%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET252-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 15:07:32 EDT 2024

% Result   : Unsatisfiable 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  329
% Syntax   : Number of formulae    :  826 ( 136 unt;   0 def)
%            Number of atoms       : 2448 ( 243 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives : 2925 (1303   ~;1397   |;   0   &)
%                                         ( 225 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :   27 (   4 avg)
%            Number of predicates  :  237 ( 235 usr; 226 prp; 0-3 aty)
%            Number of functors    :   41 (  41 usr;  15 con; 0-3 aty)
%            Number of variables   : 1128 (1128   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2250,plain,
    $false,
    inference(avatar_sat_refutation,[],[f208,f214,f219,f224,f228,f233,f237,f241,f245,f249,f254,f259,f263,f267,f272,f276,f280,f284,f288,f292,f296,f300,f304,f308,f313,f318,f324,f328,f332,f336,f340,f344,f348,f352,f356,f360,f364,f368,f381,f385,f389,f393,f398,f403,f433,f437,f441,f445,f453,f457,f461,f465,f469,f473,f477,f481,f508,f512,f516,f520,f525,f533,f537,f541,f548,f552,f561,f565,f569,f573,f577,f582,f593,f597,f601,f605,f618,f622,f633,f637,f646,f654,f659,f663,f673,f678,f682,f686,f691,f695,f700,f705,f711,f727,f732,f736,f740,f744,f748,f754,f759,f766,f770,f788,f798,f816,f820,f824,f828,f832,f893,f897,f901,f924,f928,f937,f946,f956,f960,f964,f968,f972,f982,f1013,f1017,f1021,f1025,f1029,f1033,f1092,f1096,f1100,f1109,f1113,f1117,f1164,f1168,f1172,f1176,f1180,f1230,f1239,f1248,f1252,f1256,f1282,f1291,f1295,f1299,f1303,f1307,f1325,f1329,f1360,f1370,f1374,f1378,f1382,f1386,f1453,f1457,f1461,f1465,f1473,f1477,f1515,f1523,f1532,f1539,f1552,f1558,f1565,f1587,f1593,f1606,f1618,f1624,f1643,f1660,f1664,f1708,f1713,f1719,f1753,f1781,f1801,f1811,f1816,f1872,f1910,f1917,f1927,f1932,f1944,f1954,f2003,f2007,f2060,f2071,f2084,f2097,f2101,f2114,f2119,f2129,f2133,f2146,f2148,f2232,f2236,f2249]) ).

fof(f2249,plain,
    ( spl0_2
    | ~ spl0_224 ),
    inference(avatar_contradiction_clause,[],[f2237]) ).

fof(f2237,plain,
    ( $false
    | spl0_2
    | ~ spl0_224 ),
    inference(resolution,[],[f2231,f213]) ).

fof(f213,plain,
    ( ~ subclass(intersection(x,cross_product(y,z)),x)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f211,plain,
    ( spl0_2
  <=> subclass(intersection(x,cross_product(y,z)),x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

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

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

fof(f2236,plain,
    ( spl0_225
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(avatar_split_clause,[],[f1153,f1094,f326,f2234]) ).

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

fof(f326,plain,
    ( spl0_28
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | ~ member(not_subclass_element(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

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

fof(f1153,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X1)
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(duplicate_literal_removal,[],[f1136]) ).

fof(f1136,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X1)
        | subclass(intersection(X0,X1),X1) )
    | ~ spl0_28
    | ~ spl0_136 ),
    inference(resolution,[],[f1095,f327]) ).

fof(f327,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,X1),X1)
        | subclass(X0,X1) )
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f326]) ).

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

fof(f2232,plain,
    ( spl0_224
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(avatar_split_clause,[],[f1135,f1090,f326,f2230]) ).

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

fof(f1135,plain,
    ( ! [X0,X1] : subclass(intersection(X0,X1),X0)
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(duplicate_literal_removal,[],[f1118]) ).

fof(f1118,plain,
    ( ! [X0,X1] :
        ( subclass(intersection(X0,X1),X0)
        | subclass(intersection(X0,X1),X0) )
    | ~ spl0_28
    | ~ spl0_135 ),
    inference(resolution,[],[f1091,f327]) ).

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

fof(f2148,plain,
    ( ~ spl0_3
    | ~ spl0_223 ),
    inference(avatar_contradiction_clause,[],[f2147]) ).

fof(f2147,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_223 ),
    inference(resolution,[],[f2145,f218]) ).

fof(f218,plain,
    ( inductive(omega)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f216,plain,
    ( spl0_3
  <=> inductive(omega) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f2145,plain,
    ( ! [X0] : ~ inductive(X0)
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f2144]) ).

fof(f2144,plain,
    ( spl0_223
  <=> ! [X0] : ~ inductive(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f2146,plain,
    ( spl0_223
    | spl0_81
    | ~ spl0_5
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f861,f822,f226,f639,f2144]) ).

fof(f639,plain,
    ( spl0_81
  <=> member(null_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f226,plain,
    ( spl0_5
  <=> ! [X0] : subclass(X0,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f822,plain,
    ( spl0_110
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f861,plain,
    ( ! [X0] :
        ( member(null_class,universal_class)
        | ~ inductive(X0) )
    | ~ spl0_5
    | ~ spl0_110 ),
    inference(resolution,[],[f823,f227]) ).

fof(f227,plain,
    ( ! [X0] : subclass(X0,universal_class)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f226]) ).

fof(f823,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f822]) ).

fof(f2133,plain,
    ( spl0_222
    | ~ spl0_91
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f713,f709,f693,f2131]) ).

fof(f2131,plain,
    ( spl0_222
  <=> ! [X4,X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f693,plain,
    ( spl0_91
  <=> ! [X9,X11,X10] :
        ( ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f709,plain,
    ( spl0_94
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f713,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),compose(X3,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)))),unordered_pair(unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)),unordered_pair(not_homomorphism1(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),unordered_pair(not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4),not_homomorphism2(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4))))))),cross_product(universal_class,universal_class))
        | ~ operation(X4)
        | ~ compatible(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | homomorphism(X1,domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class))),X4)
        | ~ operation(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X3),universal_class)))) )
    | ~ spl0_91
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f694]) ).

fof(f694,plain,
    ( ! [X10,X11,X9] :
        ( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11)
        | ~ operation(X10) )
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f693]) ).

fof(f710,plain,
    ( ! [X1,X7,X4,X5] :
        ( ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class)))))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f709]) ).

fof(f2129,plain,
    ( spl0_221
    | ~ spl0_51
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f762,f757,f693,f459,f2127]) ).

fof(f2127,plain,
    ( spl0_221
  <=> ! [X2,X4,X0,X3,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f459,plain,
    ( spl0_51
  <=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f757,plain,
    ( spl0_102
  <=> ! [X10,X11,X0,X9,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
        | ~ homomorphism(X9,X10,X11)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f762,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class)),universal_class)))))))),universal_class),X0),universal_class)))))))
        | ~ homomorphism(X0,X1,X2)
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_51
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(forward_demodulation,[],[f760,f460]) ).

fof(f460,plain,
    ( ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5)
    | ~ spl0_51 ),
    inference(avatar_component_clause,[],[f459]) ).

fof(f760,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)))),unordered_pair(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),unordered_pair(not_homomorphism1(X3,X1,X4),unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4))))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X3,X1,X4),not_homomorphism1(X3,X1,X4)),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X3,X1,X4),not_homomorphism2(X3,X1,X4)),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ operation(X4)
        | ~ compatible(X3,X1,X4)
        | homomorphism(X3,X1,X4)
        | ~ operation(X1) )
    | ~ spl0_91
    | ~ spl0_102 ),
    inference(resolution,[],[f758,f694]) ).

fof(f758,plain,
    ( ! [X10,X0,X11,X1,X9] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
        | ~ homomorphism(X9,X10,X11)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) )
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f757]) ).

fof(f2119,plain,
    ( ~ spl0_220
    | spl0_198
    | ~ spl0_13
    | ~ spl0_104 ),
    inference(avatar_split_clause,[],[f782,f768,f261,f1710,f2116]) ).

fof(f2116,plain,
    ( spl0_220
  <=> inductive(identity_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f1710,plain,
    ( spl0_198
  <=> member(null_class,subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f261,plain,
    ( spl0_13
  <=> ! [X0] :
        ( ~ inductive(X0)
        | member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

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

fof(f782,plain,
    ( member(null_class,subset_relation)
    | ~ inductive(identity_relation)
    | ~ spl0_13
    | ~ spl0_104 ),
    inference(resolution,[],[f769,f262]) ).

fof(f262,plain,
    ( ! [X0] :
        ( member(null_class,X0)
        | ~ inductive(X0) )
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f261]) ).

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

fof(f2114,plain,
    ( spl0_219
    | ~ spl0_71
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f761,f757,f575,f2112]) ).

fof(f2112,plain,
    ( spl0_219
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f575,plain,
    ( spl0_71
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,domain_of(X0))
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f761,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ homomorphism(X0,X1,X2)
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1),universal_class)))))))),universal_class),X0),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X3,X3),universal_class),X0),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X4,X4),universal_class),X0),universal_class))))))))))),universal_class),X2),universal_class)))))))
        | ~ member(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),universal_class)
        | null_class = intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X4,X4)))),universal_class),X1) )
    | ~ spl0_71
    | ~ spl0_102 ),
    inference(resolution,[],[f758,f576]) ).

fof(f576,plain,
    ( ! [X0,X4] :
        ( member(X4,domain_of(X0))
        | ~ member(X4,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) )
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f575]) ).

fof(f2101,plain,
    ( spl0_218
    | ~ spl0_85
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f716,f709,f661,f2099]) ).

fof(f2099,plain,
    ( spl0_218
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f661,plain,
    ( spl0_85
  <=> ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f716,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),universal_class)),universal_class)))))))))),cross_product(universal_class,universal_class))
        | ~ member(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),universal_class)
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_85
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f662]) ).

fof(f662,plain,
    ( ! [X1] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
        | ~ member(X1,universal_class)
        | null_class = X1 )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f661]) ).

fof(f2097,plain,
    ( spl0_217
    | ~ spl0_80
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f666,f661,f635,f2095]) ).

fof(f2095,plain,
    ( spl0_217
  <=> ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f635,plain,
    ( spl0_80
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f666,plain,
    ( ! [X0,X1] :
        ( ~ member(cross_product(X0,X1),universal_class)
        | cross_product(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))) = unordered_pair(unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))),unordered_pair(first(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),unordered_pair(second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class)))))))),second(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(cross_product(X0,X1),cross_product(X0,X1)),universal_class)),universal_class))))))))))) )
    | ~ spl0_80
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f636]) ).

fof(f636,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,cross_product(X0,X1))
        | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 )
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f635]) ).

fof(f2084,plain,
    ( spl0_216
    | ~ spl0_27
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f714,f709,f322,f2082]) ).

fof(f2082,plain,
    ( spl0_216
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f322,plain,
    ( spl0_27
  <=> ! [X0,X1] :
        ( subclass(X0,X1)
        | member(not_subclass_element(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f714,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3),not_subclass_element(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3)))),cross_product(universal_class,universal_class))
        | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))),X3) )
    | ~ spl0_27
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f323]) ).

fof(f323,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,X1),X0)
        | subclass(X0,X1) )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f322]) ).

fof(f2071,plain,
    ( spl0_215
    | ~ spl0_24
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f717,f709,f306,f2069]) ).

