TSTP Solution File: SET955+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:24:55 EDT 2024

% Result   : Theorem 13.47s 2.34s
% Output   : Refutation 13.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  378
% Syntax   : Number of formulae    : 1283 (  36 unt;   0 def)
%            Number of atoms       : 5865 (1311 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives : 7648 (3066   ~;4147   |;  53   &)
%                                         ( 370 <=>;  11  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   14 (   8 avg)
%            Maximal term depth    :   10 (   2 avg)
%            Number of predicates  :  366 ( 364 usr; 362 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   6 con; 0-3 aty)
%            Number of variables   : 3592 (3550   !;  42   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f9380,plain,
    $false,
    inference(avatar_sat_refutation,[],[f73,f78,f83,f87,f93,f99,f103,f107,f111,f115,f119,f128,f134,f139,f143,f147,f151,f155,f167,f171,f175,f183,f188,f193,f199,f208,f214,f218,f224,f228,f232,f236,f240,f244,f248,f252,f256,f267,f281,f287,f291,f295,f311,f315,f329,f346,f350,f354,f380,f384,f402,f406,f410,f414,f418,f442,f451,f455,f477,f481,f515,f521,f525,f544,f563,f588,f592,f596,f600,f604,f608,f612,f616,f620,f666,f672,f718,f722,f726,f730,f820,f824,f828,f832,f920,f924,f928,f932,f1032,f1036,f1040,f1044,f1065,f1120,f1124,f1128,f1195,f1214,f1218,f1222,f1362,f1391,f1414,f1418,f1422,f1426,f1430,f1434,f1438,f1544,f1718,f1755,f1869,f1873,f1877,f1947,f1951,f1965,f1969,f1973,f1987,f2123,f2127,f2141,f2145,f2149,f2153,f2157,f2593,f2597,f2601,f2634,f2638,f2642,f2646,f2650,f2679,f2710,f2714,f2718,f2722,f2780,f2838,f2842,f2848,f2852,f2856,f2860,f3017,f3021,f3025,f3029,f3097,f3101,f3105,f3109,f3113,f3117,f3191,f3303,f3307,f3311,f3315,f3427,f3431,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3679,f3683,f3687,f3691,f3695,f3699,f3703,f3707,f3711,f3715,f3719,f3723,f4499,f4503,f4507,f4511,f4515,f4523,f4527,f4531,f4535,f4715,f4719,f4723,f4727,f4731,f4735,f4775,f4779,f4783,f4787,f4791,f4795,f5274,f5278,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5419,f5423,f5567,f5571,f5575,f5579,f5583,f5587,f5591,f5595,f5599,f5607,f5615,f5619,f5623,f5627,f5636,f5640,f5644,f5648,f5652,f5729,f5733,f5737,f5741,f5745,f5749,f5753,f5757,f6043,f6047,f6051,f6055,f6060,f6064,f6068,f6072,f6076,f6226,f6230,f6234,f6238,f6242,f6246,f6250,f6254,f6259,f6263,f6267,f6621,f6625,f6629,f6633,f6637,f6641,f6645,f6649,f6654,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7086,f7090,f7094,f7099,f7246,f7250,f7254,f7258,f7262,f7266,f7270,f7274,f7275,f7559,f7563,f7610,f7614,f7618,f7622,f7626,f7630,f7634,f7638,f7642,f7646,f7651,f7655,f7659,f7663,f7667,f8275,f8279,f8283,f8287,f8291,f8295,f8299,f8303,f8310,f8320,f8324,f8328,f8332,f8336,f8340,f8344,f8348,f8439,f8533,f8537,f8541,f8545,f8549,f8553,f8557,f8561,f8576,f8580,f8581,f8585,f8589,f8593,f8597,f8601,f8605,f8609,f8613,f8617,f8621,f9050,f9124,f9128,f9132,f9136,f9280,f9284,f9288,f9292,f9296,f9300,f9304,f9308,f9379]) ).

fof(f9379,plain,
    ( spl13_286
    | ~ spl13_231
    | ~ spl13_14
    | ~ spl13_232 ),
    inference(avatar_split_clause,[],[f8622,f5633,f137,f5629,f7096]) ).

fof(f7096,plain,
    ( spl13_286
  <=> in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_286])]) ).

fof(f5629,plain,
    ( spl13_231
  <=> in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_231])]) ).

fof(f137,plain,
    ( spl13_14
  <=> ! [X0,X1] :
        ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).

fof(f5633,plain,
    ( spl13_232
  <=> sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_232])]) ).

fof(f8622,plain,
    ( ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK4))
    | ~ spl13_14
    | ~ spl13_232 ),
    inference(superposition,[],[f138,f5635]) ).

fof(f5635,plain,
    ( sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))))
    | ~ spl13_232 ),
    inference(avatar_component_clause,[],[f5633]) ).

fof(f138,plain,
    ( ! [X0,X1] :
        ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4)) )
    | ~ spl13_14 ),
    inference(avatar_component_clause,[],[f137]) ).

fof(f9308,plain,
    ( spl13_361
    | ~ spl13_51
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f557,f523,f400,f9306]) ).

fof(f9306,plain,
    ( spl13_361
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK6(sK2,X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(sK2,X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(sK2,X2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(sK2,X2,cartesian_product2(X3,X4)))))
        | sP0(sK2,X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_361])]) ).

fof(f400,plain,
    ( spl13_51
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | in(sK8(X2,X3,cartesian_product2(X1,X0)),X2)
        | sP0(X2,X3,cartesian_product2(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).

fof(f523,plain,
    ( spl13_63
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_63])]) ).

fof(f557,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK2,X2,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK6(sK2,X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(sK2,X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(sK2,X2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(sK2,X2,cartesian_product2(X3,X4)))))
        | sP0(sK2,X2,cartesian_product2(X3,X4)) )
    | ~ spl13_51
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f401]) ).

fof(f401,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK8(X2,X3,cartesian_product2(X1,X0)),X2)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | sP0(X2,X3,cartesian_product2(X1,X0)) )
    | ~ spl13_51 ),
    inference(avatar_component_clause,[],[f400]) ).

fof(f524,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X3,sK2)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X0,X1)
        | ~ in(X2,sK1) )
    | ~ spl13_63 ),
    inference(avatar_component_clause,[],[f523]) ).

fof(f9304,plain,
    ( spl13_360
    | ~ spl13_52
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f555,f523,f404,f9302]) ).

fof(f9302,plain,
    ( spl13_360
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK6(X2,sK2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(X2,sK2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(X2,sK2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(X2,sK2,cartesian_product2(X3,X4)))))
        | sP0(X2,sK2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_360])]) ).

fof(f404,plain,
    ( spl13_52
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | in(sK7(X2,X3,cartesian_product2(X1,X0)),X3)
        | sP0(X2,X3,cartesian_product2(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).

fof(f555,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK2,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK6(X2,sK2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(X2,sK2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(X2,sK2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(X2,sK2,cartesian_product2(X3,X4)))))
        | sP0(X2,sK2,cartesian_product2(X3,X4)) )
    | ~ spl13_52
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f405]) ).

fof(f405,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK7(X2,X3,cartesian_product2(X1,X0)),X3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | sP0(X2,X3,cartesian_product2(X1,X0)) )
    | ~ spl13_52 ),
    inference(avatar_component_clause,[],[f404]) ).

fof(f9300,plain,
    ( spl13_359
    | ~ spl13_54
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f553,f523,f412,f9298]) ).

fof(f9298,plain,
    ( spl13_359
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2)))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK8(cartesian_product2(X2,X3),X4,sK2) = unordered_pair(singleton(sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK2))),unordered_pair(sK10(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK2)),sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK2))))
        | sP0(cartesian_product2(X2,X3),X4,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_359])]) ).

fof(f412,plain,
    ( spl13_54
  <=> ! [X0,X3,X2,X1] :
        ( sK8(cartesian_product2(X1,X0),X2,X3) = unordered_pair(singleton(sK9(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3))),unordered_pair(sK10(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3)),sK9(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3))))
        | in(sK6(cartesian_product2(X1,X0),X2,X3),X3)
        | sP0(cartesian_product2(X1,X0),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).

fof(f553,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2)))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK2))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK8(cartesian_product2(X2,X3),X4,sK2) = unordered_pair(singleton(sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK2))),unordered_pair(sK10(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK2)),sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK2))))
        | sP0(cartesian_product2(X2,X3),X4,sK2) )
    | ~ spl13_54
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f413]) ).

fof(f413,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK6(cartesian_product2(X1,X0),X2,X3),X3)
        | sK8(cartesian_product2(X1,X0),X2,X3) = unordered_pair(singleton(sK9(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3))),unordered_pair(sK10(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3)),sK9(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3))))
        | sP0(cartesian_product2(X1,X0),X2,X3) )
    | ~ spl13_54 ),
    inference(avatar_component_clause,[],[f412]) ).

fof(f9296,plain,
    ( spl13_358
    | ~ spl13_53
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f552,f523,f408,f9294]) ).

fof(f9294,plain,
    ( spl13_358
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2)))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK7(X2,cartesian_product2(X3,X4),sK2) = unordered_pair(singleton(sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK2))),unordered_pair(sK10(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK2)),sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK2))))
        | sP0(X2,cartesian_product2(X3,X4),sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_358])]) ).

fof(f408,plain,
    ( spl13_53
  <=> ! [X0,X3,X2,X1] :
        ( sK7(X2,cartesian_product2(X1,X0),X3) = unordered_pair(singleton(sK9(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3))),unordered_pair(sK10(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3)),sK9(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3))))
        | in(sK6(X2,cartesian_product2(X1,X0),X3),X3)
        | sP0(X2,cartesian_product2(X1,X0),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).

fof(f552,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2)))))),sK9(cartesian_product2(sK3,sK4),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK2))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK1)
        | sK7(X2,cartesian_product2(X3,X4),sK2) = unordered_pair(singleton(sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK2))),unordered_pair(sK10(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK2)),sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK2))))
        | sP0(X2,cartesian_product2(X3,X4),sK2) )
    | ~ spl13_53
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f409]) ).

fof(f409,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK6(X2,cartesian_product2(X1,X0),X3),X3)
        | sK7(X2,cartesian_product2(X1,X0),X3) = unordered_pair(singleton(sK9(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3))),unordered_pair(sK10(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3)),sK9(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3))))
        | sP0(X2,cartesian_product2(X1,X0),X3) )
    | ~ spl13_53 ),
    inference(avatar_component_clause,[],[f408]) ).

fof(f9292,plain,
    ( spl13_357
    | ~ spl13_51
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f538,f519,f400,f9290]) ).

fof(f9290,plain,
    ( spl13_357
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK6(sK4,X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(sK4,X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(sK4,X2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(sK4,X2,cartesian_product2(X3,X4)))))
        | sP0(sK4,X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_357])]) ).

fof(f519,plain,
    ( spl13_62
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_62])]) ).

fof(f538,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK8(sK4,X2,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK6(sK4,X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(sK4,X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(sK4,X2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(sK4,X2,cartesian_product2(X3,X4)))))
        | sP0(sK4,X2,cartesian_product2(X3,X4)) )
    | ~ spl13_51
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f401]) ).

fof(f520,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X3,sK4)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X0,X1)
        | ~ in(X2,sK3) )
    | ~ spl13_62 ),
    inference(avatar_component_clause,[],[f519]) ).

fof(f9288,plain,
    ( spl13_356
    | ~ spl13_52
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f536,f519,f404,f9286]) ).

fof(f9286,plain,
    ( spl13_356
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK6(X2,sK4,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(X2,sK4,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(X2,sK4,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(X2,sK4,cartesian_product2(X3,X4)))))
        | sP0(X2,sK4,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_356])]) ).

fof(f536,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4)))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4))))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK7(X2,sK4,cartesian_product2(X3,X4)))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK6(X2,sK4,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(X2,sK4,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(X2,sK4,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(X2,sK4,cartesian_product2(X3,X4)))))
        | sP0(X2,sK4,cartesian_product2(X3,X4)) )
    | ~ spl13_52
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f405]) ).

fof(f9284,plain,
    ( spl13_355
    | ~ spl13_54
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f534,f519,f412,f9282]) ).

fof(f9282,plain,
    ( spl13_355
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4)))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK8(cartesian_product2(X2,X3),X4,sK4) = unordered_pair(singleton(sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK4))),unordered_pair(sK10(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK4)),sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK4))))
        | sP0(cartesian_product2(X2,X3),X4,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_355])]) ).

fof(f534,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4)))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(cartesian_product2(X2,X3),X4,sK4))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK8(cartesian_product2(X2,X3),X4,sK4) = unordered_pair(singleton(sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK4))),unordered_pair(sK10(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK4)),sK9(X3,X2,sK8(cartesian_product2(X2,X3),X4,sK4))))
        | sP0(cartesian_product2(X2,X3),X4,sK4) )
    | ~ spl13_54
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f413]) ).

fof(f9280,plain,
    ( spl13_354
    | ~ spl13_53
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f533,f519,f408,f9278]) ).

fof(f9278,plain,
    ( spl13_354
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4)))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK7(X2,cartesian_product2(X3,X4),sK4) = unordered_pair(singleton(sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK4))),unordered_pair(sK10(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK4)),sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK4))))
        | sP0(X2,cartesian_product2(X3,X4),sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_354])]) ).

fof(f533,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4)))))),sK9(cartesian_product2(sK1,sK2),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,cartesian_product2(X3,X4),sK4))))))))
        | ~ in(X0,X5)
        | ~ in(X1,sK3)
        | sK7(X2,cartesian_product2(X3,X4),sK4) = unordered_pair(singleton(sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK4))),unordered_pair(sK10(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK4)),sK9(X4,X3,sK7(X2,cartesian_product2(X3,X4),sK4))))
        | sP0(X2,cartesian_product2(X3,X4),sK4) )
    | ~ spl13_53
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f409]) ).

fof(f9136,plain,
    ( spl13_353
    | ~ spl13_58
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f1134,f1118,f453,f9134]) ).

fof(f9134,plain,
    ( spl13_353
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_353])]) ).

fof(f453,plain,
    ( spl13_58
  <=> ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).

fof(f1118,plain,
    ( spl13_94
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_94])]) ).

fof(f1134,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58
    | ~ spl13_94 ),
    inference(resolution,[],[f1119,f454]) ).

