inference(avatar_split_clause,[],[f181,f380]) ).
fof(f181,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f378,plain,
spl8_25,
inference(avatar_split_clause,[],[f179,f376]) ).
fof(f179,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f374,plain,
spl8_24,
inference(avatar_split_clause,[],[f178,f372]) ).
fof(f178,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f370,plain,
spl8_23,
inference(avatar_split_clause,[],[f164,f368]) ).
fof(f164,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn1) ).
fof(f366,plain,
spl8_22,
inference(avatar_split_clause,[],[f160,f364]) ).
fof(f160,plain,
! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f97]) ).
fof(f362,plain,
( ~ spl8_21
| ~ spl8_6
| ~ spl8_12 ),
inference(avatar_split_clause,[],[f333,f322,f295,f359]) ).
fof(f359,plain,
( spl8_21
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
fof(f333,plain,
( ~ inductive(null_class)
| ~ spl8_6
| ~ spl8_12 ),
inference(resolution,[],[f323,f296]) ).
fof(f357,plain,
spl8_20,
inference(avatar_split_clause,[],[f157,f355]) ).
fof(f157,plain,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f353,plain,
spl8_19,
inference(avatar_split_clause,[],[f153,f351]) ).
fof(f153,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( member(X0,universal_class)
=> member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class) ).
fof(f349,plain,
spl8_18,
inference(avatar_split_clause,[],[f152,f347]) ).
fof(f152,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( member(X0,universal_class)
=> member(power_class(X0),universal_class) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X2] :
( member(X2,universal_class)
=> member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class) ).
fof(f345,plain,
spl8_17,
inference(avatar_split_clause,[],[f151,f343]) ).
fof(f151,plain,
! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f73,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( null_class != X0
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( null_class != X0
=> ? [X2] :
( disjoint(X2,X0)
& member(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
fof(f341,plain,
spl8_16,
inference(avatar_split_clause,[],[f150,f339]) ).
fof(f150,plain,
! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f89]) ).
fof(f337,plain,
spl8_15,
inference(avatar_split_clause,[],[f149,f335]) ).
fof(f149,plain,
! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f89]) ).
fof(f332,plain,
spl8_14,
inference(avatar_split_clause,[],[f225,f330]) ).
fof(f225,plain,
! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f85,f134]) ).
fof(f134,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).
fof(f328,plain,
spl8_13,
inference(avatar_split_clause,[],[f163,f326]) ).
fof(f163,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f324,plain,
spl8_12,
inference(avatar_split_clause,[],[f154,f322]) ).
fof(f154,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f320,plain,
spl8_11,
inference(avatar_split_clause,[],[f140,f317]) ).
fof(f140,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).
fof(f315,plain,
spl8_10,
inference(avatar_split_clause,[],[f139,f312]) ).
fof(f139,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation) ).
fof(f310,plain,
spl8_9,
inference(avatar_split_clause,[],[f264,f308]) ).
fof(f308,plain,
( spl8_9
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f264,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f306,plain,
spl8_8,
inference(avatar_split_clause,[],[f223,f303]) ).
fof(f223,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f135]) ).
fof(f301,plain,
spl8_7,
inference(avatar_split_clause,[],[f142,f299]) ).
fof(f142,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f297,plain,
spl8_6,
inference(avatar_split_clause,[],[f141,f295]) ).
fof(f141,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f293,plain,
spl8_5,
inference(avatar_split_clause,[],[f224,f290]) ).
fof(f224,plain,
inductive(sK7),
inference(cnf_transformation,[],[f135]) ).
fof(f288,plain,
spl8_4,
inference(avatar_split_clause,[],[f221,f285]) ).
fof(f221,plain,
function(sK6),
inference(cnf_transformation,[],[f133]) ).
fof(f283,plain,
~ spl8_3,
inference(avatar_split_clause,[],[f138,f280]) ).
fof(f138,plain,
null_class != unordered_pair(sK0,sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( null_class != unordered_pair(sK0,sK1)
& ~ member(sK1,universal_class)
& ~ member(sK0,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f72,f86]) ).
fof(f86,plain,
( ? [X0,X1] :
( unordered_pair(X0,X1) != null_class
& ~ member(X1,universal_class)
& ~ member(X0,universal_class) )
=> ( null_class != unordered_pair(sK0,sK1)
& ~ member(sK1,universal_class)
& ~ member(sK0,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0,X1] :
( unordered_pair(X0,X1) != null_class
& ~ member(X1,universal_class)
& ~ member(X0,universal_class) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
? [X0,X1] :
( unordered_pair(X0,X1) != null_class
& ~ member(X1,universal_class)
& ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( ( ~ member(X1,universal_class)
& ~ member(X0,universal_class) )
=> unordered_pair(X0,X1) = null_class ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0,X1] :
( ( ~ member(X1,universal_class)
& ~ member(X0,universal_class) )
=> unordered_pair(X0,X1) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f278,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f137,f275]) ).
fof(f137,plain,
~ member(sK1,universal_class),
inference(cnf_transformation,[],[f87]) ).
fof(f273,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f136,f270]) ).
fof(f136,plain,
~ member(sK0,universal_class),
inference(cnf_transformation,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET071+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n013.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 16:37:08 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (8571)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (8574)WARNING: value z3 for option sas not known
% 0.11/0.33 % (8576)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)
% 0.11/0.33 % (8572)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33 % (8575)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33 % (8573)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33 % (8577)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)
% 0.11/0.33 % (8574)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)
% 0.11/0.34 % (8578)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)
% 0.11/0.35 TRYING [1]
% 0.11/0.36 TRYING [2]
% 0.17/0.36 TRYING [1]
% 0.17/0.36 TRYING [2]
% 0.17/0.39 TRYING [3]
% 0.17/0.39 TRYING [3]
% 0.17/0.46 TRYING [4]
% 0.17/0.54 TRYING [4]
% 2.27/0.65 TRYING [5]
% 4.56/0.98 TRYING [5]
% 5.94/1.17 TRYING [6]
% 7.38/1.44 TRYING [1]
% 7.38/1.44 TRYING [2]
% 7.38/1.45 TRYING [3]
% 8.03/1.48 TRYING [4]
% 8.65/1.56 TRYING [5]
% 10.25/1.77 TRYING [6]
% 11.72/2.04 % (8576)First to succeed.
% 12.37/2.07 % (8576)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8571"
% 12.37/2.08 % (8576)Refutation found. Thanks to Tanya!
% 12.37/2.08 % SZS status Theorem for theBenchmark
% 12.37/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 12.46/2.09 % (8576)------------------------------
% 12.46/2.09 % (8576)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 12.46/2.09 % (8576)Termination reason: Refutation
% 12.46/2.09
% 12.46/2.09 % (8576)Memory used [KB]: 15679
% 12.46/2.09 % (8576)Time elapsed: 1.739 s
% 12.46/2.09 % (8576)Instructions burned: 3688 (million)
% 12.46/2.09 % (8571)Success in time 1.751 s
%------------------------------------------------------------------------------