fof(f2069,plain,
    ( spl0_215
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f306,plain,
    ( spl0_24
  <=> ! [X0] :
        ( null_class = X0
        | member(regular(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f717,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class))))),regular(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))))))),cross_product(universal_class,universal_class))
        | null_class = domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_24
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f307]) ).

fof(f307,plain,
    ( ! [X0] :
        ( member(regular(X0),X0)
        | null_class = X0 )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f306]) ).

fof(f2060,plain,
    ( spl0_214
    | ~ spl0_78
    | ~ spl0_101 ),
    inference(avatar_split_clause,[],[f755,f752,f620,f2058]) ).

fof(f2058,plain,
    ( spl0_214
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f620,plain,
    ( spl0_78
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,X0)
        | ~ member(X3,X1)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f752,plain,
    ( spl0_101
  <=> ! [X4,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
        | ~ member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f755,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,domain_of(X1))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))))))))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class))))))))))))),application_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class) )
    | ~ spl0_78
    | ~ spl0_101 ),
    inference(resolution,[],[f753,f621]) ).

fof(f621,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
        | ~ member(X3,X1)
        | ~ member(X2,X0) )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f620]) ).

fof(f753,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class)))
        | ~ member(X1,domain_of(X0))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function) )
    | ~ spl0_101 ),
    inference(avatar_component_clause,[],[f752]) ).

fof(f2007,plain,
    ( spl0_213
    | ~ spl0_78
    | ~ spl0_100 ),
    inference(avatar_split_clause,[],[f750,f746,f620,f2005]) ).

fof(f2005,plain,
    ( spl0_213
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f746,plain,
    ( spl0_100
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f750,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_100 ),
    inference(resolution,[],[f747,f621]) ).

fof(f747,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f746]) ).

fof(f2003,plain,
    ( spl0_212
    | ~ spl0_78
    | ~ spl0_99 ),
    inference(avatar_split_clause,[],[f749,f742,f620,f2001]) ).

fof(f2001,plain,
    ( spl0_212
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f742,plain,
    ( spl0_99
  <=> ! [X3,X0,X6,X2] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f749,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),rotate(X3))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X0,X0))),X3)
        | ~ member(X2,universal_class)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_78
    | ~ spl0_99 ),
    inference(resolution,[],[f743,f621]) ).

fof(f743,plain,
    ( ! [X2,X3,X0,X6] :
        ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
        | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f742]) ).

fof(f1954,plain,
    ( spl0_211
    | ~ spl0_78
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f647,f635,f620,f1952]) ).

fof(f1952,plain,
    ( spl0_211
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f647,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))))),unordered_pair(first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))))))
        | ~ member(X1,X2)
        | ~ member(X0,X3) )
    | ~ spl0_78
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f621]) ).

fof(f1944,plain,
    ( spl0_210
    | ~ spl0_41
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f722,f709,f387,f1942]) ).

fof(f1942,plain,
    ( spl0_210
  <=> ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f387,plain,
    ( spl0_41
  <=> ! [X0] :
        ( null_class = X0
        | null_class = intersection(X0,regular(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f722,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(null_class,universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(regular(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class))
        | null_class = cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class) )
    | ~ spl0_41
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f388]) ).

fof(f388,plain,
    ( ! [X0] :
        ( null_class = intersection(X0,regular(X0))
        | null_class = X0 )
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f387]) ).

fof(f1932,plain,
    ( ~ spl0_209
    | ~ spl0_13
    | spl0_198 ),
    inference(avatar_split_clause,[],[f1812,f1710,f261,f1929]) ).

fof(f1929,plain,
    ( spl0_209
  <=> inductive(subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f1812,plain,
    ( ~ inductive(subset_relation)
    | ~ spl0_13
    | spl0_198 ),
    inference(resolution,[],[f1712,f262]) ).

fof(f1712,plain,
    ( ~ member(null_class,subset_relation)
    | spl0_198 ),
    inference(avatar_component_clause,[],[f1710]) ).

fof(f1927,plain,
    ( spl0_208
    | ~ spl0_71
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f712,f709,f575,f1925]) ).

fof(f1925,plain,
    ( spl0_208
  <=> ! [X0,X3,X2,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f712,plain,
    ( ! [X2,X3,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,X3))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ member(X1,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X1,X1),universal_class),domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X3),universal_class)))),universal_class),X2),universal_class)))) )
    | ~ spl0_71
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f576]) ).

fof(f1917,plain,
    ( spl0_207
    | ~ spl0_49
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f665,f661,f451,f1915]) ).

fof(f1915,plain,
    ( spl0_207
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f451,plain,
    ( spl0_49
  <=> ! [X2,X0,X1] :
        ( X1 = X2
        | X0 = X2
        | ~ member(X2,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f665,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(X0,X1),universal_class)
        | unordered_pair(X0,X1) = null_class
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X0
        | domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X1)),universal_class)),universal_class))))))) = X1 )
    | ~ spl0_49
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f452]) ).

fof(f452,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,unordered_pair(X0,X1))
        | X0 = X2
        | X1 = X2 )
    | ~ spl0_49 ),
    inference(avatar_component_clause,[],[f451]) ).

fof(f1910,plain,
    ( spl0_206
    | ~ spl0_41
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f719,f709,f387,f1908]) ).

fof(f1908,plain,
    ( spl0_206
  <=> ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f719,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X1,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class),X2),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),compose(X2,regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_41
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f388]) ).

fof(f1872,plain,
    ( spl0_205
    | ~ spl0_39
    | ~ spl0_93 ),
    inference(avatar_split_clause,[],[f707,f703,f379,f1870]) ).

fof(f1870,plain,
    ( spl0_205
  <=> ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f379,plain,
    ( spl0_39
  <=> ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f703,plain,
    ( spl0_93
  <=> ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f707,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | ~ subclass(composition_function,X2)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),X2) )
    | ~ spl0_39
    | ~ spl0_93 ),
    inference(resolution,[],[f704,f380]) ).

fof(f380,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X2,X0)
        | ~ subclass(X0,X1)
        | member(X2,X1) )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f379]) ).

fof(f704,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) )
    | ~ spl0_93 ),
    inference(avatar_component_clause,[],[f703]) ).

fof(f1816,plain,
    ( spl0_204
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f721,f709,f459,f1814]) ).

fof(f1814,plain,
    ( spl0_204
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f721,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X2,cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X1),universal_class)))),universal_class)),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),compose(X2,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) )
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f460]) ).

fof(f1811,plain,
    ( spl0_203
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f718,f709,f459,f1809]) ).

fof(f1809,plain,
    ( spl0_203
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f718,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X2,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(X0,X0),universal_class)),universal_class)))),universal_class),X3),universal_class)))))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),compose(X3,X1))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X2,X2))),cross_product(universal_class,universal_class)) )
    | ~ spl0_51
    | ~ spl0_94 ),
    inference(superposition,[],[f710,f460]) ).

fof(f1801,plain,
    ( spl0_202
    | ~ spl0_13
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f715,f709,f261,f1799]) ).

fof(f1799,plain,
    ( spl0_202
  <=> ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f715,plain,
    ( ! [X2,X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),compose(X1,X2))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(null_class,null_class))),cross_product(universal_class,universal_class))
        | ~ inductive(domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X2),universal_class)))),universal_class),X1),universal_class))))) )
    | ~ spl0_13
    | ~ spl0_94 ),
    inference(resolution,[],[f710,f262]) ).

fof(f1781,plain,
    ( spl0_201
    | ~ spl0_27
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f650,f635,f322,f1779]) ).

fof(f1779,plain,
    ( spl0_201
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f650,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(cross_product(X0,X1),X2) = unordered_pair(unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),first(not_subclass_element(cross_product(X0,X1),X2))),unordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),unordered_pair(second(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2)))))
        | subclass(cross_product(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f323]) ).

fof(f1753,plain,
    ( spl0_200
    | ~ spl0_39
    | ~ spl0_91 ),
    inference(avatar_split_clause,[],[f696,f693,f379,f1751]) ).

fof(f1751,plain,
    ( spl0_200
  <=> ! [X0,X3,X2,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f696,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ operation(X0)
        | ~ compatible(X1,X2,X0)
        | homomorphism(X1,X2,X0)
        | ~ operation(X2)
        | ~ subclass(domain_of(X2),X3)
        | member(unordered_pair(unordered_pair(not_homomorphism1(X1,X2,X0),not_homomorphism1(X1,X2,X0)),unordered_pair(not_homomorphism1(X1,X2,X0),unordered_pair(not_homomorphism2(X1,X2,X0),not_homomorphism2(X1,X2,X0)))),X3) )
    | ~ spl0_39
    | ~ spl0_91 ),
    inference(resolution,[],[f694,f380]) ).

fof(f1719,plain,
    ( spl0_199
    | ~ spl0_24
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f649,f635,f306,f1717]) ).

fof(f1717,plain,
    ( spl0_199
  <=> ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f649,plain,
    ( ! [X0,X1] :
        ( regular(cross_product(X0,X1)) = unordered_pair(unordered_pair(first(regular(cross_product(X0,X1))),first(regular(cross_product(X0,X1)))),unordered_pair(first(regular(cross_product(X0,X1))),unordered_pair(second(regular(cross_product(X0,X1))),second(regular(cross_product(X0,X1))))))
        | cross_product(X0,X1) = null_class )
    | ~ spl0_24
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f307]) ).

fof(f1713,plain,
    ( ~ spl0_198
    | ~ spl0_112
    | spl0_183 ),
    inference(avatar_split_clause,[],[f1553,f1545,f830,f1710]) ).

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

fof(f1545,plain,
    ( spl0_183
  <=> member(null_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f1553,plain,
    ( ~ member(null_class,subset_relation)
    | ~ spl0_112
    | spl0_183 ),
    inference(resolution,[],[f1547,f831]) ).

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

fof(f1547,plain,
    ( ~ member(null_class,cross_product(universal_class,universal_class))
    | spl0_183 ),
    inference(avatar_component_clause,[],[f1545]) ).

fof(f1708,plain,
    ( spl0_197
    | ~ spl0_78
    | ~ spl0_95 ),
    inference(avatar_split_clause,[],[f728,f725,f620,f1706]) ).

fof(f1706,plain,
    ( spl0_197
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f725,plain,
    ( spl0_95
  <=> ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f728,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
        | ~ member(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_95 ),
    inference(resolution,[],[f726,f621]) ).

fof(f726,plain,
    ( ! [X0] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
    | ~ spl0_95 ),
    inference(avatar_component_clause,[],[f725]) ).

fof(f1664,plain,
    ( spl0_196
    | ~ spl0_31
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f668,f661,f338,f1662]) ).

fof(f1662,plain,
    ( spl0_196
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f338,plain,
    ( spl0_31
  <=> ! [X4,X0,X1] :
        ( member(X4,X0)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f668,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_31
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f339]) ).

fof(f339,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X0) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f338]) ).

fof(f1660,plain,
    ( spl0_195
    | ~ spl0_33
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f667,f661,f346,f1658]) ).

fof(f1658,plain,
    ( spl0_195
  <=> ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f346,plain,
    ( spl0_33
  <=> ! [X4,X0,X1] :
        ( member(X4,X1)
        | ~ member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f667,plain,
    ( ! [X0,X1] :
        ( ~ member(intersection(X0,X1),universal_class)
        | intersection(X0,X1) = null_class
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(intersection(X0,X1),intersection(X0,X1)),universal_class)),universal_class))))))),X1) )
    | ~ spl0_33
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f347]) ).

fof(f347,plain,
    ( ! [X0,X1,X4] :
        ( ~ member(X4,intersection(X0,X1))
        | member(X4,X1) )
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f346]) ).