fof(f454,plain,
    ( ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58 ),
    inference(avatar_component_clause,[],[f453]) ).

fof(f1119,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4))) )
    | ~ spl13_94 ),
    inference(avatar_component_clause,[],[f1118]) ).

fof(f9132,plain,
    ( spl13_352
    | ~ spl13_55
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f1133,f1118,f416,f9130]) ).

fof(f9130,plain,
    ( spl13_352
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_352])]) ).

fof(f416,plain,
    ( spl13_55
  <=> ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).

fof(f1133,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55
    | ~ spl13_94 ),
    inference(resolution,[],[f1119,f417]) ).

fof(f417,plain,
    ( ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55 ),
    inference(avatar_component_clause,[],[f416]) ).

fof(f9128,plain,
    ( spl13_351
    | ~ spl13_42
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f1131,f1118,f293,f9126]) ).

fof(f9126,plain,
    ( spl13_351
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_351])]) ).

fof(f293,plain,
    ( spl13_42
  <=> ! [X0,X1] :
        ( ~ in(X0,sK1)
        | ~ in(X1,sK2)
        | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK3,sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).

fof(f1131,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42
    | ~ spl13_94 ),
    inference(resolution,[],[f1119,f294]) ).

fof(f294,plain,
    ( ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK3,sK4))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42 ),
    inference(avatar_component_clause,[],[f293]) ).

fof(f9124,plain,
    ( spl13_350
    | ~ spl13_41
    | ~ spl13_94 ),
    inference(avatar_split_clause,[],[f1130,f1118,f289,f9122]) ).

fof(f9122,plain,
    ( spl13_350
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_350])]) ).

fof(f289,plain,
    ( spl13_41
  <=> ! [X0,X1] :
        ( ~ in(X0,sK3)
        | ~ in(X1,sK4)
        | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).

fof(f1130,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4)))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41
    | ~ spl13_94 ),
    inference(resolution,[],[f1119,f290]) ).

fof(f290,plain,
    ( ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK1,sK2))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f9050,plain,
    ( ~ spl13_349
    | ~ spl13_10
    | ~ spl13_12
    | ~ spl13_232 ),
    inference(avatar_split_clause,[],[f8668,f5633,f126,f113,f9047]) ).

fof(f9047,plain,
    ( spl13_349
  <=> empty(unordered_pair(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),singleton(singleton(sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_349])]) ).

fof(f113,plain,
    ( spl13_10
  <=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).

fof(f126,plain,
    ( spl13_12
  <=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).

fof(f8668,plain,
    ( ~ empty(unordered_pair(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),singleton(singleton(sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))))))
    | ~ spl13_10
    | ~ spl13_12
    | ~ spl13_232 ),
    inference(forward_demodulation,[],[f8638,f114]) ).

fof(f114,plain,
    ( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
    | ~ spl13_10 ),
    inference(avatar_component_clause,[],[f113]) ).

fof(f8638,plain,
    ( ~ empty(unordered_pair(singleton(singleton(sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))),sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))
    | ~ spl13_12
    | ~ spl13_232 ),
    inference(superposition,[],[f127,f5635]) ).

fof(f127,plain,
    ( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
    | ~ spl13_12 ),
    inference(avatar_component_clause,[],[f126]) ).

fof(f8621,plain,
    ( spl13_348
    | ~ spl13_50
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f548,f523,f382,f8619]) ).

fof(f8619,plain,
    ( spl13_348
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | sK5(cartesian_product2(X2,X3),sK2) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK2))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),sK2)),sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK2))))
        | cartesian_product2(X2,X3) = sK2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_348])]) ).

fof(f382,plain,
    ( spl13_50
  <=> ! [X2,X0,X1] :
        ( sK5(cartesian_product2(X1,X0),X2) = unordered_pair(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),X2))),unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),X2)),sK9(X0,X1,sK5(cartesian_product2(X1,X0),X2))))
        | in(sK5(cartesian_product2(X1,X0),X2),X2)
        | cartesian_product2(X1,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).

fof(f548,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | sK5(cartesian_product2(X2,X3),sK2) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK2))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),sK2)),sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK2))))
        | cartesian_product2(X2,X3) = sK2 )
    | ~ spl13_50
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f383]) ).

fof(f383,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(cartesian_product2(X1,X0),X2),X2)
        | sK5(cartesian_product2(X1,X0),X2) = unordered_pair(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),X2))),unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),X2)),sK9(X0,X1,sK5(cartesian_product2(X1,X0),X2))))
        | cartesian_product2(X1,X0) = X2 )
    | ~ spl13_50 ),
    inference(avatar_component_clause,[],[f382]) ).

fof(f8617,plain,
    ( spl13_347
    | ~ spl13_49
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f547,f523,f378,f8615]) ).

fof(f8615,plain,
    ( spl13_347
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3))))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3)))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | sK5(sK2,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(sK2,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(sK2,cartesian_product2(X2,X3))),sK9(X3,X2,sK5(sK2,cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = sK2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_347])]) ).

fof(f378,plain,
    ( spl13_49
  <=> ! [X2,X0,X1] :
        ( sK5(X2,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK5(X2,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK5(X2,cartesian_product2(X1,X0))),sK9(X0,X1,sK5(X2,cartesian_product2(X1,X0)))))
        | in(sK5(X2,cartesian_product2(X1,X0)),X2)
        | cartesian_product2(X1,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).

fof(f547,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3))))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,cartesian_product2(X2,X3)))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | sK5(sK2,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(sK2,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(sK2,cartesian_product2(X2,X3))),sK9(X3,X2,sK5(sK2,cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = sK2 )
    | ~ spl13_49
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f379]) ).

fof(f379,plain,
    ( ! [X2,X0,X1] :
        ( in(sK5(X2,cartesian_product2(X1,X0)),X2)
        | sK5(X2,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK5(X2,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK5(X2,cartesian_product2(X1,X0))),sK9(X0,X1,sK5(X2,cartesian_product2(X1,X0)))))
        | cartesian_product2(X1,X0) = X2 )
    | ~ spl13_49 ),
    inference(avatar_component_clause,[],[f378]) ).

fof(f8613,plain,
    ( spl13_346
    | ~ spl13_50
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f529,f519,f382,f8611]) ).

fof(f8611,plain,
    ( spl13_346
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | sK5(cartesian_product2(X2,X3),sK4) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK4))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),sK4)),sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK4))))
        | cartesian_product2(X2,X3) = sK4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_346])]) ).

fof(f529,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(cartesian_product2(X2,X3),sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | sK5(cartesian_product2(X2,X3),sK4) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK4))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),sK4)),sK9(X3,X2,sK5(cartesian_product2(X2,X3),sK4))))
        | cartesian_product2(X2,X3) = sK4 )
    | ~ spl13_50
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f383]) ).

fof(f8609,plain,
    ( spl13_345
    | ~ spl13_49
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f528,f519,f378,f8607]) ).

fof(f8607,plain,
    ( spl13_345
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3))))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3)))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | sK5(sK4,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(sK4,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(sK4,cartesian_product2(X2,X3))),sK9(X3,X2,sK5(sK4,cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = sK4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_345])]) ).

fof(f528,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3))))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,cartesian_product2(X2,X3)))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | sK5(sK4,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(sK4,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(sK4,cartesian_product2(X2,X3))),sK9(X3,X2,sK5(sK4,cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = sK4 )
    | ~ spl13_49
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f379]) ).

fof(f8605,plain,
    ( spl13_344
    | ~ spl13_51
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f509,f479,f400,f8603]) ).

fof(f8603,plain,
    ( spl13_344
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0)))))
        | sK6(sK1,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(sK1,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(sK1,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(sK1,X1,cartesian_product2(X2,X3)))))
        | sP0(sK1,X1,cartesian_product2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_344])]) ).

fof(f479,plain,
    ( spl13_60
  <=> ! [X0,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | unordered_pair(singleton(X1),unordered_pair(X1,X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0))),sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).

fof(f509,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK8(sK1,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK1,X1,cartesian_product2(X2,X3)),X0)))))
        | sK6(sK1,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(sK1,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(sK1,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(sK1,X1,cartesian_product2(X2,X3)))))
        | sP0(sK1,X1,cartesian_product2(X2,X3)) )
    | ~ spl13_51
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f401]) ).

fof(f480,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,sK1)
        | ~ in(X0,sK2)
        | unordered_pair(singleton(X1),unordered_pair(X1,X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0))),sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0))))) )
    | ~ spl13_60 ),
    inference(avatar_component_clause,[],[f479]) ).

fof(f8601,plain,
    ( spl13_343
    | ~ spl13_52
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f507,f479,f404,f8599]) ).

fof(f8599,plain,
    ( spl13_343
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0)))))
        | sK6(X1,sK1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X1,sK1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X1,sK1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X1,sK1,cartesian_product2(X2,X3)))))
        | sP0(X1,sK1,cartesian_product2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_343])]) ).

fof(f507,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK7(X1,sK1,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK1,cartesian_product2(X2,X3)),X0)))))
        | sK6(X1,sK1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X1,sK1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X1,sK1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X1,sK1,cartesian_product2(X2,X3)))))
        | sP0(X1,sK1,cartesian_product2(X2,X3)) )
    | ~ spl13_52
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f405]) ).

fof(f8597,plain,
    ( spl13_342
    | ~ spl13_54
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f505,f479,f412,f8595]) ).

fof(f8595,plain,
    ( spl13_342
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0)))))
        | sK8(cartesian_product2(X1,X2),X3,sK1) = unordered_pair(singleton(sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK1))),unordered_pair(sK10(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK1)),sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK1))))
        | sP0(cartesian_product2(X1,X2),X3,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_342])]) ).

fof(f505,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK1)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK1),X0)))))
        | sK8(cartesian_product2(X1,X2),X3,sK1) = unordered_pair(singleton(sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK1))),unordered_pair(sK10(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK1)),sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK1))))
        | sP0(cartesian_product2(X1,X2),X3,sK1) )
    | ~ spl13_54
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f413]) ).

fof(f8593,plain,
    ( spl13_341
    | ~ spl13_53
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f504,f479,f408,f8591]) ).

fof(f8591,plain,
    ( spl13_341
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0)))))
        | sK7(X1,cartesian_product2(X2,X3),sK1) = unordered_pair(singleton(sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK1))),unordered_pair(sK10(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK1)),sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK1))))
        | sP0(X1,cartesian_product2(X2,X3),sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_341])]) ).

fof(f504,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK1)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK1),X0)))))
        | sK7(X1,cartesian_product2(X2,X3),sK1) = unordered_pair(singleton(sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK1))),unordered_pair(sK10(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK1)),sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK1))))
        | sP0(X1,cartesian_product2(X2,X3),sK1) )
    | ~ spl13_53
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f409]) ).

fof(f8589,plain,
    ( spl13_340
    | ~ spl13_51
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f494,f475,f400,f8587]) ).

fof(f8587,plain,
    ( spl13_340
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0)))))
        | sK6(sK3,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(sK3,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(sK3,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(sK3,X1,cartesian_product2(X2,X3)))))
        | sP0(sK3,X1,cartesian_product2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_340])]) ).

fof(f475,plain,
    ( spl13_59
  <=> ! [X0,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | unordered_pair(singleton(X1),unordered_pair(X1,X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0))),sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_59])]) ).

fof(f494,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK8(sK3,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(sK3,X1,cartesian_product2(X2,X3)),X0)))))
        | sK6(sK3,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(sK3,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(sK3,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(sK3,X1,cartesian_product2(X2,X3)))))
        | sP0(sK3,X1,cartesian_product2(X2,X3)) )
    | ~ spl13_51
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f401]) ).

fof(f476,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,sK3)
        | ~ in(X0,sK4)
        | unordered_pair(singleton(X1),unordered_pair(X1,X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0))),sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0))))) )
    | ~ spl13_59 ),
    inference(avatar_component_clause,[],[f475]) ).

fof(f8585,plain,
    ( spl13_339
    | ~ spl13_52
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f492,f475,f404,f8583]) ).

fof(f8583,plain,
    ( spl13_339
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0)))))
        | sK6(X1,sK3,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X1,sK3,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X1,sK3,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X1,sK3,cartesian_product2(X2,X3)))))
        | sP0(X1,sK3,cartesian_product2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_339])]) ).

fof(f492,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK7(X1,sK3,cartesian_product2(X2,X3))),unordered_pair(sK7(X1,sK3,cartesian_product2(X2,X3)),X0)))))
        | sK6(X1,sK3,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X1,sK3,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X1,sK3,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X1,sK3,cartesian_product2(X2,X3)))))
        | sP0(X1,sK3,cartesian_product2(X2,X3)) )
    | ~ spl13_52
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f405]) ).

fof(f8581,plain,
    ( spl13_286
    | ~ spl13_231
    | ~ spl13_14
    | ~ spl13_249 ),
    inference(avatar_split_clause,[],[f6131,f6057,f137,f5629,f7096]) ).

fof(f6057,plain,
    ( spl13_249
  <=> sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_249])]) ).

fof(f6131,plain,
    ( ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK4))
    | ~ spl13_14
    | ~ spl13_249 ),
    inference(superposition,[],[f138,f6059]) ).

fof(f6059,plain,
    ( sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))))
    | ~ spl13_249 ),
    inference(avatar_component_clause,[],[f6057]) ).

fof(f8580,plain,
    ( spl13_338
    | ~ spl13_54
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f490,f475,f412,f8578]) ).

fof(f8578,plain,
    ( spl13_338
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0)))))
        | sK8(cartesian_product2(X1,X2),X3,sK3) = unordered_pair(singleton(sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK3))),unordered_pair(sK10(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK3)),sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK3))))
        | sP0(cartesian_product2(X1,X2),X3,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_338])]) ).

fof(f490,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(cartesian_product2(X1,X2),X3,sK3)),unordered_pair(sK6(cartesian_product2(X1,X2),X3,sK3),X0)))))
        | sK8(cartesian_product2(X1,X2),X3,sK3) = unordered_pair(singleton(sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK3))),unordered_pair(sK10(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK3)),sK9(X2,X1,sK8(cartesian_product2(X1,X2),X3,sK3))))
        | sP0(cartesian_product2(X1,X2),X3,sK3) )
    | ~ spl13_54
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f413]) ).

fof(f8576,plain,
    ( spl13_337
    | ~ spl13_53
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f489,f475,f408,f8574]) ).

fof(f8574,plain,
    ( spl13_337
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0)))))
        | sK7(X1,cartesian_product2(X2,X3),sK3) = unordered_pair(singleton(sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK3))),unordered_pair(sK10(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK3)),sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK3))))
        | sP0(X1,cartesian_product2(X2,X3),sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_337])]) ).

fof(f489,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,cartesian_product2(X2,X3),sK3)),unordered_pair(sK6(X1,cartesian_product2(X2,X3),sK3),X0)))))
        | sK7(X1,cartesian_product2(X2,X3),sK3) = unordered_pair(singleton(sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK3))),unordered_pair(sK10(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK3)),sK9(X3,X2,sK7(X1,cartesian_product2(X2,X3),sK3))))
        | sP0(X1,cartesian_product2(X2,X3),sK3) )
    | ~ spl13_53
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f409]) ).

fof(f8561,plain,
    ( spl13_336
    | ~ spl13_58
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2518,f2155,f453,f8559]) ).

fof(f8559,plain,
    ( spl13_336
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK1)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_336])]) ).

fof(f2155,plain,
    ( spl13_128
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(cartesian_product2(X2,X3),X4)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_128])]) ).

fof(f2518,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK1)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_58
    | ~ spl13_128 ),
    inference(superposition,[],[f454,f2156]) ).

fof(f2156,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_128 ),
    inference(avatar_component_clause,[],[f2155]) ).

fof(f8557,plain,
    ( spl13_335
    | ~ spl13_55
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2517,f2155,f416,f8555]) ).

fof(f8555,plain,
    ( spl13_335
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK3)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_335])]) ).

fof(f2517,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))),sK3)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_55
    | ~ spl13_128 ),
    inference(superposition,[],[f417,f2156]) ).

fof(f8553,plain,
    ( spl13_334
    | ~ spl13_58
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2410,f2151,f453,f8551]) ).

fof(f8551,plain,
    ( spl13_334
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK1)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_334])]) ).

fof(f2151,plain,
    ( spl13_127
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))))
        | cartesian_product2(X0,X1) = cartesian_product2(X2,cartesian_product2(X3,X4))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_127])]) ).

fof(f2410,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK1)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_58
    | ~ spl13_127 ),
    inference(superposition,[],[f454,f2152]) ).

fof(f2152,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))))
        | cartesian_product2(X0,X1) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_127 ),
    inference(avatar_component_clause,[],[f2151]) ).

fof(f8549,plain,
    ( spl13_333
    | ~ spl13_55
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2409,f2151,f416,f8547]) ).

fof(f8547,plain,
    ( spl13_333
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK3)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_333])]) ).

fof(f2409,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK3)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_55
    | ~ spl13_127 ),
    inference(superposition,[],[f417,f2152]) ).

fof(f8545,plain,
    ( spl13_332
    | ~ spl13_58
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2302,f2147,f453,f8543]) ).

fof(f8543,plain,
    ( spl13_332
  <=> ! [X2,X4,X0,X3,X1] :
        ( in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK1)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_332])]) ).

fof(f2147,plain,
    ( spl13_126
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(X3,X4) = cartesian_product2(cartesian_product2(X0,X1),X2)
        | sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))))),unordered_pair(sK10(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))),sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_126])]) ).

fof(f2302,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK1)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_58
    | ~ spl13_126 ),
    inference(superposition,[],[f454,f2148]) ).

fof(f2148,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))))),unordered_pair(sK10(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))),sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))))))
        | sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(X3,X4) = cartesian_product2(cartesian_product2(X0,X1),X2) )
    | ~ spl13_126 ),
    inference(avatar_component_clause,[],[f2147]) ).

fof(f8541,plain,
    ( spl13_331
    | ~ spl13_55
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2301,f2147,f416,f8539]) ).

fof(f8539,plain,
    ( spl13_331
  <=> ! [X2,X4,X0,X3,X1] :
        ( in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK3)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_331])]) ).

fof(f2301,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))),sK3)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_55
    | ~ spl13_126 ),
    inference(superposition,[],[f417,f2148]) ).

fof(f8537,plain,
    ( spl13_330
    | ~ spl13_58
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2194,f2139,f453,f8535]) ).

fof(f8535,plain,
    ( spl13_330
  <=> ! [X2,X4,X0,X3,X1] :
        ( in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK1)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_330])]) ).

fof(f2139,plain,
    ( spl13_124
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X3,X4) = cartesian_product2(X0,cartesian_product2(X1,X2))
        | sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))))),unordered_pair(sK10(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))),sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_124])]) ).

fof(f2194,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK1)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_58
    | ~ spl13_124 ),
    inference(superposition,[],[f454,f2140]) ).

fof(f2140,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))))),unordered_pair(sK10(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))),sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))))))
        | sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X3,X4) = cartesian_product2(X0,cartesian_product2(X1,X2)) )
    | ~ spl13_124 ),
    inference(avatar_component_clause,[],[f2139]) ).

fof(f8533,plain,
    ( spl13_329
    | ~ spl13_55
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2193,f2139,f416,f8531]) ).

fof(f8531,plain,
    ( spl13_329
  <=> ! [X2,X4,X0,X3,X1] :
        ( in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK3)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_329])]) ).

fof(f2193,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))),sK3)
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_55
    | ~ spl13_124 ),
    inference(superposition,[],[f417,f2140]) ).

fof(f8439,plain,
    ( ~ spl13_231
    | spl13_1
    | ~ spl13_16
    | ~ spl13_286 ),
    inference(avatar_split_clause,[],[f8242,f7096,f145,f70,f5629]) ).

fof(f70,plain,
    ( spl13_1
  <=> cartesian_product2(sK1,sK2) = cartesian_product2(sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).

fof(f145,plain,
    ( spl13_16
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ in(sK5(X0,X1),X1)
        | ~ in(sK5(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).

fof(f8242,plain,
    ( cartesian_product2(sK1,sK2) = cartesian_product2(sK3,sK4)
    | ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | ~ spl13_16
    | ~ spl13_286 ),
    inference(resolution,[],[f7097,f146]) ).

fof(f146,plain,
    ( ! [X0,X1] :
        ( ~ in(sK5(X0,X1),X1)
        | X0 = X1
        | ~ in(sK5(X0,X1),X0) )
    | ~ spl13_16 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f7097,plain,
    ( in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK4))
    | ~ spl13_286 ),
    inference(avatar_component_clause,[],[f7096]) ).

fof(f8348,plain,
    ( spl13_328
    | ~ spl13_10
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1862,f1753,f453,f113,f8346]) ).

fof(f8346,plain,
    ( spl13_328
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_328])]) ).

fof(f1753,plain,
    ( spl13_112
  <=> ! [X0,X3,X2,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))))
        | cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
        | sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_112])]) ).

fof(f1862,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1812,f114]) ).

fof(f1812,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(superposition,[],[f454,f1754]) ).

fof(f1754,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))))
        | cartesian_product2(X0,X1) = cartesian_product2(X2,X3) )
    | ~ spl13_112 ),
    inference(avatar_component_clause,[],[f1753]) ).

fof(f8344,plain,
    ( spl13_327
    | ~ spl13_10
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1860,f1753,f416,f113,f8342]) ).

fof(f8342,plain,
    ( spl13_327
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_327])]) ).

fof(f1860,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1810,f114]) ).

fof(f1810,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(superposition,[],[f417,f1754]) ).

fof(f8340,plain,
    ( spl13_326
    | ~ spl13_10
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1838,f1753,f453,f113,f8338]) ).

fof(f8338,plain,
    ( spl13_326
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_326])]) ).

fof(f1838,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1782,f114]) ).

fof(f1782,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(superposition,[],[f454,f1754]) ).

fof(f8336,plain,
    ( spl13_325
    | ~ spl13_10
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1836,f1753,f416,f113,f8334]) ).

fof(f8334,plain,
    ( spl13_325
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_325])]) ).

fof(f1836,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1780,f114]) ).

fof(f1780,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(superposition,[],[f417,f1754]) ).

fof(f8332,plain,
    ( spl13_324
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1850,f1753,f173,f113,f8330]) ).

fof(f8330,plain,
    ( spl13_324
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_324])]) ).

fof(f173,plain,
    ( spl13_21
  <=> ! [X0,X1] :
        ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).

fof(f1850,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1849,f114]) ).

fof(f1849,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1800,f114]) ).

fof(f1800,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(superposition,[],[f174,f1754]) ).

fof(f174,plain,
    ( ! [X0,X1] :
        ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2)) )
    | ~ spl13_21 ),
    inference(avatar_component_clause,[],[f173]) ).

fof(f8328,plain,
    ( spl13_323
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1848,f1753,f137,f113,f8326]) ).

fof(f8326,plain,
    ( spl13_323
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_323])]) ).

fof(f1848,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1847,f114]) ).

fof(f1847,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1799,f114]) ).

fof(f1799,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(superposition,[],[f138,f1754]) ).

fof(f8324,plain,
    ( spl13_322
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1826,f1753,f173,f113,f8322]) ).

fof(f8322,plain,
    ( spl13_322
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_322])]) ).

fof(f1826,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1825,f114]) ).

fof(f1825,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1770,f114]) ).

fof(f1770,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(superposition,[],[f174,f1754]) ).

fof(f8320,plain,
    ( spl13_321
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1824,f1753,f137,f113,f8318]) ).

fof(f8318,plain,
    ( spl13_321
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_321])]) ).

fof(f1824,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1823,f114]) ).

fof(f1823,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1769,f114]) ).

fof(f1769,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(superposition,[],[f138,f1754]) ).

fof(f8310,plain,
    ( ~ spl13_320
    | ~ spl13_8
    | ~ spl13_286 ),
    inference(avatar_split_clause,[],[f8243,f7096,f105,f8307]) ).

fof(f8307,plain,
    ( spl13_320
  <=> in(cartesian_product2(sK3,sK4),sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_320])]) ).

fof(f105,plain,
    ( spl13_8
  <=> ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).

fof(f8243,plain,
    ( ~ in(cartesian_product2(sK3,sK4),sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))
    | ~ spl13_8
    | ~ spl13_286 ),
    inference(resolution,[],[f7097,f106]) ).

fof(f106,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) )
    | ~ spl13_8 ),
    inference(avatar_component_clause,[],[f105]) ).

fof(f8303,plain,
    ( spl13_319
    | ~ spl13_58
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2488,f2155,f453,f8301]) ).

fof(f8301,plain,
    ( spl13_319
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK2)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK1)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_319])]) ).

fof(f2488,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK2)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK1)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_58
    | ~ spl13_128 ),
    inference(superposition,[],[f454,f2156]) ).

fof(f8299,plain,
    ( spl13_318
    | ~ spl13_55
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2487,f2155,f416,f8297]) ).

fof(f8297,plain,
    ( spl13_318
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK4)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK3)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_318])]) ).

fof(f2487,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK4)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),sK3)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_55
    | ~ spl13_128 ),
    inference(superposition,[],[f417,f2156]) ).

fof(f8295,plain,
    ( spl13_317
    | ~ spl13_58
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2380,f2151,f453,f8293]) ).

fof(f8293,plain,
    ( spl13_317
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK2)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK1)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_317])]) ).

fof(f2380,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK2)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK1)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_58
    | ~ spl13_127 ),
    inference(superposition,[],[f454,f2152]) ).

fof(f8291,plain,
    ( spl13_316
    | ~ spl13_55
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2379,f2151,f416,f8289]) ).

fof(f8289,plain,
    ( spl13_316
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK4)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK3)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_316])]) ).

fof(f2379,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK4)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),sK3)
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_55
    | ~ spl13_127 ),
    inference(superposition,[],[f417,f2152]) ).

fof(f8287,plain,
    ( spl13_315
    | ~ spl13_58
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2272,f2147,f453,f8285]) ).

fof(f8285,plain,
    ( spl13_315
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK2)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK1)
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_315])]) ).

fof(f2272,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK2)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK1)
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_58
    | ~ spl13_126 ),
    inference(superposition,[],[f454,f2148]) ).

fof(f8283,plain,
    ( spl13_314
    | ~ spl13_55
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2271,f2147,f416,f8281]) ).

fof(f8281,plain,
    ( spl13_314
  <=> ! [X4,X0,X3,X2,X1] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK4)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK3)
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_314])]) ).

fof(f2271,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK4)
        | ~ in(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),sK3)
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_55
    | ~ spl13_126 ),
    inference(superposition,[],[f417,f2148]) ).

fof(f8279,plain,
    ( spl13_313
    | ~ spl13_58
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2164,f2139,f453,f8277]) ).

fof(f8277,plain,
    ( spl13_313
  <=> ! [X2,X4,X0,X3,X1] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK2)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK1)
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_313])]) ).

fof(f2164,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK2)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK1)
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_58
    | ~ spl13_124 ),
    inference(superposition,[],[f454,f2140]) ).

fof(f8275,plain,
    ( spl13_312
    | ~ spl13_55
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2163,f2139,f416,f8273]) ).

fof(f8273,plain,
    ( spl13_312
  <=> ! [X2,X4,X0,X3,X1] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK4)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK3)
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_312])]) ).

fof(f2163,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK4)
        | ~ in(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),sK3)
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_55
    | ~ spl13_124 ),
    inference(superposition,[],[f417,f2140]) ).

fof(f7667,plain,
    ( spl13_311
    | ~ spl13_58
    | ~ spl13_80 ),
    inference(avatar_split_clause,[],[f801,f728,f453,f7665]) ).

fof(f7665,plain,
    ( spl13_311
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_311])]) ).

fof(f728,plain,
    ( spl13_80
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_80])]) ).

fof(f801,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58
    | ~ spl13_80 ),
    inference(resolution,[],[f729,f454]) ).

fof(f729,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4) )
    | ~ spl13_80 ),
    inference(avatar_component_clause,[],[f728]) ).

fof(f7663,plain,
    ( spl13_310
    | ~ spl13_55
    | ~ spl13_80 ),
    inference(avatar_split_clause,[],[f800,f728,f416,f7661]) ).

fof(f7661,plain,
    ( spl13_310
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_310])]) ).

fof(f800,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55
    | ~ spl13_80 ),
    inference(resolution,[],[f729,f417]) ).