fof(f1643,plain,
    ( spl0_194
    | ~ spl0_21
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f669,f661,f294,f1641]) ).

fof(f1641,plain,
    ( spl0_194
  <=> ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f294,plain,
    ( spl0_21
  <=> ! [X4,X0] :
        ( ~ member(X4,X0)
        | ~ member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f669,plain,
    ( ! [X0] :
        ( ~ member(complement(X0),universal_class)
        | complement(X0) = null_class
        | ~ member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(complement(X0),complement(X0)),universal_class)),universal_class))))))),X0) )
    | ~ spl0_21
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f295]) ).

fof(f295,plain,
    ( ! [X0,X4] :
        ( ~ member(X4,complement(X0))
        | ~ member(X4,X0) )
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f294]) ).

fof(f1624,plain,
    ( spl0_193
    | ~ spl0_39
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f664,f661,f379,f1622]) ).

fof(f1622,plain,
    ( spl0_193
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f664,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = X0
        | ~ subclass(X0,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X0,X0),universal_class)),universal_class))))))),X1) )
    | ~ spl0_39
    | ~ spl0_85 ),
    inference(resolution,[],[f662,f380]) ).

fof(f1618,plain,
    ( spl0_192
    | ~ spl0_40
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f544,f539,f383,f1616]) ).

fof(f1616,plain,
    ( spl0_192
  <=> ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f383,plain,
    ( spl0_40
  <=> ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | ~ subclass(X1,X0)
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f539,plain,
    ( spl0_64
  <=> ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f544,plain,
    ( ! [X0] :
        ( ~ inductive(X0)
        | ~ subclass(X0,domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))))
        | domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))) = X0 )
    | ~ spl0_40
    | ~ spl0_64 ),
    inference(resolution,[],[f540,f384]) ).

fof(f384,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X1,X0)
        | ~ subclass(X0,X1)
        | X0 = X1 )
    | ~ spl0_40 ),
    inference(avatar_component_clause,[],[f383]) ).

fof(f540,plain,
    ( ! [X0] :
        ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | ~ inductive(X0) )
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f539]) ).

fof(f1606,plain,
    ( ~ spl0_189
    | ~ spl0_190
    | spl0_191
    | ~ spl0_74
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f623,f615,f595,f1603,f1599,f1595]) ).

fof(f1595,plain,
    ( spl0_189
  <=> function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1599,plain,
    ( spl0_190
  <=> member(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1603,plain,
    ( spl0_191
  <=> member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f595,plain,
    ( spl0_74
  <=> ! [X0,X8] :
        ( ~ function(X8)
        | ~ member(X0,universal_class)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f615,plain,
    ( spl0_77
  <=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f623,plain,
    ( member(domain_of(domain_of(flip(cross_product(subset_relation,universal_class)))),universal_class)
    | ~ member(universal_class,universal_class)
    | ~ function(intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_74
    | ~ spl0_77 ),
    inference(superposition,[],[f596,f617]) ).

fof(f617,plain,
    ( subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f615]) ).

fof(f596,plain,
    ( ! [X0,X8] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X8) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f1593,plain,
    ( spl0_188
    | ~ spl0_28
    | ~ spl0_51
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f589,f575,f459,f326,f1591]) ).

fof(f1591,plain,
    ( spl0_188
  <=> ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f589,plain,
    ( ! [X0,X1] :
        ( null_class = intersection(X1,cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class))
        | ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_51
    | ~ spl0_71 ),
    inference(forward_demodulation,[],[f588,f460]) ).

fof(f588,plain,
    ( ! [X0,X1] :
        ( ~ member(not_subclass_element(X0,domain_of(X1)),universal_class)
        | null_class = intersection(cross_product(unordered_pair(not_subclass_element(X0,domain_of(X1)),not_subclass_element(X0,domain_of(X1))),universal_class),X1)
        | subclass(X0,domain_of(X1)) )
    | ~ spl0_28
    | ~ spl0_71 ),
    inference(resolution,[],[f576,f327]) ).

fof(f1587,plain,
    ( spl0_187
    | ~ spl0_78
    | ~ spl0_89 ),
    inference(avatar_split_clause,[],[f687,f684,f620,f1585]) ).

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

fof(f684,plain,
    ( spl0_89
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f687,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(compose(X1,X0),compose(X1,X0)))),compose_class(X1))
        | ~ member(compose(X1,X0),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_89 ),
    inference(resolution,[],[f685,f621]) ).

fof(f685,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0)) )
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f684]) ).

fof(f1565,plain,
    ( spl0_186
    | ~ spl0_50
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f624,f615,f455,f1563]) ).

fof(f1563,plain,
    ( spl0_186
  <=> ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f455,plain,
    ( spl0_50
  <=> ! [X4,X0,X1] :
        ( ~ member(X4,X0)
        | ~ member(X4,X1)
        | member(X4,intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f624,plain,
    ( ! [X0] :
        ( member(X0,subset_relation)
        | ~ member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))
        | ~ member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_50
    | ~ spl0_77 ),
    inference(superposition,[],[f456,f617]) ).

fof(f456,plain,
    ( ! [X0,X1,X4] :
        ( member(X4,intersection(X0,X1))
        | ~ member(X4,X1)
        | ~ member(X4,X0) )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f455]) ).

fof(f1558,plain,
    ( spl0_185
    | ~ spl0_39
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f629,f620,f379,f1556]) ).

fof(f1556,plain,
    ( spl0_185
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f629,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ member(X0,X1)
        | ~ member(X2,X3)
        | ~ subclass(cross_product(X3,X1),X4)
        | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X0,X0))),X4) )
    | ~ spl0_39
    | ~ spl0_78 ),
    inference(resolution,[],[f621,f380]) ).

fof(f1552,plain,
    ( ~ spl0_182
    | ~ spl0_183
    | spl0_184
    | ~ spl0_23
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f613,f603,f302,f1549,f1545,f1541]) ).

fof(f1541,plain,
    ( spl0_182
  <=> function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f1549,plain,
    ( spl0_184
  <=> inductive(cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f302,plain,
    ( spl0_23
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(X8,cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f603,plain,
    ( spl0_76
  <=> ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f613,plain,
    ( inductive(cross_product(universal_class,universal_class))
    | ~ member(null_class,cross_product(universal_class,universal_class))
    | ~ function(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(cross_product(universal_class,universal_class),universal_class)),universal_class)))))
    | ~ spl0_23
    | ~ spl0_76 ),
    inference(resolution,[],[f604,f303]) ).

fof(f303,plain,
    ( ! [X8] :
        ( subclass(X8,cross_product(universal_class,universal_class))
        | ~ function(X8) )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f302]) ).

fof(f604,plain,
    ( ! [X0] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
        | inductive(X0)
        | ~ member(null_class,X0) )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f1539,plain,
    ( spl0_181
    | ~ spl0_40
    | ~ spl0_58 ),
    inference(avatar_split_clause,[],[f521,f510,f383,f1537]) ).

fof(f1537,plain,
    ( spl0_181
  <=> ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f510,plain,
    ( spl0_58
  <=> ! [X8] :
        ( ~ operation(X8)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f521,plain,
    ( ! [X0] :
        ( ~ operation(X0)
        | ~ subclass(domain_of(domain_of(X0)),domain_of(domain_of(flip(cross_product(X0,universal_class)))))
        | domain_of(domain_of(flip(cross_product(X0,universal_class)))) = domain_of(domain_of(X0)) )
    | ~ spl0_40
    | ~ spl0_58 ),
    inference(resolution,[],[f511,f384]) ).

fof(f511,plain,
    ( ! [X8] :
        ( subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | ~ operation(X8) )
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f510]) ).

fof(f1532,plain,
    ( ~ spl0_179
    | spl0_180
    | ~ spl0_15
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f920,f899,f269,f1529,f1525]) ).

fof(f1525,plain,
    ( spl0_179
  <=> single_valued_class(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1529,plain,
    ( spl0_180
  <=> function(domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f269,plain,
    ( spl0_15
  <=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

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

fof(f920,plain,
    ( function(domain_relation)
    | ~ single_valued_class(domain_relation)
    | ~ spl0_15
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f271]) ).

fof(f271,plain,
    ( subclass(domain_relation,cross_product(universal_class,universal_class))
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f269]) ).

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

fof(f1523,plain,
    ( spl0_177
    | spl0_178
    | ~ spl0_41
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f608,f595,f387,f1520,f1517]) ).

fof(f1517,plain,
    ( spl0_177
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | null_class = cross_product(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f1520,plain,
    ( spl0_178
  <=> member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f608,plain,
    ( ! [X0] :
        ( member(domain_of(domain_of(flip(cross_product(null_class,universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(regular(cross_product(X0,universal_class)))
        | null_class = cross_product(X0,universal_class) )
    | ~ spl0_41
    | ~ spl0_74 ),
    inference(superposition,[],[f596,f388]) ).

fof(f1515,plain,
    ( spl0_176
    | ~ spl0_64
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f554,f550,f539,f1513]) ).

fof(f1513,plain,
    ( spl0_176
  <=> ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f550,plain,
    ( spl0_66
  <=> ! [X1,X8] :
        ( ~ function(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | maps(X8,domain_of(X8),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f554,plain,
    ( ! [X0] :
        ( ~ function(intersection(successor_relation,cross_product(X0,universal_class)))
        | maps(intersection(successor_relation,cross_product(X0,universal_class)),domain_of(intersection(successor_relation,cross_product(X0,universal_class))),X0)
        | ~ inductive(X0) )
    | ~ spl0_64
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f540]) ).

fof(f551,plain,
    ( ! [X1,X8] :
        ( ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
        | ~ function(X8)
        | maps(X8,domain_of(X8),X1) )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f550]) ).

fof(f1477,plain,
    ( spl0_175
    | ~ spl0_78
    | ~ spl0_86 ),
    inference(avatar_split_clause,[],[f674,f671,f620,f1475]) ).

fof(f1475,plain,
    ( spl0_175
  <=> ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f671,plain,
    ( spl0_86
  <=> ! [X0,X1] :
        ( ~ member(X0,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f674,plain,
    ( ! [X0,X1] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1)
        | ~ member(X1,universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_78
    | ~ spl0_86 ),
    inference(resolution,[],[f672,f621]) ).

fof(f672,plain,
    ( ! [X0,X1] :
        ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
        | ~ member(X0,X1) )
    | ~ spl0_86 ),
    inference(avatar_component_clause,[],[f671]) ).

fof(f1473,plain,
    ( spl0_173
    | spl0_174
    | ~ spl0_13
    | ~ spl0_80 ),
    inference(avatar_split_clause,[],[f648,f635,f261,f1470,f1467]) ).

fof(f1467,plain,
    ( spl0_173
  <=> ! [X0,X1] : ~ inductive(cross_product(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1470,plain,
    ( spl0_174
  <=> null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f648,plain,
    ( ! [X0,X1] :
        ( null_class = unordered_pair(unordered_pair(first(null_class),first(null_class)),unordered_pair(first(null_class),unordered_pair(second(null_class),second(null_class))))
        | ~ inductive(cross_product(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_80 ),
    inference(resolution,[],[f636,f262]) ).

fof(f1465,plain,
    ( spl0_172
    | ~ spl0_39
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f610,f599,f379,f1463]) ).

fof(f1463,plain,
    ( spl0_172
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f599,plain,
    ( spl0_75
  <=> ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f610,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X0),universal_class)),universal_class))))),X1) )
    | ~ spl0_39
    | ~ spl0_75 ),
    inference(resolution,[],[f600,f380]) ).