fof(f7659,plain,
    ( spl13_309
    | ~ spl13_42
    | ~ spl13_80 ),
    inference(avatar_split_clause,[],[f798,f728,f293,f7657]) ).

fof(f7657,plain,
    ( spl13_309
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_309])]) ).

fof(f798,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42
    | ~ spl13_80 ),
    inference(resolution,[],[f729,f294]) ).

fof(f7655,plain,
    ( spl13_308
    | ~ spl13_41
    | ~ spl13_80 ),
    inference(avatar_split_clause,[],[f797,f728,f289,f7653]) ).

fof(f7653,plain,
    ( spl13_308
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_308])]) ).

fof(f797,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41
    | ~ spl13_80 ),
    inference(resolution,[],[f729,f290]) ).

fof(f7651,plain,
    ( ~ spl13_307
    | ~ spl13_8
    | ~ spl13_231 ),
    inference(avatar_split_clause,[],[f7578,f5629,f105,f7648]) ).

fof(f7648,plain,
    ( spl13_307
  <=> in(cartesian_product2(sK1,sK2),sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_307])]) ).

fof(f7578,plain,
    ( ~ in(cartesian_product2(sK1,sK2),sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))
    | ~ spl13_8
    | ~ spl13_231 ),
    inference(resolution,[],[f5630,f106]) ).

fof(f5630,plain,
    ( in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | ~ spl13_231 ),
    inference(avatar_component_clause,[],[f5629]) ).

fof(f7646,plain,
    ( spl13_306
    | ~ spl13_58
    | ~ spl13_79 ),
    inference(avatar_split_clause,[],[f778,f724,f453,f7644]) ).

fof(f7644,plain,
    ( spl13_306
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_306])]) ).

fof(f724,plain,
    ( spl13_79
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_79])]) ).

fof(f778,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58
    | ~ spl13_79 ),
    inference(resolution,[],[f725,f454]) ).

fof(f725,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4) )
    | ~ spl13_79 ),
    inference(avatar_component_clause,[],[f724]) ).

fof(f7642,plain,
    ( spl13_305
    | ~ spl13_55
    | ~ spl13_79 ),
    inference(avatar_split_clause,[],[f777,f724,f416,f7640]) ).

fof(f7640,plain,
    ( spl13_305
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_305])]) ).

fof(f777,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55
    | ~ spl13_79 ),
    inference(resolution,[],[f725,f417]) ).

fof(f7638,plain,
    ( spl13_304
    | ~ spl13_42
    | ~ spl13_79 ),
    inference(avatar_split_clause,[],[f775,f724,f293,f7636]) ).

fof(f7636,plain,
    ( spl13_304
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_304])]) ).

fof(f775,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42
    | ~ spl13_79 ),
    inference(resolution,[],[f725,f294]) ).

fof(f7634,plain,
    ( spl13_303
    | ~ spl13_41
    | ~ spl13_79 ),
    inference(avatar_split_clause,[],[f774,f724,f289,f7632]) ).

fof(f7632,plain,
    ( spl13_303
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_303])]) ).

fof(f774,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41
    | ~ spl13_79 ),
    inference(resolution,[],[f725,f290]) ).

fof(f7630,plain,
    ( spl13_302
    | ~ spl13_58
    | ~ spl13_78 ),
    inference(avatar_split_clause,[],[f757,f720,f453,f7628]) ).

fof(f7628,plain,
    ( spl13_302
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_302])]) ).

fof(f720,plain,
    ( spl13_78
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).

fof(f757,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58
    | ~ spl13_78 ),
    inference(resolution,[],[f721,f454]) ).

fof(f721,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4) )
    | ~ spl13_78 ),
    inference(avatar_component_clause,[],[f720]) ).

fof(f7626,plain,
    ( spl13_301
    | ~ spl13_55
    | ~ spl13_78 ),
    inference(avatar_split_clause,[],[f756,f720,f416,f7624]) ).

fof(f7624,plain,
    ( spl13_301
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_301])]) ).

fof(f756,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55
    | ~ spl13_78 ),
    inference(resolution,[],[f721,f417]) ).

fof(f7622,plain,
    ( spl13_300
    | ~ spl13_42
    | ~ spl13_78 ),
    inference(avatar_split_clause,[],[f754,f720,f293,f7620]) ).

fof(f7620,plain,
    ( spl13_300
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_300])]) ).

fof(f754,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42
    | ~ spl13_78 ),
    inference(resolution,[],[f721,f294]) ).

fof(f7618,plain,
    ( spl13_299
    | ~ spl13_41
    | ~ spl13_78 ),
    inference(avatar_split_clause,[],[f753,f720,f289,f7616]) ).

fof(f7616,plain,
    ( spl13_299
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_299])]) ).

fof(f753,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41
    | ~ spl13_78 ),
    inference(resolution,[],[f721,f290]) ).

fof(f7614,plain,
    ( spl13_298
    | ~ spl13_58
    | ~ spl13_77 ),
    inference(avatar_split_clause,[],[f736,f716,f453,f7612]) ).

fof(f7612,plain,
    ( spl13_298
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_298])]) ).

fof(f716,plain,
    ( spl13_77
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).

fof(f736,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58
    | ~ spl13_77 ),
    inference(resolution,[],[f717,f454]) ).

fof(f717,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4) )
    | ~ spl13_77 ),
    inference(avatar_component_clause,[],[f716]) ).

fof(f7610,plain,
    ( spl13_297
    | ~ spl13_55
    | ~ spl13_77 ),
    inference(avatar_split_clause,[],[f735,f716,f416,f7608]) ).

fof(f7608,plain,
    ( spl13_297
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_297])]) ).

fof(f735,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55
    | ~ spl13_77 ),
    inference(resolution,[],[f717,f417]) ).

fof(f7563,plain,
    ( spl13_296
    | ~ spl13_42
    | ~ spl13_77 ),
    inference(avatar_split_clause,[],[f733,f716,f293,f7561]) ).

fof(f7561,plain,
    ( spl13_296
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_296])]) ).

fof(f733,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42
    | ~ spl13_77 ),
    inference(resolution,[],[f717,f294]) ).

fof(f7559,plain,
    ( spl13_295
    | ~ spl13_41
    | ~ spl13_77 ),
    inference(avatar_split_clause,[],[f732,f716,f289,f7557]) ).

fof(f7557,plain,
    ( spl13_295
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_295])]) ).

fof(f732,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))),unordered_pair(sK10(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4)))),sK9(X4,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4)
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41
    | ~ spl13_77 ),
    inference(resolution,[],[f717,f290]) ).

fof(f7275,plain,
    ( spl13_1
    | spl13_231
    | ~ spl13_15
    | spl13_286 ),
    inference(avatar_split_clause,[],[f7242,f7096,f141,f5629,f70]) ).

fof(f141,plain,
    ( spl13_15
  <=> ! [X0,X1] :
        ( X0 = X1
        | in(sK5(X0,X1),X1)
        | in(sK5(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).

fof(f7242,plain,
    ( in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | cartesian_product2(sK1,sK2) = cartesian_product2(sK3,sK4)
    | ~ spl13_15
    | spl13_286 ),
    inference(resolution,[],[f7098,f142]) ).

fof(f142,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1),X1)
        | in(sK5(X0,X1),X0)
        | X0 = X1 )
    | ~ spl13_15 ),
    inference(avatar_component_clause,[],[f141]) ).

fof(f7098,plain,
    ( ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK4))
    | spl13_286 ),
    inference(avatar_component_clause,[],[f7096]) ).

fof(f7274,plain,
    ( spl13_294
    | ~ spl13_58
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f1368,f1360,f453,f7272]) ).

fof(f7272,plain,
    ( spl13_294
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X5,X4))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X5,X4)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK2)
        | ~ in(X4,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_294])]) ).

fof(f1360,plain,
    ( spl13_101
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,X0)
        | ~ in(X5,X1)
        | in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),cartesian_product2(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_101])]) ).

fof(f1368,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X5,X4))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X5,X4)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK2)
        | ~ in(X4,sK1) )
    | ~ spl13_58
    | ~ spl13_101 ),
    inference(resolution,[],[f1361,f454]) ).

fof(f1361,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ in(X5,X1)
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,X0)
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),cartesian_product2(X2,X3)) )
    | ~ spl13_101 ),
    inference(avatar_component_clause,[],[f1360]) ).

fof(f7270,plain,
    ( spl13_293
    | ~ spl13_55
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f1367,f1360,f416,f7268]) ).

fof(f7268,plain,
    ( spl13_293
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X5,X4))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X5,X4)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK4)
        | ~ in(X4,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_293])]) ).

fof(f1367,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X5,X4))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X5,X4)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK4)
        | ~ in(X4,sK3) )
    | ~ spl13_55
    | ~ spl13_101 ),
    inference(resolution,[],[f1361,f417]) ).

fof(f7266,plain,
    ( spl13_292
    | ~ spl13_42
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f1365,f1360,f293,f7264]) ).

fof(f7264,plain,
    ( spl13_292
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X4,X5))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK2)
        | ~ in(X4,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_292])]) ).

fof(f1365,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK3,sK4),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X4,X5))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK2)
        | ~ in(X4,sK1) )
    | ~ spl13_42
    | ~ spl13_101 ),
    inference(resolution,[],[f1361,f294]) ).

fof(f7262,plain,
    ( spl13_291
    | ~ spl13_41
    | ~ spl13_101 ),
    inference(avatar_split_clause,[],[f1364,f1360,f289,f7260]) ).

fof(f7260,plain,
    ( spl13_291
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X4,X5))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK4)
        | ~ in(X4,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_291])]) ).

fof(f1364,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),unordered_pair(sK8(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)),sK7(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))))
        | ~ in(X3,X0)
        | sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2))),sK9(X2,X1,sK6(X0,cartesian_product2(sK1,sK2),cartesian_product2(X1,X2)))))
        | in(unordered_pair(singleton(unordered_pair(singleton(X4),unordered_pair(X4,X5))),unordered_pair(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X3)),cartesian_product2(X1,X2))
        | ~ in(X5,sK4)
        | ~ in(X4,sK3) )
    | ~ spl13_41
    | ~ spl13_101 ),
    inference(resolution,[],[f1361,f290]) ).

fof(f7258,plain,
    ( spl13_290
    | ~ spl13_50
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f500,f479,f382,f7256]) ).

fof(f7256,plain,
    ( spl13_290
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0)))))
        | sK5(cartesian_product2(X1,X2),sK1) = unordered_pair(singleton(sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK1))),unordered_pair(sK10(X2,X1,sK5(cartesian_product2(X1,X2),sK1)),sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK1))))
        | sK1 = cartesian_product2(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_290])]) ).

fof(f500,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK1)),unordered_pair(sK5(cartesian_product2(X1,X2),sK1),X0)))))
        | sK5(cartesian_product2(X1,X2),sK1) = unordered_pair(singleton(sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK1))),unordered_pair(sK10(X2,X1,sK5(cartesian_product2(X1,X2),sK1)),sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK1))))
        | sK1 = cartesian_product2(X1,X2) )
    | ~ spl13_50
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f383]) ).

fof(f7254,plain,
    ( spl13_289
    | ~ spl13_49
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f499,f479,f378,f7252]) ).

fof(f7252,plain,
    ( spl13_289
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0)))))
        | sK5(sK1,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(sK1,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(sK1,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(sK1,cartesian_product2(X1,X2)))))
        | sK1 = cartesian_product2(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_289])]) ).

fof(f499,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,cartesian_product2(X1,X2))),unordered_pair(sK5(sK1,cartesian_product2(X1,X2)),X0)))))
        | sK5(sK1,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(sK1,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(sK1,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(sK1,cartesian_product2(X1,X2)))))
        | sK1 = cartesian_product2(X1,X2) )
    | ~ spl13_49
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f379]) ).

fof(f7250,plain,
    ( spl13_288
    | ~ spl13_50
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f485,f475,f382,f7248]) ).

fof(f7248,plain,
    ( spl13_288
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0)))))
        | sK5(cartesian_product2(X1,X2),sK3) = unordered_pair(singleton(sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK3))),unordered_pair(sK10(X2,X1,sK5(cartesian_product2(X1,X2),sK3)),sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK3))))
        | sK3 = cartesian_product2(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_288])]) ).

fof(f485,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(cartesian_product2(X1,X2),sK3)),unordered_pair(sK5(cartesian_product2(X1,X2),sK3),X0)))))
        | sK5(cartesian_product2(X1,X2),sK3) = unordered_pair(singleton(sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK3))),unordered_pair(sK10(X2,X1,sK5(cartesian_product2(X1,X2),sK3)),sK9(X2,X1,sK5(cartesian_product2(X1,X2),sK3))))
        | sK3 = cartesian_product2(X1,X2) )
    | ~ spl13_50
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f383]) ).

fof(f7246,plain,
    ( spl13_287
    | ~ spl13_49
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f484,f475,f378,f7244]) ).

fof(f7244,plain,
    ( spl13_287
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0)))))
        | sK5(sK3,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(sK3,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(sK3,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(sK3,cartesian_product2(X1,X2)))))
        | sK3 = cartesian_product2(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_287])]) ).

fof(f484,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,cartesian_product2(X1,X2))),unordered_pair(sK5(sK3,cartesian_product2(X1,X2)),X0)))))
        | sK5(sK3,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(sK3,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(sK3,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(sK3,cartesian_product2(X1,X2)))))
        | sK3 = cartesian_product2(X1,X2) )
    | ~ spl13_49
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f379]) ).

fof(f7099,plain,
    ( spl13_231
    | ~ spl13_286
    | ~ spl13_21
    | ~ spl13_249 ),
    inference(avatar_split_clause,[],[f6132,f6057,f173,f7096,f5629]) ).

fof(f6132,plain,
    ( ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK3,sK4))
    | in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | ~ spl13_21
    | ~ spl13_249 ),
    inference(superposition,[],[f174,f6059]) ).

fof(f7094,plain,
    ( spl13_285
    | ~ spl13_10
    | ~ spl13_57
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1861,f1753,f449,f113,f7092]) ).

fof(f7092,plain,
    ( spl13_285
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_285])]) ).

fof(f449,plain,
    ( spl13_57
  <=> ! [X0,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(X1),unordered_pair(X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).

fof(f1861,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_57
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1811,f114]) ).

fof(f1811,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_57
    | ~ spl13_112 ),
    inference(superposition,[],[f450,f1754]) ).

fof(f450,plain,
    ( ! [X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(X1),unordered_pair(X1,X0)))
        | ~ in(X1,sK1)
        | ~ in(X0,sK2) )
    | ~ spl13_57 ),
    inference(avatar_component_clause,[],[f449]) ).

fof(f7090,plain,
    ( spl13_284
    | ~ spl13_10
    | ~ spl13_48
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1859,f1753,f352,f113,f7088]) ).

fof(f7088,plain,
    ( spl13_284
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_284])]) ).

fof(f352,plain,
    ( spl13_48
  <=> ! [X0,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(X1),unordered_pair(X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).

fof(f1859,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_48
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1809,f114]) ).

fof(f1809,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_48
    | ~ spl13_112 ),
    inference(superposition,[],[f353,f1754]) ).

fof(f353,plain,
    ( ! [X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(X1),unordered_pair(X1,X0)))
        | ~ in(X1,sK3)
        | ~ in(X0,sK4) )
    | ~ spl13_48 ),
    inference(avatar_component_clause,[],[f352]) ).

fof(f7086,plain,
    ( spl13_283
    | ~ spl13_10
    | ~ spl13_42
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1856,f1753,f293,f113,f7084]) ).

fof(f7084,plain,
    ( spl13_283
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_283])]) ).

fof(f1856,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_42
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1806,f114]) ).

fof(f1806,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_42
    | ~ spl13_112 ),
    inference(superposition,[],[f294,f1754]) ).

fof(f7082,plain,
    ( spl13_282
    | ~ spl13_10
    | ~ spl13_41
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1855,f1753,f289,f113,f7080]) ).

fof(f7080,plain,
    ( spl13_282
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_282])]) ).

fof(f1855,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_41
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1805,f114]) ).

fof(f1805,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_41
    | ~ spl13_112 ),
    inference(superposition,[],[f290,f1754]) ).

fof(f7078,plain,
    ( spl13_281
    | ~ spl13_10
    | ~ spl13_57
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1837,f1753,f449,f113,f7076]) ).

fof(f7076,plain,
    ( spl13_281
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_281])]) ).

fof(f1837,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_57
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1781,f114]) ).

fof(f1781,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_57
    | ~ spl13_112 ),
    inference(superposition,[],[f450,f1754]) ).

fof(f7074,plain,
    ( spl13_280
    | ~ spl13_10
    | ~ spl13_48
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1835,f1753,f352,f113,f7072]) ).

fof(f7072,plain,
    ( spl13_280
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_280])]) ).

fof(f1835,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_48
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1779,f114]) ).

fof(f1779,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_48
    | ~ spl13_112 ),
    inference(superposition,[],[f353,f1754]) ).

fof(f7070,plain,
    ( spl13_279
    | ~ spl13_10
    | ~ spl13_42
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1832,f1753,f293,f113,f7068]) ).

fof(f7068,plain,
    ( spl13_279
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_279])]) ).

fof(f1832,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_42
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1776,f114]) ).

fof(f1776,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_42
    | ~ spl13_112 ),
    inference(superposition,[],[f294,f1754]) ).

fof(f7066,plain,
    ( spl13_278
    | ~ spl13_10
    | ~ spl13_41
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1831,f1753,f289,f113,f7064]) ).

fof(f7064,plain,
    ( spl13_278
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_278])]) ).

fof(f1831,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_10
    | ~ spl13_41
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1775,f114]) ).

fof(f1775,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_41
    | ~ spl13_112 ),
    inference(superposition,[],[f290,f1754]) ).

fof(f7062,plain,
    ( spl13_277
    | ~ spl13_58
    | ~ spl13_111 ),
    inference(avatar_split_clause,[],[f1724,f1716,f453,f7060]) ).

fof(f7060,plain,
    ( spl13_277
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | unordered_pair(singleton(X2),unordered_pair(X3,X2)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_277])]) ).

fof(f1716,plain,
    ( spl13_111
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,cartesian_product2(X2,X3))
        | unordered_pair(singleton(sK9(X0,X1,X4)),unordered_pair(sK10(X0,X1,X4),sK9(X0,X1,X4))) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_111])]) ).

fof(f1724,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | unordered_pair(singleton(X2),unordered_pair(X3,X2)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_111 ),
    inference(resolution,[],[f1717,f454]) ).

fof(f1717,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X4,cartesian_product2(X2,X3))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | unordered_pair(singleton(sK9(X0,X1,X4)),unordered_pair(sK10(X0,X1,X4),sK9(X0,X1,X4))) = X4 )
    | ~ spl13_111 ),
    inference(avatar_component_clause,[],[f1716]) ).

fof(f7058,plain,
    ( spl13_276
    | ~ spl13_55
    | ~ spl13_111 ),
    inference(avatar_split_clause,[],[f1723,f1716,f416,f7056]) ).

fof(f7056,plain,
    ( spl13_276
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | unordered_pair(singleton(X2),unordered_pair(X3,X2)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_276])]) ).

fof(f1723,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | unordered_pair(singleton(X2),unordered_pair(X3,X2)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_111 ),
    inference(resolution,[],[f1717,f417]) ).

fof(f7054,plain,
    ( spl13_275
    | ~ spl13_42
    | ~ spl13_111 ),
    inference(avatar_split_clause,[],[f1721,f1716,f293,f7052]) ).

fof(f7052,plain,
    ( spl13_275
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | unordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_275])]) ).

fof(f1721,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | unordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_111 ),
    inference(resolution,[],[f1717,f294]) ).

fof(f7050,plain,
    ( spl13_274
    | ~ spl13_41
    | ~ spl13_111 ),
    inference(avatar_split_clause,[],[f1720,f1716,f289,f7048]) ).

fof(f7048,plain,
    ( spl13_274
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | unordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_274])]) ).

fof(f1720,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | unordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_111 ),
    inference(resolution,[],[f1717,f290]) ).

fof(f6654,plain,
    ( ~ spl13_273
    | ~ spl13_10
    | ~ spl13_12
    | ~ spl13_249 ),
    inference(avatar_split_clause,[],[f6177,f6057,f126,f113,f6651]) ).

fof(f6651,plain,
    ( spl13_273
  <=> empty(unordered_pair(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),singleton(singleton(sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_273])]) ).

fof(f6177,plain,
    ( ~ empty(unordered_pair(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),singleton(singleton(sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))))))
    | ~ spl13_10
    | ~ spl13_12
    | ~ spl13_249 ),
    inference(forward_demodulation,[],[f6147,f114]) ).

fof(f6147,plain,
    ( ~ empty(unordered_pair(singleton(singleton(sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))),sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))))
    | ~ spl13_12
    | ~ spl13_249 ),
    inference(superposition,[],[f127,f6059]) ).

fof(f6649,plain,
    ( spl13_272
    | ~ spl13_58
    | ~ spl13_82 ),
    inference(avatar_split_clause,[],[f859,f822,f453,f6647]) ).

fof(f6647,plain,
    ( spl13_272
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_272])]) ).

fof(f822,plain,
    ( spl13_82
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))))))
        | ~ in(X3,cartesian_product2(X1,X2))
        | ~ in(X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_82])]) ).

fof(f859,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_58
    | ~ spl13_82 ),
    inference(resolution,[],[f823,f454]) ).

fof(f823,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X3,cartesian_product2(X1,X2))
        | sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))))))
        | ~ in(X4,X0) )
    | ~ spl13_82 ),
    inference(avatar_component_clause,[],[f822]) ).

fof(f6645,plain,
    ( spl13_271
    | ~ spl13_55
    | ~ spl13_82 ),
    inference(avatar_split_clause,[],[f858,f822,f416,f6643]) ).

fof(f6643,plain,
    ( spl13_271
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_271])]) ).

fof(f858,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_55
    | ~ spl13_82 ),
    inference(resolution,[],[f823,f417]) ).

fof(f6641,plain,
    ( spl13_270
    | ~ spl13_42
    | ~ spl13_82 ),
    inference(avatar_split_clause,[],[f856,f822,f293,f6639]) ).

fof(f6639,plain,
    ( spl13_270
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_270])]) ).

fof(f856,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_42
    | ~ spl13_82 ),
    inference(resolution,[],[f823,f294]) ).

fof(f6637,plain,
    ( spl13_269
    | ~ spl13_41
    | ~ spl13_82 ),
    inference(avatar_split_clause,[],[f855,f822,f289,f6635]) ).

fof(f6635,plain,
    ( spl13_269
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_269])]) ).

fof(f855,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(X3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_41
    | ~ spl13_82 ),
    inference(resolution,[],[f823,f290]) ).

fof(f6633,plain,
    ( spl13_268
    | ~ spl13_58
    | ~ spl13_81 ),
    inference(avatar_split_clause,[],[f838,f818,f453,f6631]) ).

fof(f6631,plain,
    ( spl13_268
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3)))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_268])]) ).

fof(f818,plain,
    ( spl13_81
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))))))
        | ~ in(X3,cartesian_product2(X1,X2))
        | ~ in(X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_81])]) ).

fof(f838,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3)))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_58
    | ~ spl13_81 ),
    inference(resolution,[],[f819,f454]) ).

fof(f819,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X3,cartesian_product2(X1,X2))
        | sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))))))
        | ~ in(X4,X0) )
    | ~ spl13_81 ),
    inference(avatar_component_clause,[],[f818]) ).

fof(f6629,plain,
    ( spl13_267
    | ~ spl13_55
    | ~ spl13_81 ),
    inference(avatar_split_clause,[],[f837,f818,f416,f6627]) ).

fof(f6627,plain,
    ( spl13_267
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3)))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_267])]) ).

fof(f837,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3)))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X2,X1))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X2,X1)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_55
    | ~ spl13_81 ),
    inference(resolution,[],[f819,f417]) ).

fof(f6625,plain,
    ( spl13_266
    | ~ spl13_42
    | ~ spl13_81 ),
    inference(avatar_split_clause,[],[f835,f818,f293,f6623]) ).

fof(f6623,plain,
    ( spl13_266
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_266])]) ).

fof(f835,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))) = unordered_pair(singleton(sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))),unordered_pair(sK10(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)))),sK9(sK4,sK3,sK9(X0,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_42
    | ~ spl13_81 ),
    inference(resolution,[],[f819,f294]) ).

fof(f6621,plain,
    ( spl13_265
    | ~ spl13_41
    | ~ spl13_81 ),
    inference(avatar_split_clause,[],[f834,f818,f289,f6619]) ).

fof(f6619,plain,
    ( spl13_265
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_265])]) ).

fof(f834,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))) = unordered_pair(singleton(sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))),unordered_pair(sK10(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3)))),sK9(sK2,sK1,sK9(X0,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X1),unordered_pair(X1,X2))),unordered_pair(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X3))))))
        | ~ in(X3,X0)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_41
    | ~ spl13_81 ),
    inference(resolution,[],[f819,f290]) ).

fof(f6267,plain,
    ( spl13_264
    | ~ spl13_58
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f647,f618,f453,f6265]) ).

fof(f6265,plain,
    ( spl13_264
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_264])]) ).

fof(f618,plain,
    ( spl13_74
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).

fof(f647,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58
    | ~ spl13_74 ),
    inference(resolution,[],[f619,f454]) ).

fof(f619,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3 )
    | ~ spl13_74 ),
    inference(avatar_component_clause,[],[f618]) ).

fof(f6263,plain,
    ( spl13_263
    | ~ spl13_55
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f646,f618,f416,f6261]) ).

fof(f6261,plain,
    ( spl13_263
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_263])]) ).

fof(f646,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55
    | ~ spl13_74 ),
    inference(resolution,[],[f619,f417]) ).

fof(f6259,plain,
    ( ~ spl13_262
    | ~ spl13_26
    | ~ spl13_249 ),
    inference(avatar_split_clause,[],[f6133,f6057,f206,f6256]) ).

fof(f6256,plain,
    ( spl13_262
  <=> empty(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_262])]) ).

fof(f206,plain,
    ( spl13_26
  <=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).

fof(f6133,plain,
    ( ~ empty(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))
    | ~ spl13_26
    | ~ spl13_249 ),
    inference(superposition,[],[f207,f6059]) ).

fof(f207,plain,
    ( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0)))
    | ~ spl13_26 ),
    inference(avatar_component_clause,[],[f206]) ).

fof(f6254,plain,
    ( spl13_261
    | ~ spl13_42
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f644,f618,f293,f6252]) ).

fof(f6252,plain,
    ( spl13_261
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_261])]) ).

fof(f644,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42
    | ~ spl13_74 ),
    inference(resolution,[],[f619,f294]) ).

fof(f6250,plain,
    ( spl13_260
    | ~ spl13_41
    | ~ spl13_74 ),
    inference(avatar_split_clause,[],[f643,f618,f289,f6248]) ).

fof(f6248,plain,
    ( spl13_260
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_260])]) ).

fof(f643,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X2,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41
    | ~ spl13_74 ),
    inference(resolution,[],[f619,f290]) ).

fof(f6246,plain,
    ( spl13_259
    | ~ spl13_58
    | ~ spl13_73 ),
    inference(avatar_split_clause,[],[f626,f614,f453,f6244]) ).

fof(f6244,plain,
    ( spl13_259
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_259])]) ).

fof(f614,plain,
    ( spl13_73
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).

fof(f626,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_58
    | ~ spl13_73 ),
    inference(resolution,[],[f615,f454]) ).

fof(f615,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3 )
    | ~ spl13_73 ),
    inference(avatar_component_clause,[],[f614]) ).

fof(f6242,plain,
    ( spl13_258
    | ~ spl13_55
    | ~ spl13_73 ),
    inference(avatar_split_clause,[],[f625,f614,f416,f6240]) ).

fof(f6240,plain,
    ( spl13_258
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_258])]) ).

fof(f625,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_55
    | ~ spl13_73 ),
    inference(resolution,[],[f615,f417]) ).

fof(f6238,plain,
    ( spl13_257
    | ~ spl13_42
    | ~ spl13_73 ),
    inference(avatar_split_clause,[],[f623,f614,f293,f6236]) ).

fof(f6236,plain,
    ( spl13_257
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_257])]) ).

fof(f623,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK3,sK4),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_42
    | ~ spl13_73 ),
    inference(resolution,[],[f615,f294]) ).