fof(f600,plain,
    ( ! [X2] :
        ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
        | ~ member(X2,universal_class) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f599]) ).

fof(f1461,plain,
    ( spl0_171
    | ~ spl0_39
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f606,f595,f379,f1459]) ).

fof(f1459,plain,
    ( spl0_171
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f606,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ function(X1)
        | ~ subclass(universal_class,X2)
        | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X1),universal_class)))),X2) )
    | ~ spl0_39
    | ~ spl0_74 ),
    inference(resolution,[],[f596,f380]) ).

fof(f1457,plain,
    ( spl0_170
    | ~ spl0_40
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f501,f467,f383,f1455]) ).

fof(f1455,plain,
    ( spl0_170
  <=> ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f467,plain,
    ( spl0_53
  <=> ! [X8] :
        ( ~ function(X8)
        | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f501,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_40
    | ~ spl0_53 ),
    inference(resolution,[],[f468,f384]) ).

fof(f468,plain,
    ( ! [X8] :
        ( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ function(X8) )
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f467]) ).

fof(f1453,plain,
    ( spl0_169
    | ~ spl0_40
    | ~ spl0_52 ),
    inference(avatar_split_clause,[],[f500,f463,f383,f1451]) ).

fof(f1451,plain,
    ( spl0_169
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f463,plain,
    ( spl0_52
  <=> ! [X0] :
        ( ~ single_valued_class(X0)
        | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f500,plain,
    ( ! [X0] :
        ( ~ single_valued_class(X0)
        | ~ subclass(identity_relation,compose(X0,domain_of(flip(cross_product(X0,universal_class)))))
        | identity_relation = compose(X0,domain_of(flip(cross_product(X0,universal_class)))) )
    | ~ spl0_40
    | ~ spl0_52 ),
    inference(resolution,[],[f464,f384]) ).

fof(f464,plain,
    ( ! [X0] :
        ( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | ~ single_valued_class(X0) )
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f463]) ).

fof(f1386,plain,
    ( spl0_168
    | ~ spl0_83 ),
    inference(avatar_split_clause,[],[f655,f652,f1384]) ).

fof(f1384,plain,
    ( spl0_168
  <=> ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f652,plain,
    ( spl0_83
  <=> ! [X9,X11,X10] :
        ( ~ function(X9)
        | compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) != domain_of(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f655,plain,
    ( ! [X0,X1] :
        ( compatible(domain_of(X0),X0,X1)
        | ~ function(domain_of(X0))
        | ~ subclass(domain_of(domain_of(flip(cross_product(domain_of(X0),universal_class)))),domain_of(domain_of(X1))) )
    | ~ spl0_83 ),
    inference(equality_resolution,[],[f653]) ).

fof(f653,plain,
    ( ! [X10,X11,X9] :
        ( domain_of(domain_of(X10)) != domain_of(X9)
        | compatible(X9,X10,X11)
        | ~ function(X9)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f652]) ).

fof(f1382,plain,
    ( spl0_167
    | ~ spl0_39
    | ~ spl0_71 ),
    inference(avatar_split_clause,[],[f587,f575,f379,f1380]) ).

fof(f1380,plain,
    ( spl0_167
  <=> ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f587,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(X0,universal_class)
        | null_class = intersection(cross_product(unordered_pair(X0,X0),universal_class),X1)
        | ~ subclass(domain_of(X1),X2)
        | member(X0,X2) )
    | ~ spl0_39
    | ~ spl0_71 ),
    inference(resolution,[],[f576,f380]) ).

fof(f1378,plain,
    ( spl0_166
    | ~ spl0_39
    | ~ spl0_67 ),
    inference(avatar_split_clause,[],[f584,f559,f379,f1376]) ).

fof(f1376,plain,
    ( spl0_166
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f559,plain,
    ( spl0_67
  <=> ! [X0] :
        ( ~ member(X0,universal_class)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f584,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(domain_relation,X1)
        | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),X1) )
    | ~ spl0_39
    | ~ spl0_67 ),
    inference(resolution,[],[f560,f380]) ).

fof(f560,plain,
    ( ! [X0] :
        ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation)
        | ~ member(X0,universal_class) )
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f559]) ).

fof(f1374,plain,
    ( spl0_165
    | ~ spl0_28
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f490,f455,f326,f1372]) ).

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

fof(f490,plain,
    ( ! [X2,X0,X1] :
        ( ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
        | ~ member(not_subclass_element(X0,intersection(X1,X2)),X1)
        | subclass(X0,intersection(X1,X2)) )
    | ~ spl0_28
    | ~ spl0_50 ),
    inference(resolution,[],[f456,f327]) ).

fof(f1370,plain,
    ( spl0_164
    | ~ spl0_27
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f486,f451,f322,f1368]) ).

fof(f1368,plain,
    ( spl0_164
  <=> ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f486,plain,
    ( ! [X2,X0,X1] :
        ( not_subclass_element(unordered_pair(X0,X1),X2) = X0
        | not_subclass_element(unordered_pair(X0,X1),X2) = X1
        | subclass(unordered_pair(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_49 ),
    inference(resolution,[],[f452,f323]) ).

fof(f1360,plain,
    ( spl0_163
    | ~ spl0_33
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f625,f615,f346,f1358]) ).

fof(f1358,plain,
    ( spl0_163
  <=> ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f625,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) )
    | ~ spl0_33
    | ~ spl0_77 ),
    inference(superposition,[],[f347,f617]) ).

fof(f1329,plain,
    ( spl0_162
    | ~ spl0_51
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f607,f595,f459,f1327]) ).

fof(f1327,plain,
    ( spl0_162
  <=> ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f607,plain,
    ( ! [X0,X1] :
        ( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
        | ~ member(X0,universal_class)
        | ~ function(X1) )
    | ~ spl0_51
    | ~ spl0_74 ),
    inference(superposition,[],[f596,f460]) ).

fof(f1325,plain,
    ( spl0_161
    | ~ spl0_24
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f485,f451,f306,f1323]) ).

fof(f1323,plain,
    ( spl0_161
  <=> ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f485,plain,
    ( ! [X0,X1] :
        ( regular(unordered_pair(X0,X1)) = X0
        | regular(unordered_pair(X0,X1)) = X1
        | unordered_pair(X0,X1) = null_class )
    | ~ spl0_24
    | ~ spl0_49 ),
    inference(resolution,[],[f452,f307]) ).

fof(f1307,plain,
    ( spl0_160
    | ~ spl0_23
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f557,f550,f302,f1305]) ).

fof(f1305,plain,
    ( spl0_160
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f557,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),cross_product(universal_class,universal_class))
        | ~ function(domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_23
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f303]) ).

fof(f1303,plain,
    ( spl0_159
    | ~ spl0_41
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f529,f523,f387,f1301]) ).

fof(f1301,plain,
    ( spl0_159
  <=> ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f523,plain,
    ( spl0_61
  <=> ! [X4,X0] :
        ( ~ member(X4,domain_of(X0))
        | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f529,plain,
    ( ! [X0] :
        ( ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_41
    | ~ spl0_61 ),
    inference(trivial_inequality_removal,[],[f527]) ).

fof(f527,plain,
    ( ! [X0] :
        ( null_class != null_class
        | ~ member(X0,domain_of(regular(cross_product(unordered_pair(X0,X0),universal_class))))
        | null_class = cross_product(unordered_pair(X0,X0),universal_class) )
    | ~ spl0_41
    | ~ spl0_61 ),
    inference(superposition,[],[f524,f388]) ).

fof(f524,plain,
    ( ! [X0,X4] :
        ( null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0)
        | ~ member(X4,domain_of(X0)) )
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f523]) ).

fof(f1299,plain,
    ( spl0_158
    | ~ spl0_28
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f448,f431,f326,f1297]) ).

fof(f1297,plain,
    ( spl0_158
  <=> ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f431,plain,
    ( spl0_45
  <=> ! [X4,X0] :
        ( ~ member(X4,universal_class)
        | member(X4,X0)
        | member(X4,complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f448,plain,
    ( ! [X0,X1] :
        ( member(not_subclass_element(X0,complement(X1)),X1)
        | ~ member(not_subclass_element(X0,complement(X1)),universal_class)
        | subclass(X0,complement(X1)) )
    | ~ spl0_28
    | ~ spl0_45 ),
    inference(resolution,[],[f432,f327]) ).

fof(f432,plain,
    ( ! [X0,X4] :
        ( member(X4,complement(X0))
        | member(X4,X0)
        | ~ member(X4,universal_class) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f431]) ).

fof(f1295,plain,
    ( spl0_157
    | ~ spl0_35
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f416,f383,f354,f1293]) ).

fof(f1293,plain,
    ( spl0_157
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f354,plain,
    ( spl0_35
  <=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f416,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
        | cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) )
    | ~ spl0_35
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f355]) ).

fof(f355,plain,
    ( ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f354]) ).

fof(f1291,plain,
    ( ~ spl0_155
    | spl0_156
    | ~ spl0_12
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f916,f899,f256,f1288,f1284]) ).

fof(f1284,plain,
    ( spl0_155
  <=> single_valued_class(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f1288,plain,
    ( spl0_156
  <=> function(successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f256,plain,
    ( spl0_12
  <=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f916,plain,
    ( function(successor_relation)
    | ~ single_valued_class(successor_relation)
    | ~ spl0_12
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f258]) ).

fof(f258,plain,
    ( subclass(successor_relation,cross_product(universal_class,universal_class))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f1282,plain,
    ( spl0_154
    | ~ spl0_34
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f415,f383,f350,f1280]) ).

fof(f1280,plain,
    ( spl0_154
  <=> ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f350,plain,
    ( spl0_34
  <=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f415,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
        | rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) )
    | ~ spl0_34
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f351]) ).

fof(f351,plain,
    ( ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class))
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f350]) ).

fof(f1256,plain,
    ( spl0_153
    | ~ spl0_39
    | ~ spl0_55 ),
    inference(avatar_split_clause,[],[f504,f475,f379,f1254]) ).

fof(f1254,plain,
    ( spl0_153
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f475,plain,
    ( spl0_55
  <=> ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f504,plain,
    ( ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | ~ subclass(universal_class,X1)
        | member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),X1) )
    | ~ spl0_39
    | ~ spl0_55 ),
    inference(resolution,[],[f476,f380]) ).

fof(f476,plain,
    ( ! [X0] :
        ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
        | ~ member(X0,universal_class) )
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f475]) ).

fof(f1252,plain,
    ( spl0_152
    | ~ spl0_39
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f489,f455,f379,f1250]) ).

fof(f1250,plain,
    ( spl0_152
  <=> ! [X0,X3,X2,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f489,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ member(X0,X1)
        | ~ member(X0,X2)
        | ~ subclass(intersection(X2,X1),X3)
        | member(X0,X3) )
    | ~ spl0_39
    | ~ spl0_50 ),
    inference(resolution,[],[f456,f380]) ).

fof(f1248,plain,
    ( spl0_150
    | ~ spl0_151
    | ~ spl0_26
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f423,f383,f315,f1245,f1241]) ).

fof(f1241,plain,
    ( spl0_150
  <=> cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f1245,plain,
    ( spl0_151
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f315,plain,
    ( spl0_26
  <=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f423,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
    | cross_product(universal_class,cross_product(universal_class,universal_class)) = application_function
    | ~ spl0_26
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f317]) ).

fof(f317,plain,
    ( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f315]) ).

fof(f1239,plain,
    ( spl0_148
    | ~ spl0_149
    | ~ spl0_25
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f421,f383,f310,f1236,f1232]) ).