fof(f6234,plain,
    ( spl13_256
    | ~ spl13_41
    | ~ spl13_73 ),
    inference(avatar_split_clause,[],[f622,f614,f289,f6232]) ).

fof(f6232,plain,
    ( spl13_256
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_256])]) ).

fof(f622,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))),unordered_pair(sK10(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3)))),sK9(X3,cartesian_product2(sK1,sK2),unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),unordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_41
    | ~ spl13_73 ),
    inference(resolution,[],[f615,f290]) ).

fof(f6230,plain,
    ( spl13_255
    | ~ spl13_25
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f549,f523,f197,f6228]) ).

fof(f6228,plain,
    ( spl13_255
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | sP0(X2,X3,sK2)
        | sK6(X2,X3,sK2) = unordered_pair(singleton(sK7(X2,X3,sK2)),unordered_pair(sK8(X2,X3,sK2),sK7(X2,X3,sK2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_255])]) ).

fof(f197,plain,
    ( spl13_25
  <=> ! [X2,X0,X1] :
        ( sK6(X0,X1,X2) = unordered_pair(singleton(sK7(X0,X1,X2)),unordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2)))
        | sP0(X0,X1,X2)
        | in(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).

fof(f549,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | sP0(X2,X3,sK2)
        | sK6(X2,X3,sK2) = unordered_pair(singleton(sK7(X2,X3,sK2)),unordered_pair(sK8(X2,X3,sK2),sK7(X2,X3,sK2))) )
    | ~ spl13_25
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f198]) ).

fof(f198,plain,
    ( ! [X2,X0,X1] :
        ( in(sK6(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | sK6(X0,X1,X2) = unordered_pair(singleton(sK7(X0,X1,X2)),unordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2))) )
    | ~ spl13_25 ),
    inference(avatar_component_clause,[],[f197]) ).

fof(f6226,plain,
    ( spl13_254
    | ~ spl13_25
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f530,f519,f197,f6224]) ).

fof(f6224,plain,
    ( spl13_254
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | sP0(X2,X3,sK4)
        | sK6(X2,X3,sK4) = unordered_pair(singleton(sK7(X2,X3,sK4)),unordered_pair(sK8(X2,X3,sK4),sK7(X2,X3,sK4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_254])]) ).

fof(f530,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | sP0(X2,X3,sK4)
        | sK6(X2,X3,sK4) = unordered_pair(singleton(sK7(X2,X3,sK4)),unordered_pair(sK8(X2,X3,sK4),sK7(X2,X3,sK4))) )
    | ~ spl13_25
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f198]) ).

fof(f6076,plain,
    ( spl13_253
    | ~ spl13_21
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2513,f2155,f173,f6074]) ).

fof(f6074,plain,
    ( spl13_253
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK1,sK2))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_253])]) ).

fof(f2513,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK1,sK2))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_21
    | ~ spl13_128 ),
    inference(superposition,[],[f174,f2156]) ).

fof(f6072,plain,
    ( spl13_252
    | ~ spl13_14
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2512,f2155,f137,f6070]) ).

fof(f6070,plain,
    ( spl13_252
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK3,sK4))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_252])]) ).

fof(f2512,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)),cartesian_product2(sK3,sK4))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X1,X0),cartesian_product2(cartesian_product2(X2,X3),X4))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_14
    | ~ spl13_128 ),
    inference(superposition,[],[f138,f2156]) ).

fof(f6068,plain,
    ( spl13_251
    | ~ spl13_21
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2405,f2151,f173,f6066]) ).

fof(f6066,plain,
    ( spl13_251
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_251])]) ).

fof(f2405,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_21
    | ~ spl13_127 ),
    inference(superposition,[],[f174,f2152]) ).

fof(f6064,plain,
    ( spl13_250
    | ~ spl13_14
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2404,f2151,f137,f6062]) ).

fof(f6062,plain,
    ( spl13_250
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_250])]) ).

fof(f2404,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,cartesian_product2(X3,X4)))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_14
    | ~ spl13_127 ),
    inference(superposition,[],[f138,f2152]) ).

fof(f6060,plain,
    ( spl13_1
    | spl13_249
    | ~ spl13_175
    | spl13_231 ),
    inference(avatar_split_clause,[],[f5723,f5629,f3685,f6057,f70]) ).

fof(f3685,plain,
    ( spl13_175
  <=> ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_175])]) ).

fof(f5723,plain,
    ( sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),sK9(sK2,sK1,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))))
    | cartesian_product2(sK1,sK2) = cartesian_product2(sK3,sK4)
    | ~ spl13_175
    | spl13_231 ),
    inference(resolution,[],[f5631,f3686]) ).

fof(f3686,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4) )
    | ~ spl13_175 ),
    inference(avatar_component_clause,[],[f3685]) ).

fof(f5631,plain,
    ( ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | spl13_231 ),
    inference(avatar_component_clause,[],[f5629]) ).

fof(f6055,plain,
    ( spl13_248
    | ~ spl13_21
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2297,f2147,f173,f6053]) ).

fof(f6053,plain,
    ( spl13_248
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_248])]) ).

fof(f2297,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_21
    | ~ spl13_126 ),
    inference(superposition,[],[f174,f2148]) ).

fof(f6051,plain,
    ( spl13_247
    | ~ spl13_14
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2296,f2147,f137,f6049]) ).

fof(f6049,plain,
    ( spl13_247
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_247])]) ).

fof(f2296,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(cartesian_product2(X2,X3),X4),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(cartesian_product2(X2,X3),X4) )
    | ~ spl13_14
    | ~ spl13_126 ),
    inference(superposition,[],[f138,f2148]) ).

fof(f6047,plain,
    ( spl13_246
    | ~ spl13_21
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2189,f2139,f173,f6045]) ).

fof(f6045,plain,
    ( spl13_246
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_246])]) ).

fof(f2189,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_21
    | ~ spl13_124 ),
    inference(superposition,[],[f174,f2140]) ).

fof(f6043,plain,
    ( spl13_245
    | ~ spl13_14
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2188,f2139,f137,f6041]) ).

fof(f6041,plain,
    ( spl13_245
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_245])]) ).

fof(f2188,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0)))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X2,cartesian_product2(X3,X4)),cartesian_product2(X1,X0))))))
        | cartesian_product2(X1,X0) = cartesian_product2(X2,cartesian_product2(X3,X4)) )
    | ~ spl13_14
    | ~ spl13_124 ),
    inference(superposition,[],[f138,f2140]) ).

fof(f5757,plain,
    ( spl13_244
    | ~ spl13_58
    | ~ spl13_87 ),
    inference(avatar_split_clause,[],[f959,f926,f453,f5755]) ).

fof(f5755,plain,
    ( spl13_244
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_244])]) ).

fof(f926,plain,
    ( spl13_87
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))),unordered_pair(sK10(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))),sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))
        | ~ in(X2,X4)
        | ~ in(X3,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_87])]) ).

fof(f959,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_87 ),
    inference(resolution,[],[f927,f454]) ).

fof(f927,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ in(X3,X5)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))),unordered_pair(sK10(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))),sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))
        | ~ in(X2,X4)
        | ~ in(X0,X1) )
    | ~ spl13_87 ),
    inference(avatar_component_clause,[],[f926]) ).

fof(f5753,plain,
    ( spl13_243
    | ~ spl13_55
    | ~ spl13_87 ),
    inference(avatar_split_clause,[],[f958,f926,f416,f5751]) ).

fof(f5751,plain,
    ( spl13_243
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_243])]) ).

fof(f958,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_87 ),
    inference(resolution,[],[f927,f417]) ).

fof(f5749,plain,
    ( spl13_242
    | ~ spl13_42
    | ~ spl13_87 ),
    inference(avatar_split_clause,[],[f956,f926,f293,f5747]) ).

fof(f5747,plain,
    ( spl13_242
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_242])]) ).

fof(f956,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_87 ),
    inference(resolution,[],[f927,f294]) ).

fof(f5745,plain,
    ( spl13_241
    | ~ spl13_41
    | ~ spl13_87 ),
    inference(avatar_split_clause,[],[f955,f926,f289,f5743]) ).

fof(f5743,plain,
    ( spl13_241
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_241])]) ).

fof(f955,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X1)))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_87 ),
    inference(resolution,[],[f927,f290]) ).

fof(f5741,plain,
    ( spl13_240
    | ~ spl13_58
    | ~ spl13_85 ),
    inference(avatar_split_clause,[],[f938,f918,f453,f5739]) ).

fof(f5739,plain,
    ( spl13_240
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_240])]) ).

fof(f918,plain,
    ( spl13_85
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X2,X4)
        | ~ in(X3,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_85])]) ).

fof(f938,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_85 ),
    inference(resolution,[],[f919,f454]) ).

fof(f919,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ in(X3,X5)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X2,X4)
        | ~ in(X0,X1) )
    | ~ spl13_85 ),
    inference(avatar_component_clause,[],[f918]) ).

fof(f5737,plain,
    ( spl13_239
    | ~ spl13_55
    | ~ spl13_85 ),
    inference(avatar_split_clause,[],[f937,f918,f416,f5735]) ).

fof(f5735,plain,
    ( spl13_239
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_239])]) ).

fof(f937,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_85 ),
    inference(resolution,[],[f919,f417]) ).

fof(f5733,plain,
    ( spl13_238
    | ~ spl13_42
    | ~ spl13_85 ),
    inference(avatar_split_clause,[],[f935,f918,f293,f5731]) ).

fof(f5731,plain,
    ( spl13_238
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_238])]) ).

fof(f935,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),sK9(cartesian_product2(X4,cartesian_product2(sK3,sK4)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_85 ),
    inference(resolution,[],[f919,f294]) ).

fof(f5729,plain,
    ( spl13_237
    | ~ spl13_41
    | ~ spl13_85 ),
    inference(avatar_split_clause,[],[f934,f918,f289,f5727]) ).

fof(f5727,plain,
    ( spl13_237
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_237])]) ).

fof(f934,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))) = unordered_pair(singleton(sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))),unordered_pair(sK10(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),sK9(cartesian_product2(X4,cartesian_product2(sK1,sK2)),X5,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))))
        | ~ in(X1,X4)
        | ~ in(X0,X5)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_85 ),
    inference(resolution,[],[f919,f290]) ).

fof(f5652,plain,
    ( spl13_236
    | ~ spl13_10
    | ~ spl13_58
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1025,f930,f453,f113,f5650]) ).

fof(f5650,plain,
    ( spl13_236
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_236])]) ).

fof(f930,plain,
    ( spl13_88
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_88])]) ).

fof(f1025,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_58
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f1001,f114]) ).

fof(f1001,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_58
    | ~ spl13_88 ),
    inference(superposition,[],[f454,f931]) ).

fof(f931,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_88 ),
    inference(avatar_component_clause,[],[f930]) ).

fof(f5648,plain,
    ( spl13_235
    | ~ spl13_10
    | ~ spl13_55
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1023,f930,f416,f113,f5646]) ).

fof(f5646,plain,
    ( spl13_235
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_235])]) ).

fof(f1023,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_55
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f999,f114]) ).

fof(f999,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_55
    | ~ spl13_88 ),
    inference(superposition,[],[f417,f931]) ).

fof(f5644,plain,
    ( spl13_234
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1013,f930,f173,f113,f5642]) ).

fof(f5642,plain,
    ( spl13_234
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_234])]) ).

fof(f1013,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f1012,f114]) ).

fof(f1012,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_21
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f989,f114]) ).

fof(f989,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_21
    | ~ spl13_88 ),
    inference(superposition,[],[f174,f931]) ).

fof(f5640,plain,
    ( spl13_233
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1011,f930,f137,f113,f5638]) ).

fof(f5638,plain,
    ( spl13_233
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_233])]) ).

fof(f1011,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f1010,f114]) ).

fof(f1010,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_14
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f988,f114]) ).

fof(f988,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_14
    | ~ spl13_88 ),
    inference(superposition,[],[f138,f931]) ).

fof(f5636,plain,
    ( ~ spl13_231
    | spl13_1
    | spl13_232
    | ~ spl13_16
    | ~ spl13_184 ),
    inference(avatar_split_clause,[],[f4988,f3721,f145,f5633,f70,f5629]) ).

fof(f3721,plain,
    ( spl13_184
  <=> ! [X0,X1] :
        ( in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_184])]) ).

fof(f4988,plain,
    ( sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))))
    | cartesian_product2(sK1,sK2) = cartesian_product2(sK3,sK4)
    | ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | ~ spl13_16
    | ~ spl13_184 ),
    inference(duplicate_literal_removal,[],[f4966]) ).

fof(f4966,plain,
    ( sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)))))
    | cartesian_product2(sK1,sK2) = cartesian_product2(sK3,sK4)
    | cartesian_product2(sK1,sK2) = cartesian_product2(sK3,sK4)
    | ~ in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
    | ~ spl13_16
    | ~ spl13_184 ),
    inference(resolution,[],[f3722,f146]) ).

fof(f3722,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) )
    | ~ spl13_184 ),
    inference(avatar_component_clause,[],[f3721]) ).

fof(f5627,plain,
    ( spl13_230
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1845,f1753,f113,f101,f5625]) ).

fof(f5625,plain,
    ( spl13_230
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_230])]) ).

fof(f101,plain,
    ( spl13_7
  <=> ! [X4,X5] :
        ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK3,sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).

fof(f1845,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1844,f114]) ).

fof(f1844,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1797,f114]) ).

fof(f1797,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_7
    | ~ spl13_112 ),
    inference(superposition,[],[f102,f1754]) ).

fof(f102,plain,
    ( ! [X4,X5] :
        ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK3,sK4)) )
    | ~ spl13_7 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f5623,plain,
    ( spl13_229
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1843,f1753,f113,f97,f5621]) ).

fof(f5621,plain,
    ( spl13_229
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_229])]) ).

fof(f97,plain,
    ( spl13_6
  <=> ! [X4,X5] :
        ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).

fof(f1843,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1842,f114]) ).

fof(f1842,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1796,f114]) ).

fof(f1796,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))))),sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_6
    | ~ spl13_112 ),
    inference(superposition,[],[f98,f1754]) ).

fof(f98,plain,
    ( ! [X4,X5] :
        ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK1,sK2)) )
    | ~ spl13_6 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f5619,plain,
    ( spl13_228
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1821,f1753,f113,f101,f5617]) ).

fof(f5617,plain,
    ( spl13_228
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_228])]) ).

fof(f1821,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1820,f114]) ).

fof(f1820,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1767,f114]) ).

fof(f1767,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_7
    | ~ spl13_112 ),
    inference(superposition,[],[f102,f1754]) ).

fof(f5615,plain,
    ( spl13_227
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1819,f1753,f113,f97,f5613]) ).

fof(f5613,plain,
    ( spl13_227
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_227])]) ).

fof(f1819,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1818,f114]) ).

fof(f1818,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_112 ),
    inference(forward_demodulation,[],[f1766,f114]) ).

fof(f1766,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))))),sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_6
    | ~ spl13_112 ),
    inference(superposition,[],[f98,f1754]) ).

fof(f5607,plain,
    ( spl13_226
    | ~ spl13_8
    | ~ spl13_184 ),
    inference(avatar_split_clause,[],[f4967,f3721,f105,f5605]) ).

fof(f5605,plain,
    ( spl13_226
  <=> ! [X0,X1] :
        ( sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2)
        | ~ in(cartesian_product2(sK3,sK4),sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_226])]) ).

fof(f4967,plain,
    ( ! [X0,X1] :
        ( sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2)
        | ~ in(cartesian_product2(sK3,sK4),sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))) )
    | ~ spl13_8
    | ~ spl13_184 ),
    inference(resolution,[],[f3722,f106]) ).

fof(f5599,plain,
    ( spl13_225
    | ~ spl13_21
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2483,f2155,f173,f5597]) ).

fof(f5597,plain,
    ( spl13_225
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK3,sK4))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_225])]) ).

fof(f2483,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK3,sK4))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_21
    | ~ spl13_128 ),
    inference(superposition,[],[f174,f2156]) ).

fof(f5595,plain,
    ( spl13_224
    | ~ spl13_14
    | ~ spl13_128 ),
    inference(avatar_split_clause,[],[f2482,f2155,f137,f5593]) ).

fof(f5593,plain,
    ( spl13_224
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK1,sK2))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_224])]) ).

fof(f2482,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK1,sK2))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(cartesian_product2(X1,X0),X2)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_14
    | ~ spl13_128 ),
    inference(superposition,[],[f138,f2156]) ).

fof(f5591,plain,
    ( spl13_223
    | ~ spl13_21
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2375,f2151,f173,f5589]) ).

fof(f5589,plain,
    ( spl13_223
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK3,sK4))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_223])]) ).

fof(f2375,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK3,sK4))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_21
    | ~ spl13_127 ),
    inference(superposition,[],[f174,f2152]) ).

fof(f5587,plain,
    ( spl13_222
    | ~ spl13_14
    | ~ spl13_127 ),
    inference(avatar_split_clause,[],[f2374,f2151,f137,f5585]) ).

fof(f5585,plain,
    ( spl13_222
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK1,sK2))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_222])]) ).

fof(f2374,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK1,sK2))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0)))),sK9(X4,X3,sK5(cartesian_product2(X3,X4),cartesian_product2(X2,cartesian_product2(X1,X0))))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_14
    | ~ spl13_127 ),
    inference(superposition,[],[f138,f2152]) ).

fof(f5583,plain,
    ( spl13_221
    | ~ spl13_21
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2267,f2147,f173,f5581]) ).

fof(f5581,plain,
    ( spl13_221
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_221])]) ).

fof(f2267,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_21
    | ~ spl13_126 ),
    inference(superposition,[],[f174,f2148]) ).

fof(f5579,plain,
    ( spl13_220
    | ~ spl13_14
    | ~ spl13_126 ),
    inference(avatar_split_clause,[],[f2266,f2147,f137,f5577]) ).

fof(f5577,plain,
    ( spl13_220
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_220])]) ).

fof(f2266,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | in(sK9(X2,cartesian_product2(X1,X0),sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X1,X0),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(cartesian_product2(X1,X0),X2) = cartesian_product2(X3,X4) )
    | ~ spl13_14
    | ~ spl13_126 ),
    inference(superposition,[],[f138,f2148]) ).

fof(f5575,plain,
    ( spl13_219
    | ~ spl13_8
    | ~ spl13_175 ),
    inference(avatar_split_clause,[],[f4749,f3685,f105,f5573]) ).

fof(f5573,plain,
    ( spl13_219
  <=> ! [X0,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4)
        | ~ in(cartesian_product2(sK1,sK2),sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_219])]) ).

fof(f4749,plain,
    ( ! [X0,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4)
        | ~ in(cartesian_product2(sK1,sK2),sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))) )
    | ~ spl13_8
    | ~ spl13_175 ),
    inference(resolution,[],[f3686,f106]) ).

fof(f5571,plain,
    ( spl13_218
    | ~ spl13_21
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2159,f2139,f173,f5569]) ).

fof(f5569,plain,
    ( spl13_218
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_218])]) ).

fof(f2159,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_21
    | ~ spl13_124 ),
    inference(superposition,[],[f174,f2140]) ).

fof(f5567,plain,
    ( spl13_217
    | ~ spl13_14
    | ~ spl13_124 ),
    inference(avatar_split_clause,[],[f2158,f2139,f137,f5565]) ).

fof(f5565,plain,
    ( spl13_217
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_217])]) ).

fof(f2158,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK1,sK2))
        | in(sK10(cartesian_product2(X1,X0),X2,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X2,cartesian_product2(X1,X0)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X2,cartesian_product2(X1,X0)) = cartesian_product2(X3,X4) )
    | ~ spl13_14
    | ~ spl13_124 ),
    inference(superposition,[],[f138,f2140]) ).

fof(f5423,plain,
    ( spl13_216
    | ~ spl13_19
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f551,f523,f165,f5421]) ).

fof(f5421,plain,
    ( spl13_216
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | in(sK7(X2,X3,sK2),X3)
        | sP0(X2,X3,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_216])]) ).

fof(f165,plain,
    ( spl13_19
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | in(sK7(X0,X1,X2),X1)
        | in(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).

fof(f551,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | in(sK7(X2,X3,sK2),X3)
        | sP0(X2,X3,sK2) )
    | ~ spl13_19
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f166]) ).

fof(f166,plain,
    ( ! [X2,X0,X1] :
        ( in(sK7(X0,X1,X2),X1)
        | in(sK6(X0,X1,X2),X2)
        | sP0(X0,X1,X2) )
    | ~ spl13_19 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f5419,plain,
    ( spl13_215
    | ~ spl13_20
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f550,f523,f169,f5417]) ).

fof(f5417,plain,
    ( spl13_215
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | in(sK8(X2,X3,sK2),X2)
        | sP0(X2,X3,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_215])]) ).

fof(f169,plain,
    ( spl13_20
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | in(sK8(X0,X1,X2),X0)
        | in(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).

fof(f550,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK2))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | in(sK8(X2,X3,sK2),X2)
        | sP0(X2,X3,sK2) )
    | ~ spl13_20
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f170]) ).

fof(f170,plain,
    ( ! [X2,X0,X1] :
        ( in(sK8(X0,X1,X2),X0)
        | in(sK6(X0,X1,X2),X2)
        | sP0(X0,X1,X2) )
    | ~ spl13_20 ),
    inference(avatar_component_clause,[],[f169]) ).

fof(f5415,plain,
    ( spl13_214
    | ~ spl13_19
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f532,f519,f165,f5413]) ).

fof(f5413,plain,
    ( spl13_214
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | in(sK7(X2,X3,sK4),X3)
        | sP0(X2,X3,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_214])]) ).

fof(f532,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | in(sK7(X2,X3,sK4),X3)
        | sP0(X2,X3,sK4) )
    | ~ spl13_19
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f166]) ).

fof(f5411,plain,
    ( spl13_213
    | ~ spl13_20
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f531,f519,f169,f5409]) ).

fof(f5409,plain,
    ( spl13_213
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | in(sK8(X2,X3,sK4),X2)
        | sP0(X2,X3,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_213])]) ).

fof(f531,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK6(X2,X3,sK4))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | in(sK8(X2,X3,sK4),X2)
        | sP0(X2,X3,sK4) )
    | ~ spl13_20
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f170]) ).

fof(f5407,plain,
    ( spl13_212
    | ~ spl13_8
    | ~ spl13_172 ),
    inference(avatar_split_clause,[],[f4549,f3457,f105,f5405]) ).

fof(f5405,plain,
    ( spl13_212
  <=> ! [X0,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2)
        | ~ in(cartesian_product2(sK3,sK4),sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_212])]) ).

fof(f3457,plain,
    ( spl13_172
  <=> ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_172])]) ).

fof(f4549,plain,
    ( ! [X0,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2)
        | ~ in(cartesian_product2(sK3,sK4),sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))) )
    | ~ spl13_8
    | ~ spl13_172 ),
    inference(resolution,[],[f3458,f106]) ).

fof(f3458,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) )
    | ~ spl13_172 ),
    inference(avatar_component_clause,[],[f3457]) ).

fof(f5403,plain,
    ( spl13_211
    | ~ spl13_10
    | ~ spl13_57
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1024,f930,f449,f113,f5401]) ).

fof(f5401,plain,
    ( spl13_211
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_211])]) ).

fof(f1024,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_57
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f1000,f114]) ).

fof(f1000,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_57
    | ~ spl13_88 ),
    inference(superposition,[],[f450,f931]) ).

fof(f5399,plain,
    ( spl13_210
    | ~ spl13_10
    | ~ spl13_48
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1022,f930,f352,f113,f5397]) ).

fof(f5397,plain,
    ( spl13_210
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_210])]) ).

fof(f1022,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_48
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f998,f114]) ).

fof(f998,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))))
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_48
    | ~ spl13_88 ),
    inference(superposition,[],[f353,f931]) ).

fof(f5395,plain,
    ( spl13_209
    | ~ spl13_10
    | ~ spl13_42
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1019,f930,f293,f113,f5393]) ).

fof(f5393,plain,
    ( spl13_209
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_209])]) ).

fof(f1019,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_42
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f995,f114]) ).

fof(f995,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK2)
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_42
    | ~ spl13_88 ),
    inference(superposition,[],[f294,f931]) ).

fof(f5391,plain,
    ( spl13_208
    | ~ spl13_10
    | ~ spl13_41
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1018,f930,f289,f113,f5389]) ).

fof(f5389,plain,
    ( spl13_208
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_208])]) ).

fof(f1018,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_10
    | ~ spl13_41
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f994,f114]) ).

fof(f994,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK4)
        | ~ in(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_41
    | ~ spl13_88 ),
    inference(superposition,[],[f290,f931]) ).

fof(f5278,plain,
    ( spl13_207
    | ~ spl13_25
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f501,f479,f197,f5276]) ).

fof(f5276,plain,
    ( spl13_207
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))))
        | sP0(X1,X2,sK1)
        | sK6(X1,X2,sK1) = unordered_pair(singleton(sK7(X1,X2,sK1)),unordered_pair(sK8(X1,X2,sK1),sK7(X1,X2,sK1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_207])]) ).

fof(f501,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))))
        | sP0(X1,X2,sK1)
        | sK6(X1,X2,sK1) = unordered_pair(singleton(sK7(X1,X2,sK1)),unordered_pair(sK8(X1,X2,sK1),sK7(X1,X2,sK1))) )
    | ~ spl13_25
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f198]) ).

fof(f5274,plain,
    ( spl13_206
    | ~ spl13_25
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f486,f475,f197,f5272]) ).

fof(f5272,plain,
    ( spl13_206
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))))
        | sP0(X1,X2,sK3)
        | sK6(X1,X2,sK3) = unordered_pair(singleton(sK7(X1,X2,sK3)),unordered_pair(sK8(X1,X2,sK3),sK7(X1,X2,sK3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_206])]) ).

fof(f486,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))))
        | sP0(X1,X2,sK3)
        | sK6(X1,X2,sK3) = unordered_pair(singleton(sK7(X1,X2,sK3)),unordered_pair(sK8(X1,X2,sK3),sK7(X1,X2,sK3))) )
    | ~ spl13_25
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f198]) ).

fof(f4795,plain,
    ( spl13_205
    | ~ spl13_58
    | ~ spl13_84 ),
    inference(avatar_split_clause,[],[f901,f830,f453,f4793]) ).

fof(f4793,plain,
    ( spl13_205
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_205])]) ).

fof(f830,plain,
    ( spl13_84
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3)))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))))))
        | ~ in(X3,X2)
        | ~ in(X4,cartesian_product2(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_84])]) ).

fof(f901,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_84 ),
    inference(resolution,[],[f831,f454]) ).

fof(f831,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X4,cartesian_product2(X0,X1))
        | ~ in(X3,X2)
        | sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3)))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3)))))) )
    | ~ spl13_84 ),
    inference(avatar_component_clause,[],[f830]) ).

fof(f4791,plain,
    ( spl13_204
    | ~ spl13_55
    | ~ spl13_84 ),
    inference(avatar_split_clause,[],[f900,f830,f416,f4789]) ).

fof(f4789,plain,
    ( spl13_204
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_204])]) ).

fof(f900,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_84 ),
    inference(resolution,[],[f831,f417]) ).

fof(f4787,plain,
    ( spl13_203
    | ~ spl13_42
    | ~ spl13_84 ),
    inference(avatar_split_clause,[],[f898,f830,f293,f4785]) ).

fof(f4785,plain,
    ( spl13_203
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_203])]) ).

fof(f898,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_84 ),
    inference(resolution,[],[f831,f294]) ).

fof(f4783,plain,
    ( spl13_202
    | ~ spl13_41
    | ~ spl13_84 ),
    inference(avatar_split_clause,[],[f897,f830,f289,f4781]) ).

fof(f4781,plain,
    ( spl13_202
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_202])]) ).

fof(f897,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_84 ),
    inference(resolution,[],[f831,f290]) ).

fof(f4779,plain,
    ( spl13_201
    | ~ spl13_58
    | ~ spl13_83 ),
    inference(avatar_split_clause,[],[f880,f826,f453,f4777]) ).

fof(f4777,plain,
    ( spl13_201
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_201])]) ).

fof(f826,plain,
    ( spl13_83
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4)))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))))))
        | ~ in(X3,X2)
        | ~ in(X4,cartesian_product2(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_83])]) ).