fof(f1232,plain,
    ( spl0_148
  <=> composition_function = cross_product(universal_class,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f1236,plain,
    ( spl0_149
  <=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f310,plain,
    ( spl0_25
  <=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f421,plain,
    ( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
    | composition_function = cross_product(universal_class,cross_product(universal_class,universal_class))
    | ~ spl0_25
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f312]) ).

fof(f312,plain,
    ( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f310]) ).

fof(f1230,plain,
    ( spl0_147
    | ~ spl0_22
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f419,f383,f298,f1228]) ).

fof(f1228,plain,
    ( spl0_147
  <=> ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f298,plain,
    ( spl0_22
  <=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f419,plain,
    ( ! [X0,X1] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
        | cross_product(universal_class,universal_class) = compose(X0,X1) )
    | ~ spl0_22
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f299]) ).

fof(f299,plain,
    ( ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class))
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f298]) ).

fof(f1180,plain,
    ( spl0_146
    | ~ spl0_51
    | ~ spl0_61 ),
    inference(avatar_split_clause,[],[f526,f523,f459,f1178]) ).

fof(f1178,plain,
    ( spl0_146
  <=> ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f526,plain,
    ( ! [X0,X1] :
        ( null_class != intersection(X1,cross_product(unordered_pair(X0,X0),universal_class))
        | ~ member(X0,domain_of(X1)) )
    | ~ spl0_51
    | ~ spl0_61 ),
    inference(superposition,[],[f524,f460]) ).

fof(f1176,plain,
    ( spl0_145
    | ~ spl0_44
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f493,f455,f400,f1174]) ).

fof(f1174,plain,
    ( spl0_145
  <=> ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f400,plain,
    ( spl0_44
  <=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f493,plain,
    ( ! [X0] :
        ( member(X0,identity_relation)
        | ~ member(X0,subset_relation)
        | ~ member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_44
    | ~ spl0_50 ),
    inference(superposition,[],[f456,f402]) ).

fof(f402,plain,
    ( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f400]) ).

fof(f1172,plain,
    ( spl0_144
    | ~ spl0_43
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f492,f455,f395,f1170]) ).

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

fof(f395,plain,
    ( spl0_43
  <=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f492,plain,
    ( ! [X0] :
        ( member(X0,singleton_relation)
        | ~ member(X0,element_relation)
        | ~ member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_43
    | ~ spl0_50 ),
    inference(superposition,[],[f456,f397]) ).

fof(f397,plain,
    ( intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f395]) ).

fof(f1168,plain,
    ( spl0_143
    | ~ spl0_41
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f491,f455,f387,f1166]) ).

fof(f1166,plain,
    ( spl0_143
  <=> ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f491,plain,
    ( ! [X0,X1] :
        ( member(X1,null_class)
        | ~ member(X1,regular(X0))
        | ~ member(X1,X0)
        | null_class = X0 )
    | ~ spl0_41
    | ~ spl0_50 ),
    inference(superposition,[],[f456,f388]) ).

fof(f1164,plain,
    ( spl0_142
    | ~ spl0_39
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f447,f431,f379,f1162]) ).

fof(f1162,plain,
    ( spl0_142
  <=> ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f447,plain,
    ( ! [X2,X0,X1] :
        ( member(X0,X1)
        | ~ member(X0,universal_class)
        | ~ subclass(complement(X1),X2)
        | member(X0,X2) )
    | ~ spl0_39
    | ~ spl0_45 ),
    inference(resolution,[],[f432,f380]) ).

fof(f1117,plain,
    ( spl0_141
    | ~ spl0_7
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f556,f550,f235,f1115]) ).

fof(f1115,plain,
    ( spl0_141
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f235,plain,
    ( spl0_7
  <=> ! [X1] : subclass(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f556,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(flip(cross_product(X0,universal_class))))) )
    | ~ spl0_7
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f236]) ).

fof(f236,plain,
    ( ! [X1] : subclass(X1,X1)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f235]) ).

fof(f1113,plain,
    ( spl0_140
    | ~ spl0_19
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f420,f383,f286,f1111]) ).

fof(f1111,plain,
    ( spl0_140
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f286,plain,
    ( spl0_19
  <=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f420,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),compose_class(X0))
        | cross_product(universal_class,universal_class) = compose_class(X0) )
    | ~ spl0_19
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f287]) ).

fof(f287,plain,
    ( ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class))
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f286]) ).

fof(f1109,plain,
    ( ~ spl0_138
    | spl0_139
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(avatar_split_clause,[],[f914,f899,f251,f1106,f1102]) ).

fof(f1102,plain,
    ( spl0_138
  <=> single_valued_class(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f1106,plain,
    ( spl0_139
  <=> function(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f251,plain,
    ( spl0_11
  <=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f914,plain,
    ( function(element_relation)
    | ~ single_valued_class(element_relation)
    | ~ spl0_11
    | ~ spl0_115 ),
    inference(resolution,[],[f900,f253]) ).

fof(f253,plain,
    ( subclass(element_relation,cross_product(universal_class,universal_class))
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f251]) ).

fof(f1100,plain,
    ( spl0_137
    | ~ spl0_23
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f413,f383,f302,f1098]) ).

fof(f1098,plain,
    ( spl0_137
  <=> ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f413,plain,
    ( ! [X0] :
        ( ~ subclass(cross_product(universal_class,universal_class),X0)
        | cross_product(universal_class,universal_class) = X0
        | ~ function(X0) )
    | ~ spl0_23
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f303]) ).

fof(f1096,plain,
    ( spl0_136
    | ~ spl0_27
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f377,f346,f322,f1094]) ).

fof(f377,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X1)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_33 ),
    inference(resolution,[],[f347,f323]) ).

fof(f1092,plain,
    ( spl0_135
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f374,f338,f322,f1090]) ).

fof(f374,plain,
    ( ! [X2,X0,X1] :
        ( member(not_subclass_element(intersection(X0,X1),X2),X0)
        | subclass(intersection(X0,X1),X2) )
    | ~ spl0_27
    | ~ spl0_31 ),
    inference(resolution,[],[f339,f323]) ).

fof(f1033,plain,
    ( spl0_134
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f553,f550,f510,f1031]) ).

fof(f1031,plain,
    ( spl0_134
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f553,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),domain_of(domain_of(X0)))
        | ~ operation(X0) )
    | ~ spl0_58
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f511]) ).

fof(f1029,plain,
    ( spl0_133
    | ~ spl0_30
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f410,f379,f334,f1027]) ).

fof(f1027,plain,
    ( spl0_133
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f334,plain,
    ( spl0_30
  <=> ! [X0,X1] :
        ( ~ member(X1,universal_class)
        | member(X1,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f410,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X1,X2)
        | ~ member(X1,universal_class) )
    | ~ spl0_30
    | ~ spl0_39 ),
    inference(resolution,[],[f380,f335]) ).

fof(f335,plain,
    ( ! [X0,X1] :
        ( member(X1,unordered_pair(X0,X1))
        | ~ member(X1,universal_class) )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f334]) ).

fof(f1025,plain,
    ( spl0_132
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f409,f379,f330,f1023]) ).

fof(f1023,plain,
    ( spl0_132
  <=> ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f330,plain,
    ( spl0_29
  <=> ! [X0,X1] :
        ( ~ member(X0,universal_class)
        | member(X0,unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f409,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(unordered_pair(X0,X1),X2)
        | member(X0,X2)
        | ~ member(X0,universal_class) )
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(resolution,[],[f380,f331]) ).

fof(f331,plain,
    ( ! [X0,X1] :
        ( member(X0,unordered_pair(X0,X1))
        | ~ member(X0,universal_class) )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f330]) ).

fof(f1021,plain,
    ( spl0_131
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f408,f379,f322,f1019]) ).

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

fof(f408,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(X0,X1)
        | member(not_subclass_element(X0,X2),X1)
        | subclass(X0,X2) )
    | ~ spl0_27
    | ~ spl0_39 ),
    inference(resolution,[],[f380,f323]) ).

fof(f1017,plain,
    ( spl0_130
    | ~ spl0_24
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f376,f346,f306,f1015]) ).

fof(f1015,plain,
    ( spl0_130
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f376,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X1)
        | intersection(X0,X1) = null_class )
    | ~ spl0_24
    | ~ spl0_33 ),
    inference(resolution,[],[f347,f307]) ).

fof(f1013,plain,
    ( spl0_129
    | ~ spl0_24
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f373,f338,f306,f1011]) ).

fof(f1011,plain,
    ( spl0_129
  <=> ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f373,plain,
    ( ! [X0,X1] :
        ( member(regular(intersection(X0,X1)),X0)
        | intersection(X0,X1) = null_class )
    | ~ spl0_24
    | ~ spl0_31 ),
    inference(resolution,[],[f339,f307]) ).

fof(f982,plain,
    ( ~ spl0_128
    | ~ spl0_13
    | spl0_108 ),
    inference(avatar_split_clause,[],[f947,f813,f261,f979]) ).

fof(f979,plain,
    ( spl0_128
  <=> inductive(element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f813,plain,
    ( spl0_108
  <=> member(null_class,element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f947,plain,
    ( ~ inductive(element_relation)
    | ~ spl0_13
    | spl0_108 ),
    inference(resolution,[],[f814,f262]) ).

fof(f814,plain,
    ( ~ member(null_class,element_relation)
    | spl0_108 ),
    inference(avatar_component_clause,[],[f813]) ).

fof(f972,plain,
    ( spl0_127
    | ~ spl0_13
    | ~ spl0_49 ),
    inference(avatar_split_clause,[],[f484,f451,f261,f970]) ).

fof(f970,plain,
    ( spl0_127
  <=> ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f484,plain,
    ( ! [X0,X1] :
        ( null_class = X0
        | null_class = X1
        | ~ inductive(unordered_pair(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_49 ),
    inference(resolution,[],[f452,f262]) ).

fof(f968,plain,
    ( spl0_126
    | ~ spl0_31
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f429,f400,f338,f966]) ).

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

fof(f429,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,domain_of(flip(cross_product(subset_relation,universal_class)))) )
    | ~ spl0_31
    | ~ spl0_44 ),
    inference(superposition,[],[f339,f402]) ).

fof(f964,plain,
    ( spl0_125
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f427,f395,f338,f962]) ).

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

fof(f427,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,complement(compose(element_relation,complement(identity_relation)))) )
    | ~ spl0_31
    | ~ spl0_43 ),
    inference(superposition,[],[f339,f397]) ).

fof(f960,plain,
    ( spl0_124
    | ~ spl0_33
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f424,f387,f346,f958]) ).

fof(f958,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f424,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,regular(X0))
        | null_class = X0 )
    | ~ spl0_33
    | ~ spl0_41 ),
    inference(superposition,[],[f347,f388]) ).

fof(f956,plain,
    ( spl0_122
    | ~ spl0_123
    | ~ spl0_15
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f422,f383,f269,f953,f949]) ).

fof(f949,plain,
    ( spl0_122
  <=> cross_product(universal_class,universal_class) = domain_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f953,plain,
    ( spl0_123
  <=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f422,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
    | cross_product(universal_class,universal_class) = domain_relation
    | ~ spl0_15
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f271]) ).

fof(f946,plain,
    ( spl0_120
    | ~ spl0_121
    | ~ spl0_12
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f417,f383,f256,f943,f939]) ).

fof(f939,plain,
    ( spl0_120
  <=> cross_product(universal_class,universal_class) = successor_relation ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f943,plain,
    ( spl0_121
  <=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f417,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
    | cross_product(universal_class,universal_class) = successor_relation
    | ~ spl0_12
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f258]) ).

fof(f937,plain,
    ( spl0_118
    | ~ spl0_119
    | ~ spl0_11
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f414,f383,f251,f934,f930]) ).

fof(f930,plain,
    ( spl0_118
  <=> element_relation = cross_product(universal_class,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f934,plain,
    ( spl0_119
  <=> subclass(cross_product(universal_class,universal_class),element_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f414,plain,
    ( ~ subclass(cross_product(universal_class,universal_class),element_relation)
    | element_relation = cross_product(universal_class,universal_class)
    | ~ spl0_11
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f253]) ).

fof(f928,plain,
    ( spl0_117
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f407,f379,f306,f926]) ).

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

fof(f407,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(regular(X0),X1)
        | null_class = X0 )
    | ~ spl0_24
    | ~ spl0_39 ),
    inference(resolution,[],[f380,f307]) ).

fof(f924,plain,
    ( spl0_116
    | ~ spl0_21
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f369,f322,f294,f922]) ).

fof(f922,plain,
    ( spl0_116
  <=> ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f369,plain,
    ( ! [X0,X1] :
        ( subclass(complement(X0),X1)
        | ~ member(not_subclass_element(complement(X0),X1),X0) )
    | ~ spl0_21
    | ~ spl0_27 ),
    inference(resolution,[],[f323,f295]) ).

fof(f901,plain,
    ( spl0_115
    | ~ spl0_52
    | ~ spl0_70 ),
    inference(avatar_split_clause,[],[f586,f571,f463,f899]) ).

fof(f571,plain,
    ( spl0_70
  <=> ! [X8] :
        ( function(X8)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f586,plain,
    ( ! [X0] :
        ( ~ subclass(X0,cross_product(universal_class,universal_class))
        | function(X0)
        | ~ single_valued_class(X0) )
    | ~ spl0_52
    | ~ spl0_70 ),
    inference(resolution,[],[f572,f464]) ).

fof(f572,plain,
    ( ! [X8] :
        ( ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
        | ~ subclass(X8,cross_product(universal_class,universal_class))
        | function(X8) )
    | ~ spl0_70 ),
    inference(avatar_component_clause,[],[f571]) ).

fof(f897,plain,
    ( spl0_114
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f425,f387,f338,f895]) ).

fof(f895,plain,
    ( spl0_114
  <=> ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f425,plain,
    ( ! [X0,X1] :
        ( ~ member(X1,null_class)
        | member(X1,X0)
        | null_class = X0 )
    | ~ spl0_31
    | ~ spl0_41 ),
    inference(superposition,[],[f339,f388]) ).

fof(f893,plain,
    ( spl0_113
    | ~ spl0_21
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f320,f306,f294,f891]) ).

fof(f891,plain,
    ( spl0_113
  <=> ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f320,plain,
    ( ! [X0] :
        ( complement(X0) = null_class
        | ~ member(regular(complement(X0)),X0) )
    | ~ spl0_21
    | ~ spl0_24 ),
    inference(resolution,[],[f307,f295]) ).

fof(f832,plain,
    ( spl0_112
    | ~ spl0_31
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f626,f615,f338,f830]) ).

fof(f626,plain,
    ( ! [X0] :
        ( ~ member(X0,subset_relation)
        | member(X0,cross_product(universal_class,universal_class)) )
    | ~ spl0_31
    | ~ spl0_77 ),
    inference(superposition,[],[f339,f617]) ).

fof(f828,plain,
    ( spl0_111
    | ~ spl0_14
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f418,f383,f265,f826]) ).

fof(f826,plain,
    ( spl0_111
  <=> ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f265,plain,
    ( spl0_14
  <=> ! [X1] :
        ( ~ inductive(X1)
        | subclass(omega,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f418,plain,
    ( ! [X0] :
        ( ~ subclass(X0,omega)
        | omega = X0
        | ~ inductive(X0) )
    | ~ spl0_14
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f266]) ).

fof(f266,plain,
    ( ! [X1] :
        ( subclass(omega,X1)
        | ~ inductive(X1) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f824,plain,
    ( spl0_110
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f406,f379,f261,f822]) ).

fof(f406,plain,
    ( ! [X0,X1] :
        ( ~ subclass(X0,X1)
        | member(null_class,X1)
        | ~ inductive(X0) )
    | ~ spl0_13
    | ~ spl0_39 ),
    inference(resolution,[],[f380,f262]) ).

fof(f820,plain,
    ( spl0_109
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f405,f379,f247,f818]) ).

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

fof(f247,plain,
    ( spl0_10
  <=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f405,plain,
    ( ! [X2,X0,X1] :
        ( ~ subclass(universal_class,X0)
        | member(unordered_pair(X1,X2),X0) )
    | ~ spl0_10
    | ~ spl0_39 ),
    inference(resolution,[],[f380,f248]) ).

fof(f248,plain,
    ( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f247]) ).

fof(f816,plain,
    ( ~ spl0_107
    | spl0_108
    | ~ spl0_13
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f778,f738,f261,f813,f809]) ).

fof(f809,plain,
    ( spl0_107
  <=> inductive(singleton_relation) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f738,plain,
    ( spl0_98
  <=> ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f778,plain,
    ( member(null_class,element_relation)
    | ~ inductive(singleton_relation)
    | ~ spl0_13
    | ~ spl0_98 ),
    inference(resolution,[],[f739,f262]) ).

fof(f739,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f738]) ).

fof(f798,plain,
    ( spl0_106
    | ~ spl0_5
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f555,f550,f226,f796]) ).

fof(f796,plain,
    ( spl0_106
  <=> ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f555,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | maps(X0,domain_of(X0),universal_class) )
    | ~ spl0_5
    | ~ spl0_66 ),
    inference(resolution,[],[f551,f227]) ).

fof(f788,plain,
    ( spl0_105
    | ~ spl0_13
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f375,f346,f261,f786]) ).

fof(f786,plain,
    ( spl0_105
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f375,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X1,X0)) )
    | ~ spl0_13
    | ~ spl0_33 ),
    inference(resolution,[],[f347,f262]) ).

fof(f770,plain,
    ( spl0_104
    | ~ spl0_33
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f428,f400,f346,f768]) ).

fof(f428,plain,
    ( ! [X0] :
        ( ~ member(X0,identity_relation)
        | member(X0,subset_relation) )
    | ~ spl0_33
    | ~ spl0_44 ),
    inference(superposition,[],[f347,f402]) ).

fof(f766,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f203,f764]) ).

fof(f764,plain,
    ( spl0_103
  <=> ! [X9,X11,X10] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
        | ~ operation(X10)
        | ~ operation(X11)
        | ~ compatible(X9,X10,X11)
        | homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f203,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f202,f129]) ).

fof(f129,plain,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
    inference(definition_unfolding,[],[f28,f29]) ).

fof(f29,axiom,
    ! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).

fof(f28,axiom,
    ! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).

fof(f202,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f201,f129]) ).

fof(f201,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f200,f129]) ).

fof(f200,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f199,f129]) ).

fof(f199,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f198,f129]) ).

fof(f198,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f197,f129]) ).

fof(f197,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f196,f129]) ).

fof(f196,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f195,f129]) ).

fof(f195,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f194,f129]) ).

fof(f194,plain,
    ! [X10,X11,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11) ),
    inference(forward_demodulation,[],[f176,f129]) ).

fof(f176,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f91,f117,f118,f117,f117,f117,f117,f118]) ).

fof(f118,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).

fof(f117,plain,
    ! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
    inference(definition_unfolding,[],[f68,f114,f116,f12]) ).

fof(f116,plain,
    ! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
    inference(definition_unfolding,[],[f42,f115,f29]) ).

fof(f115,plain,
    ! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
    inference(definition_unfolding,[],[f39,f38]) ).

fof(f38,axiom,
    ! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).

fof(f39,axiom,
    ! [X4] : domain_of(inverse(X4)) = range_of(X4),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).

fof(f42,axiom,
    ! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).

fof(f114,plain,
    ! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
    inference(definition_unfolding,[],[f53,f29]) ).

fof(f53,axiom,
    ! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).

fof(f68,axiom,
    ! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).

fof(f91,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).

fof(f759,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f193,f757]) ).

fof(f193,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f192,f129]) ).

fof(f192,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f191,f129]) ).

fof(f191,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f190,f129]) ).

fof(f190,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f189,f129]) ).

fof(f189,plain,
    ! [X10,X0,X11,X1,X9] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
      | ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
    inference(forward_demodulation,[],[f168,f129]) ).

fof(f168,plain,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
      | domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
    inference(definition_unfolding,[],[f89,f118,f117,f118,f117,f117,f117,f117,f118]) ).

fof(f89,axiom,
    ! [X10,X0,X11,X1,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | ~ member(ordered_pair(X0,X1),domain_of(X10))
      | apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).

fof(f754,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f188,f752]) ).

fof(f188,plain,
    ! [X0,X1,X4] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class)))))))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))))))))),application_function)
      | ~ member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(forward_demodulation,[],[f167,f129]) ).

fof(f167,plain,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation))))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)))))))),application_function)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    inference(definition_unfolding,[],[f108,f118,f118,f117,f118,f118]) ).

fof(f108,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X1,domain_of(X0))
      | member(ordered_pair(X0,ordered_pair(X1,apply(X0,X1))),application_function)
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),cross_product(universal_class,cross_product(universal_class,universal_class))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn4) ).

fof(f748,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f172,f746]) ).

fof(f172,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f37,f118,f118,f118,f118,f118,f118]) ).

fof(f37,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).

fof(f744,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f171,f742]) ).

fof(f171,plain,
    ! [X2,X3,X0,X6] :
      ( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    inference(definition_unfolding,[],[f34,f118,f118,f118,f118,f118,f118]) ).

fof(f34,axiom,
    ! [X2,X3,X0,X6] :
      ( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).

fof(f740,plain,
    ( spl0_98
    | ~ spl0_33
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f426,f395,f346,f738]) ).

fof(f426,plain,
    ( ! [X0] :
        ( ~ member(X0,singleton_relation)
        | member(X0,element_relation) )
    | ~ spl0_33
    | ~ spl0_43 ),
    inference(superposition,[],[f347,f397]) ).

fof(f736,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f156,f734]) ).

fof(f734,plain,
    ( spl0_97
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f156,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
    inference(definition_unfolding,[],[f36,f118,f118,f118,f118]) ).

fof(f36,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).

fof(f732,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f155,f730]) ).

fof(f730,plain,
    ( spl0_96
  <=> ! [X3,X0,X6,X2] :
        ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
        | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f155,plain,
    ! [X2,X3,X0,X6] :
      ( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
      | ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
    inference(definition_unfolding,[],[f33,f118,f118,f118,f118]) ).

fof(f33,axiom,
    ! [X2,X3,X0,X6] :
      ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
      | ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).

fof(f727,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f179,f725]) ).

fof(f179,plain,
    ! [X0] :
      ( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f166]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f46,f124,f118,f118]) ).

fof(f124,plain,
    ! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
    inference(definition_unfolding,[],[f43,f26,f12]) ).

fof(f26,axiom,
    ! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).

fof(f43,axiom,
    ! [X0] : union(X0,singleton(X0)) = successor(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).

fof(f46,axiom,
    ! [X0,X1] :
      ( successor(X0) != X1
      | member(ordered_pair(X0,X1),successor_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).

fof(f711,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f170,f709]) ).

fof(f170,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f59,f118,f118,f116,f116,f12]) ).

fof(f59,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
      | member(ordered_pair(X1,X4),compose(X7,X5))
      | ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).

fof(f705,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f153,f703]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class))
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1))))))),composition_function) ),
    inference(definition_unfolding,[],[f97,f118,f118,f118]) ).

fof(f97,axiom,
    ! [X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
      | member(ordered_pair(X0,ordered_pair(X1,compose(X0,X1))),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function3) ).

fof(f700,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f184,f698]) ).

fof(f698,plain,
    ( spl0_92
  <=> ! [X4,X0,X1] :
        ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f184,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))))) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(forward_demodulation,[],[f150,f129]) ).

fof(f150,plain,
    ! [X0,X1,X4] :
      ( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X0),universal_class))))),element_relation)) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f107,f117,f118,f118]) ).

fof(f107,axiom,
    ! [X0,X1,X4] :
      ( apply(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn3) ).

fof(f695,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f175,f693]) ).

fof(f175,plain,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
    inference(definition_unfolding,[],[f90,f118]) ).

fof(f90,axiom,
    ! [X10,X11,X9] :
      ( ~ operation(X10)
      | ~ operation(X11)
      | ~ compatible(X9,X10,X11)
      | homomorphism(X9,X10,X11)
      | member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).

fof(f691,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f154,f689]) ).

fof(f689,plain,
    ( spl0_90
  <=> ! [X4,X7,X5,X1] :
        ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
        | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f154,plain,
    ! [X1,X7,X4,X5] :
      ( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
      | member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
    inference(definition_unfolding,[],[f58,f118,f116,f116,f12]) ).

fof(f58,axiom,
    ! [X1,X7,X4,X5] :
      ( ~ member(ordered_pair(X1,X4),compose(X7,X5))
      | member(X4,image(X7,image(X5,singleton(X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).

fof(f686,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f180,f684]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(compose(X0,X1),compose(X0,X1)))),cross_product(universal_class,universal_class)) ),
    inference(equality_resolution,[],[f169]) ).

fof(f169,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0))
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f94,f118,f118]) ).

fof(f94,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) != X4
      | member(ordered_pair(X1,X4),compose_class(X0))
      | ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition3) ).

fof(f682,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f152,f680]) ).

fof(f680,plain,
    ( spl0_88
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f152,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),composition_function) ),
    inference(definition_unfolding,[],[f96,f118,f118]) ).

fof(f96,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),composition_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function2) ).

fof(f678,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f148,f676]) ).

fof(f676,plain,
    ( spl0_87
  <=> ! [X4,X0,X1] :
        ( member(X1,domain_of(X0))
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f148,plain,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))))),application_function) ),
    inference(definition_unfolding,[],[f106,f118,f118]) ).

fof(f106,axiom,
    ! [X0,X1,X4] :
      ( member(X1,domain_of(X0))
      | ~ member(ordered_pair(X0,ordered_pair(X1,X4)),application_function) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn2) ).

fof(f673,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f163,f671]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
    inference(definition_unfolding,[],[f20,f118,f118]) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(ordered_pair(X0,X1),element_relation)
      | ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).

fof(f663,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f187,f661]) ).

fof(f187,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f186,f129]) ).

fof(f186,plain,
    ! [X1] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
      | ~ member(X1,universal_class)
      | null_class = X1 ),
    inference(forward_demodulation,[],[f164,f129]) ).

fof(f164,plain,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
    inference(definition_unfolding,[],[f70,f117]) ).

fof(f70,axiom,
    ! [X1] :
      ( ~ member(X1,universal_class)
      | null_class = X1
      | member(apply(choice,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).

fof(f659,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f173,f657]) ).

fof(f657,plain,
    ( spl0_84
  <=> ! [X8] :
        ( ~ function(X8)
        | operation(X8)
        | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
        | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f173,plain,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f81,f115]) ).

fof(f81,axiom,
    ! [X8] :
      ( ~ function(X8)
      | operation(X8)
      | ~ subclass(range_of(X8),domain_of(domain_of(X8)))
      | domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).

fof(f654,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f174,f652]) ).

fof(f174,plain,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f85,f115]) ).

fof(f85,axiom,
    ! [X10,X11,X9] :
      ( ~ function(X9)
      | compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) != domain_of(X9)
      | ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).

fof(f646,plain,
    ( ~ spl0_81
    | spl0_82
    | ~ spl0_5
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f612,f603,f226,f643,f639]) ).

fof(f643,plain,
    ( spl0_82
  <=> inductive(universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f612,plain,
    ( inductive(universal_class)
    | ~ member(null_class,universal_class)
    | ~ spl0_5
    | ~ spl0_76 ),
    inference(resolution,[],[f604,f227]) ).

fof(f637,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f149,f635]) ).

fof(f149,plain,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
    inference(definition_unfolding,[],[f17,f118]) ).

fof(f17,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,cross_product(X0,X1))
      | ordered_pair(first(X4),second(X4)) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).

fof(f633,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f146,f631]) ).

fof(f631,plain,
    ( spl0_79
  <=> ! [X0,X1] :
        ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
    inference(definition_unfolding,[],[f45,f124,f118]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ( successor(X0) = X1
      | ~ member(ordered_pair(X0,X1),successor_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).

fof(f622,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f162,f620]) ).

fof(f162,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f16,f118]) ).

fof(f16,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ member(X2,X0)
      | ~ member(X3,X1)
      | member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).

fof(f618,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f130,f615]) ).

fof(f130,plain,
    subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
    inference(definition_unfolding,[],[f74,f38]) ).

fof(f74,axiom,
    intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).

fof(f605,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f185,f603]) ).

fof(f185,plain,
    ! [X0] :
      ( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | inductive(X0)
      | ~ member(null_class,X0) ),
    inference(forward_demodulation,[],[f160,f129]) ).

fof(f160,plain,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f49,f116]) ).

fof(f49,axiom,
    ! [X0] :
      ( inductive(X0)
      | ~ member(null_class,X0)
      | ~ subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).

fof(f601,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f182,f599]) ).

fof(f182,plain,
    ! [X2] :
      ( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
      | ~ member(X2,universal_class) ),
    inference(forward_demodulation,[],[f137,f129]) ).

fof(f137,plain,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
    inference(definition_unfolding,[],[f56,f125]) ).

fof(f125,plain,
    ! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
    inference(definition_unfolding,[],[f55,f116]) ).

fof(f55,axiom,
    ! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).

fof(f56,axiom,
    ! [X2] :
      ( ~ member(X2,universal_class)
      | member(power_class(X2),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).

fof(f597,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f158,f595]) ).

fof(f158,plain,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
    inference(definition_unfolding,[],[f65,f116]) ).

fof(f65,axiom,
    ! [X0,X8] :
      ( ~ function(X8)
      | ~ member(X0,universal_class)
      | member(image(X8,X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).

fof(f593,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f151,f591]) ).

fof(f591,plain,
    ( spl0_73
  <=> ! [X4,X0,X1] :
        ( compose(X0,X1) = X4
        | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f151,plain,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
    inference(definition_unfolding,[],[f93,f118]) ).

fof(f93,axiom,
    ! [X0,X1,X4] :
      ( compose(X0,X1) = X4
      | ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).

fof(f582,plain,
    ( spl0_72
    | ~ spl0_4
    | ~ spl0_60 ),
    inference(avatar_split_clause,[],[f542,f518,f221,f579]) ).

fof(f579,plain,
    ( spl0_72
  <=> single_valued_class(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f221,plain,
    ( spl0_4
  <=> function(choice) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f518,plain,
    ( spl0_60
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f542,plain,
    ( single_valued_class(choice)
    | ~ spl0_4
    | ~ spl0_60 ),
    inference(resolution,[],[f519,f223]) ).

fof(f223,plain,
    ( function(choice)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f221]) ).

fof(f519,plain,
    ( ! [X0] :
        ( ~ function(X0)
        | single_valued_class(X0) )
    | ~ spl0_60 ),
    inference(avatar_component_clause,[],[f518]) ).

fof(f577,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f165,f575]) ).

fof(f165,plain,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f31,f29,f12]) ).

fof(f31,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).

fof(f573,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f161,f571]) ).

fof(f161,plain,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f64,f38]) ).

fof(f64,axiom,
    ! [X8] :
      ( function(X8)
      | ~ subclass(X8,cross_product(universal_class,universal_class))
      | ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).

fof(f569,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f142,f567]) ).

fof(f567,plain,
    ( spl0_69
  <=> ! [X0,X3,X2,X1] :
        ( member(X2,X0)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f14,f118]) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).

fof(f565,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f141,f563]) ).

fof(f563,plain,
    ( spl0_68
  <=> ! [X0,X3,X2,X1] :
        ( member(X3,X1)
        | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
    inference(definition_unfolding,[],[f15,f118]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).

fof(f561,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f139,f559]) ).

fof(f139,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
    inference(definition_unfolding,[],[f100,f118]) ).

fof(f100,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).

fof(f552,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f159,f550]) ).

fof(f159,plain,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
      | maps(X8,domain_of(X8),X1) ),
    inference(definition_unfolding,[],[f112,f115]) ).

fof(f112,axiom,
    ! [X1,X8] :
      ( ~ function(X8)
      | ~ subclass(range_of(X8),X1)
      | maps(X8,domain_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).

fof(f548,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f147,f546]) ).

fof(f546,plain,
    ( spl0_65
  <=> ! [X0,X1] :
        ( domain_of(X0) = X1
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
    inference(definition_unfolding,[],[f99,f118]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( domain_of(X0) = X1
      | ~ member(ordered_pair(X0,X1),domain_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).

fof(f541,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f181,f539]) ).

fof(f181,plain,
    ! [X0] :
      ( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
      | ~ inductive(X0) ),
    inference(forward_demodulation,[],[f133,f129]) ).

fof(f133,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
    inference(definition_unfolding,[],[f48,f116]) ).

fof(f48,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | subclass(image(successor_relation,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).

fof(f537,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f145,f535]) ).

fof(f535,plain,
    ( spl0_63
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f145,plain,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
    inference(definition_unfolding,[],[f84,f115]) ).

fof(f84,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | subclass(range_of(X9),domain_of(domain_of(X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).

fof(f533,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f140,f531]) ).

fof(f531,plain,
    ( spl0_62
  <=> ! [X0,X1] :
        ( member(X0,X1)
        | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
    inference(definition_unfolding,[],[f19,f118]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(ordered_pair(X0,X1),element_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).

fof(f525,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f143,f523]) ).

fof(f143,plain,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
    inference(definition_unfolding,[],[f30,f29,f12]) ).

fof(f30,axiom,
    ! [X0,X4] :
      ( ~ member(X4,domain_of(X0))
      | restrict(X0,singleton(X4),universal_class) != null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).

fof(f520,plain,
    ( spl0_60
    | ~ spl0_53
    | ~ spl0_54 ),
    inference(avatar_split_clause,[],[f502,f471,f467,f518]) ).

fof(f471,plain,
    ( spl0_54
  <=> ! [X0] :
        ( single_valued_class(X0)
        | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f502,plain,
    ( ! [X0] :
        ( single_valued_class(X0)
        | ~ function(X0) )
    | ~ spl0_53
    | ~ spl0_54 ),
    inference(resolution,[],[f472,f468]) ).

fof(f472,plain,
    ( ! [X0] :
        ( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
        | single_valued_class(X0) )
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f471]) ).

fof(f516,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f144,f514]) ).

fof(f514,plain,
    ( spl0_59
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f144,plain,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
    inference(definition_unfolding,[],[f111,f115]) ).

fof(f111,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | subclass(range_of(X8),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).

fof(f512,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f134,f510]) ).

fof(f134,plain,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
    inference(definition_unfolding,[],[f80,f115]) ).

fof(f80,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | subclass(range_of(X8),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).

fof(f508,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f79,f506]) ).

fof(f506,plain,
    ( spl0_57
  <=> ! [X8] :
        ( ~ operation(X8)
        | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f79,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).

fof(f481,plain,
    ( spl0_56
    | ~ spl0_5
    | ~ spl0_40 ),
    inference(avatar_split_clause,[],[f411,f383,f226,f479]) ).

fof(f479,plain,
    ( spl0_56
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f411,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | universal_class = X0 )
    | ~ spl0_5
    | ~ spl0_40 ),
    inference(resolution,[],[f384,f227]) ).

fof(f477,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f183,f475]) ).

fof(f183,plain,
    ! [X0] :
      ( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
      | ~ member(X0,universal_class) ),
    inference(forward_demodulation,[],[f138,f129]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
    inference(definition_unfolding,[],[f54,f114]) ).

fof(f54,axiom,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | member(sum_class(X0),universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).

fof(f473,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f136,f471]) ).

fof(f136,plain,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f61,f38]) ).

fof(f61,axiom,
    ! [X0] :
      ( single_valued_class(X0)
      | ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).

fof(f469,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f135,f467]) ).

fof(f135,plain,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f63,f38]) ).

fof(f63,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(compose(X8,inverse(X8)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).

fof(f465,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f131,f463]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
    inference(definition_unfolding,[],[f60,f38]) ).

fof(f60,axiom,
    ! [X0] :
      ( ~ single_valued_class(X0)
      | subclass(compose(X0,inverse(X0)),identity_relation) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).

fof(f461,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f129,f459]) ).

fof(f457,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f23,f455]) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,X1)
      | member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).

fof(f453,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f8,f451]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( X1 = X2
      | X0 = X2
      | ~ member(X2,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f445,plain,
    ( spl0_48
    | ~ spl0_6
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f404,f379,f230,f443]) ).

fof(f443,plain,
    ( spl0_48
  <=> ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f230,plain,
    ( spl0_6
  <=> member(omega,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f404,plain,
    ( ! [X0] :
        ( ~ subclass(universal_class,X0)
        | member(omega,X0) )
    | ~ spl0_6
    | ~ spl0_39 ),
    inference(resolution,[],[f380,f232]) ).

fof(f232,plain,
    ( member(omega,universal_class)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f230]) ).

fof(f441,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f157,f439]) ).

fof(f439,plain,
    ( spl0_47
  <=> ! [X8] :
        ( ~ function(X8)
        | one_to_one(X8)
        | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f157,plain,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f73,f38]) ).

fof(f73,axiom,
    ! [X8] :
      ( ~ function(X8)
      | one_to_one(X8)
      | ~ function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).

fof(f437,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f83,f435]) ).

fof(f435,plain,
    ( spl0_46
  <=> ! [X9,X11,X10] :
        ( ~ compatible(X9,X10,X11)
        | domain_of(domain_of(X10)) = domain_of(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f83,axiom,
    ! [X10,X11,X9] :
      ( ~ compatible(X9,X10,X11)
      | domain_of(domain_of(X10)) = domain_of(X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).

fof(f433,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f25,f431]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( ~ member(X4,universal_class)
      | member(X4,X0)
      | member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).

fof(f403,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f128,f400]) ).

fof(f128,plain,
    identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
    inference(definition_unfolding,[],[f75,f38]) ).

fof(f75,axiom,
    identity_relation = intersection(inverse(subset_relation),subset_relation),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).

fof(f398,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f104,f395]) ).

fof(f104,axiom,
    intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).

fof(f393,plain,
    ( spl0_42
    | ~ spl0_13
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f372,f338,f261,f391]) ).

fof(f391,plain,
    ( spl0_42
  <=> ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f372,plain,
    ( ! [X0,X1] :
        ( member(null_class,X0)
        | ~ inductive(intersection(X0,X1)) )
    | ~ spl0_13
    | ~ spl0_31 ),
    inference(resolution,[],[f339,f262]) ).

fof(f389,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f67,f387]) ).

fof(f67,axiom,
    ! [X0] :
      ( null_class = X0
      | null_class = intersection(X0,regular(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).

fof(f385,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f7,f383]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).

fof(f381,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f1,f379]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).

fof(f368,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f132,f366]) ).

fof(f366,plain,
    ( spl0_38
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f132,plain,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(domain_of(flip(cross_product(X8,universal_class)))) ),
    inference(definition_unfolding,[],[f72,f38]) ).

fof(f72,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(inverse(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).

fof(f364,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f110,f362]) ).

fof(f362,plain,
    ( spl0_37
  <=> ! [X0,X1,X8] :
        ( ~ maps(X8,X0,X1)
        | domain_of(X8) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f110,axiom,
    ! [X0,X1,X8] :
      ( ~ maps(X8,X0,X1)
      | domain_of(X8) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).

fof(f360,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f88,f358]) ).

fof(f358,plain,
    ( spl0_36
  <=> ! [X9,X11,X10] :
        ( ~ homomorphism(X9,X10,X11)
        | compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f88,axiom,
    ! [X10,X11,X9] :
      ( ~ homomorphism(X9,X10,X11)
      | compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).

fof(f356,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f35,f354]) ).

fof(f35,axiom,
    ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).

fof(f352,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f32,f350]) ).

fof(f32,axiom,
    ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).

fof(f348,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f22,f346]) ).

fof(f22,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X1)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).

fof(f344,plain,
    ( spl0_32
    | ~ spl0_13
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f319,f294,f261,f342]) ).

fof(f342,plain,
    ( spl0_32
  <=> ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f319,plain,
    ( ! [X0] :
        ( ~ member(null_class,X0)
        | ~ inductive(complement(X0)) )
    | ~ spl0_13
    | ~ spl0_21 ),
    inference(resolution,[],[f295,f262]) ).

fof(f340,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f21,f338]) ).

fof(f21,axiom,
    ! [X0,X1,X4] :
      ( member(X4,X0)
      | ~ member(X4,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).

fof(f336,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f10,f334]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ member(X1,universal_class)
      | member(X1,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f332,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f9,f330]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).

fof(f328,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f3,f326]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f324,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f2,f322]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f318,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f105,f315]) ).

fof(f105,axiom,
    subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).

fof(f313,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f95,f310]) ).

fof(f95,axiom,
    subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).

fof(f308,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f66,f306]) ).

fof(f66,axiom,
    ! [X0] :
      ( null_class = X0
      | member(regular(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).

fof(f304,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f62,f302]) ).

fof(f62,axiom,
    ! [X8] :
      ( ~ function(X8)
      | subclass(X8,cross_product(universal_class,universal_class)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f300,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f57,f298]) ).

fof(f57,axiom,
    ! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).

fof(f296,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f24,f294]) ).

fof(f24,axiom,
    ! [X0,X4] :
      ( ~ member(X4,X0)
      | ~ member(X4,complement(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).

fof(f292,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f109,f290]) ).

fof(f290,plain,
    ( spl0_20
  <=> ! [X0,X1,X8] :
        ( function(X8)
        | ~ maps(X8,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f109,axiom,
    ! [X0,X1,X8] :
      ( function(X8)
      | ~ maps(X8,X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).

fof(f288,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f92,f286]) ).

fof(f92,axiom,
    ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).

fof(f284,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f87,f282]) ).

fof(f282,plain,
    ( spl0_18
  <=> ! [X9,X11,X10] :
        ( operation(X11)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f87,axiom,
    ! [X10,X11,X9] :
      ( operation(X11)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).

fof(f280,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f86,f278]) ).

fof(f278,plain,
    ( spl0_17
  <=> ! [X9,X11,X10] :
        ( operation(X10)
        | ~ homomorphism(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f86,axiom,
    ! [X10,X11,X9] :
      ( operation(X10)
      | ~ homomorphism(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).

fof(f276,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f82,f274]) ).

fof(f274,plain,
    ( spl0_16
  <=> ! [X9,X11,X10] :
        ( function(X9)
        | ~ compatible(X9,X10,X11) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f82,axiom,
    ! [X10,X11,X9] :
      ( function(X9)
      | ~ compatible(X9,X10,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).

fof(f272,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f98,f269]) ).

fof(f98,axiom,
    subclass(domain_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).

fof(f267,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f51,f265]) ).

fof(f51,axiom,
    ! [X1] :
      ( ~ inductive(X1)
      | subclass(omega,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).

fof(f263,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f47,f261]) ).

fof(f47,axiom,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).

fof(f259,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f44,f256]) ).

fof(f44,axiom,
    subclass(successor_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).

fof(f254,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f18,f251]) ).

fof(f18,axiom,
    subclass(element_relation,cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).

fof(f249,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f11,f247]) ).

fof(f11,axiom,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).

fof(f245,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f78,f243]) ).

fof(f243,plain,
    ( spl0_9
  <=> ! [X8] :
        ( ~ operation(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f78,axiom,
    ! [X8] :
      ( ~ operation(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).

fof(f241,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f71,f239]) ).

fof(f239,plain,
    ( spl0_8
  <=> ! [X8] :
        ( ~ one_to_one(X8)
        | function(X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f71,axiom,
    ! [X8] :
      ( ~ one_to_one(X8)
      | function(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).

fof(f237,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f177,f235]) ).

fof(f177,plain,
    ! [X1] : subclass(X1,X1),
    inference(equality_resolution,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).

fof(f233,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f52,f230]) ).

fof(f52,axiom,
    member(omega,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).

fof(f228,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f4,f226]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f224,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f69,f221]) ).

fof(f69,axiom,
    function(choice),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f219,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f50,f216]) ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).

fof(f214,plain,
    ( ~ spl0_2
    | spl0_1 ),
    inference(avatar_split_clause,[],[f209,f205,f211]) ).

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

fof(f209,plain,
    ( ~ subclass(intersection(x,cross_product(y,z)),x)
    | spl0_1 ),
    inference(forward_demodulation,[],[f207,f129]) ).

fof(f207,plain,
    ( ~ subclass(intersection(cross_product(y,z),x),x)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f205]) ).

fof(f208,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f127,f205]) ).

fof(f127,plain,
    ~ subclass(intersection(cross_product(y,z),x),x),
    inference(definition_unfolding,[],[f113,f29]) ).

fof(f113,axiom,
    ~ subclass(restrict(x,y,z),x),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_restriction_property3_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET252-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n011.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 01:10:16 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (25437)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (25440)WARNING: value z3 for option sas not known
% 0.15/0.37  % (25440)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)
% 0.15/0.38  % (25439)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (25441)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (25438)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (25442)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)
% 0.15/0.38  % (25443)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)
% 0.15/0.38  % (25444)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)
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [2]
% 0.21/0.45  TRYING [1]
% 0.21/0.45  TRYING [2]
% 0.21/0.46  TRYING [3]
% 0.21/0.49  TRYING [3]
% 0.21/0.50  % (25442)First to succeed.
% 0.21/0.51  % (25442)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (25442)------------------------------
% 0.21/0.52  % (25442)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.52  % (25442)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (25442)Memory used [KB]: 2886
% 0.21/0.52  % (25442)Time elapsed: 0.134 s
% 0.21/0.52  % (25442)Instructions burned: 277 (million)
% 0.21/0.52  % (25442)------------------------------
% 0.21/0.52  % (25442)------------------------------
% 0.21/0.52  % (25437)Success in time 0.147 s
%------------------------------------------------------------------------------