fof(f880,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_83 ),
    inference(resolution,[],[f827,f454]) ).

fof(f827,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X4,cartesian_product2(X0,X1))
        | ~ in(X3,X2)
        | sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4)))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4)))))) )
    | ~ spl13_83 ),
    inference(avatar_component_clause,[],[f826]) ).

fof(f4775,plain,
    ( spl13_200
    | ~ spl13_55
    | ~ spl13_83 ),
    inference(avatar_split_clause,[],[f879,f826,f416,f4773]) ).

fof(f4773,plain,
    ( spl13_200
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_200])]) ).

fof(f879,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_83 ),
    inference(resolution,[],[f827,f417]) ).

fof(f4735,plain,
    ( spl13_199
    | ~ spl13_42
    | ~ spl13_83 ),
    inference(avatar_split_clause,[],[f877,f826,f293,f4733]) ).

fof(f4733,plain,
    ( spl13_199
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_199])]) ).

fof(f877,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))) = unordered_pair(singleton(sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),unordered_pair(sK10(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),sK9(sK4,sK3,sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_83 ),
    inference(resolution,[],[f827,f294]) ).

fof(f4731,plain,
    ( spl13_198
    | ~ spl13_41
    | ~ spl13_83 ),
    inference(avatar_split_clause,[],[f876,f826,f289,f4729]) ).

fof(f4729,plain,
    ( spl13_198
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_198])]) ).

fof(f876,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))) = unordered_pair(singleton(sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))),unordered_pair(sK10(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),sK9(sK2,sK1,sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_83 ),
    inference(resolution,[],[f827,f290]) ).

fof(f4727,plain,
    ( spl13_197
    | ~ spl13_28
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f559,f523,f216,f4725]) ).

fof(f4725,plain,
    ( spl13_197
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | ~ in(X3,cartesian_product2(X2,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_197])]) ).

fof(f216,plain,
    ( spl13_28
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | in(sK10(X2,X1,X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).

fof(f559,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK2,X2,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | ~ in(X3,cartesian_product2(X2,sK2)) )
    | ~ spl13_28
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f217]) ).

fof(f217,plain,
    ( ! [X2,X0,X1] :
        ( in(sK10(X2,X1,X0),X2)
        | ~ in(X0,cartesian_product2(X1,X2)) )
    | ~ spl13_28 ),
    inference(avatar_component_clause,[],[f216]) ).

fof(f4723,plain,
    ( spl13_196
    | ~ spl13_27
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f558,f523,f212,f4721]) ).

fof(f4721,plain,
    ( spl13_196
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | ~ in(X3,cartesian_product2(sK2,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_196])]) ).

fof(f212,plain,
    ( spl13_27
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | in(sK9(X2,X1,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).

fof(f558,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3)))))),sK9(cartesian_product2(sK3,sK4),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK2,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK1)
        | ~ in(X3,cartesian_product2(sK2,X2)) )
    | ~ spl13_27
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f213]) ).

fof(f213,plain,
    ( ! [X2,X0,X1] :
        ( in(sK9(X2,X1,X0),X1)
        | ~ in(X0,cartesian_product2(X1,X2)) )
    | ~ spl13_27 ),
    inference(avatar_component_clause,[],[f212]) ).

fof(f4719,plain,
    ( spl13_195
    | ~ spl13_28
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f540,f519,f216,f4717]) ).

fof(f4717,plain,
    ( spl13_195
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | ~ in(X3,cartesian_product2(X2,sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_195])]) ).

fof(f540,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK10(sK4,X2,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | ~ in(X3,cartesian_product2(X2,sK4)) )
    | ~ spl13_28
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f217]) ).

fof(f4715,plain,
    ( spl13_194
    | ~ spl13_27
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f539,f519,f212,f4713]) ).

fof(f4713,plain,
    ( spl13_194
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | ~ in(X3,cartesian_product2(sK4,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_194])]) ).

fof(f539,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3)))))),sK9(cartesian_product2(sK1,sK2),X4,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK9(X2,sK4,X3))))))))
        | ~ in(X0,X4)
        | ~ in(X1,sK3)
        | ~ in(X3,cartesian_product2(sK4,X2)) )
    | ~ spl13_27
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f213]) ).

fof(f4535,plain,
    ( spl13_193
    | ~ spl13_15
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f546,f523,f141,f4533]) ).

fof(f4533,plain,
    ( spl13_193
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2)))))),sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK1)
        | in(sK5(sK2,X2),X2)
        | sK2 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_193])]) ).

fof(f546,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2)))))),sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK2,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK1)
        | in(sK5(sK2,X2),X2)
        | sK2 = X2 )
    | ~ spl13_15
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f142]) ).

fof(f4531,plain,
    ( spl13_192
    | ~ spl13_15
    | ~ spl13_63 ),
    inference(avatar_split_clause,[],[f545,f523,f141,f4529]) ).

fof(f4529,plain,
    ( spl13_192
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2)))))),sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK1)
        | in(sK5(X2,sK2),X2)
        | sK2 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_192])]) ).

fof(f545,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2))))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2)))))),sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK2))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK1)
        | in(sK5(X2,sK2),X2)
        | sK2 = X2 )
    | ~ spl13_15
    | ~ spl13_63 ),
    inference(resolution,[],[f524,f142]) ).

fof(f4527,plain,
    ( spl13_191
    | ~ spl13_15
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f527,f519,f141,f4525]) ).

fof(f4525,plain,
    ( spl13_191
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2)))))),sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK3)
        | in(sK5(sK4,X2),X2)
        | sK4 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_191])]) ).

fof(f527,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2)))))),sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(sK4,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK3)
        | in(sK5(sK4,X2),X2)
        | sK4 = X2 )
    | ~ spl13_15
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f142]) ).

fof(f4523,plain,
    ( spl13_190
    | ~ spl13_15
    | ~ spl13_62 ),
    inference(avatar_split_clause,[],[f526,f519,f141,f4521]) ).

fof(f4521,plain,
    ( spl13_190
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4)))))),sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK3)
        | in(sK5(X2,sK4),X2)
        | sK4 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_190])]) ).

fof(f526,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4))))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4))))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4)))))),sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X1),unordered_pair(X1,sK5(X2,sK4))))))))
        | ~ in(X0,X3)
        | ~ in(X1,sK3)
        | in(sK5(X2,sK4),X2)
        | sK4 = X2 )
    | ~ spl13_15
    | ~ spl13_62 ),
    inference(resolution,[],[f520,f142]) ).

fof(f4515,plain,
    ( spl13_189
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1792,f1753,f453,f4513]) ).

fof(f4513,plain,
    ( spl13_189
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_189])]) ).

fof(f1792,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK1)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(superposition,[],[f454,f1754]) ).

fof(f4511,plain,
    ( spl13_188
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1791,f1753,f416,f4509]) ).

fof(f4509,plain,
    ( spl13_188
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_188])]) ).

fof(f1791,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK3)
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(superposition,[],[f417,f1754]) ).

fof(f4507,plain,
    ( spl13_187
    | ~ spl13_49
    | ~ spl13_152 ),
    inference(avatar_split_clause,[],[f3090,f3027,f378,f4505]) ).

fof(f4505,plain,
    ( spl13_187
  <=> ! [X0,X1] :
        ( in(sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_187])]) ).

fof(f3027,plain,
    ( spl13_152
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_152])]) ).

fof(f3090,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4) )
    | ~ spl13_49
    | ~ spl13_152 ),
    inference(duplicate_literal_removal,[],[f3081]) ).

fof(f3081,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4)
        | sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK3,sK4),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4) )
    | ~ spl13_49
    | ~ spl13_152 ),
    inference(resolution,[],[f3028,f379]) ).

fof(f3028,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_152 ),
    inference(avatar_component_clause,[],[f3027]) ).

fof(f4503,plain,
    ( spl13_186
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1762,f1753,f453,f4501]) ).

fof(f4501,plain,
    ( spl13_186
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_186])]) ).

fof(f1762,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK1)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_58
    | ~ spl13_112 ),
    inference(superposition,[],[f454,f1754]) ).

fof(f4499,plain,
    ( spl13_185
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1761,f1753,f416,f4497]) ).

fof(f4497,plain,
    ( spl13_185
  <=> ! [X0,X3,X2,X1] :
        ( in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_185])]) ).

fof(f1761,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK3)
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_55
    | ~ spl13_112 ),
    inference(superposition,[],[f417,f1754]) ).

fof(f3723,plain,
    ( spl13_184
    | ~ spl13_49
    | ~ spl13_151 ),
    inference(avatar_split_clause,[],[f3074,f3023,f378,f3721]) ).

fof(f3023,plain,
    ( spl13_151
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_151])]) ).

fof(f3074,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) )
    | ~ spl13_49
    | ~ spl13_151 ),
    inference(duplicate_literal_removal,[],[f3065]) ).

fof(f3065,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2)
        | sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1))),sK9(X1,X0,sK5(cartesian_product2(sK1,sK2),cartesian_product2(X0,X1)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) )
    | ~ spl13_49
    | ~ spl13_151 ),
    inference(resolution,[],[f3024,f379]) ).

fof(f3024,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_151 ),
    inference(avatar_component_clause,[],[f3023]) ).

fof(f3719,plain,
    ( spl13_183
    | ~ spl13_58
    | ~ spl13_96 ),
    inference(avatar_split_clause,[],[f1176,f1126,f453,f3717]) ).

fof(f3717,plain,
    ( spl13_183
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X1)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_183])]) ).

fof(f1126,plain,
    ( spl13_96
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,cartesian_product2(X2,X3))
        | in(sK9(X0,X1,X4),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_96])]) ).

fof(f1176,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X1)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_96 ),
    inference(resolution,[],[f1127,f454]) ).

fof(f1127,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X4,cartesian_product2(X2,X3))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | in(sK9(X0,X1,X4),X1) )
    | ~ spl13_96 ),
    inference(avatar_component_clause,[],[f1126]) ).

fof(f3715,plain,
    ( spl13_182
    | ~ spl13_55
    | ~ spl13_96 ),
    inference(avatar_split_clause,[],[f1175,f1126,f416,f3713]) ).

fof(f3713,plain,
    ( spl13_182
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X1)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_182])]) ).

fof(f1175,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X1)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_96 ),
    inference(resolution,[],[f1127,f417]) ).

fof(f3711,plain,
    ( spl13_181
    | ~ spl13_42
    | ~ spl13_96 ),
    inference(avatar_split_clause,[],[f1173,f1126,f293,f3709]) ).

fof(f3709,plain,
    ( spl13_181
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X1)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_181])]) ).

fof(f1173,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X1)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_96 ),
    inference(resolution,[],[f1127,f294]) ).

fof(f3707,plain,
    ( spl13_180
    | ~ spl13_41
    | ~ spl13_96 ),
    inference(avatar_split_clause,[],[f1172,f1126,f289,f3705]) ).

fof(f3705,plain,
    ( spl13_180
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X1)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_180])]) ).

fof(f1172,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X1)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_96 ),
    inference(resolution,[],[f1127,f290]) ).

fof(f3703,plain,
    ( spl13_179
    | ~ spl13_58
    | ~ spl13_95 ),
    inference(avatar_split_clause,[],[f1155,f1122,f453,f3701]) ).

fof(f3701,plain,
    ( spl13_179
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X0)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_179])]) ).

fof(f1122,plain,
    ( spl13_95
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,cartesian_product2(X2,X3))
        | in(sK10(X0,X1,X4),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_95])]) ).

fof(f1155,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X0)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_95 ),
    inference(resolution,[],[f1123,f454]) ).

fof(f1123,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X4,cartesian_product2(X2,X3))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | in(sK10(X0,X1,X4),X0) )
    | ~ spl13_95 ),
    inference(avatar_component_clause,[],[f1122]) ).

fof(f3699,plain,
    ( spl13_178
    | ~ spl13_55
    | ~ spl13_95 ),
    inference(avatar_split_clause,[],[f1154,f1122,f416,f3697]) ).

fof(f3697,plain,
    ( spl13_178
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X0)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_178])]) ).

fof(f1154,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X3,X2))),X0)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_95 ),
    inference(resolution,[],[f1123,f417]) ).

fof(f3695,plain,
    ( spl13_177
    | ~ spl13_42
    | ~ spl13_95 ),
    inference(avatar_split_clause,[],[f1152,f1122,f293,f3693]) ).

fof(f3693,plain,
    ( spl13_177
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X0)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_177])]) ).

fof(f1152,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))),unordered_pair(sK10(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4))),sK9(sK4,sK3,sK6(X0,X1,cartesian_product2(sK3,sK4)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X0)
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_95 ),
    inference(resolution,[],[f1123,f294]) ).

fof(f3691,plain,
    ( spl13_176
    | ~ spl13_41
    | ~ spl13_95 ),
    inference(avatar_split_clause,[],[f1151,f1122,f289,f3689]) ).

fof(f3689,plain,
    ( spl13_176
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X0)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_176])]) ).

fof(f1151,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))),unordered_pair(sK10(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2))),sK9(sK2,sK1,sK6(X0,X1,cartesian_product2(sK1,sK2)))))
        | in(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),X0)
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_95 ),
    inference(resolution,[],[f1123,f290]) ).

fof(f3687,plain,
    ( spl13_175
    | ~ spl13_50
    | ~ spl13_150 ),
    inference(avatar_split_clause,[],[f3061,f3019,f382,f3685]) ).

fof(f3019,plain,
    ( spl13_150
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_150])]) ).

fof(f3061,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4) )
    | ~ spl13_50
    | ~ spl13_150 ),
    inference(duplicate_literal_removal,[],[f3046]) ).

fof(f3046,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4)
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK3,sK4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK3,sK4) )
    | ~ spl13_50
    | ~ spl13_150 ),
    inference(resolution,[],[f3020,f383]) ).

fof(f3020,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_150 ),
    inference(avatar_component_clause,[],[f3019]) ).

fof(f3683,plain,
    ( spl13_174
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1008,f930,f113,f101,f3681]) ).

fof(f3681,plain,
    ( spl13_174
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_174])]) ).

fof(f1008,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f1007,f114]) ).

fof(f1007,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_7
    | ~ spl13_10
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f986,f114]) ).

fof(f986,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_7
    | ~ spl13_88 ),
    inference(superposition,[],[f102,f931]) ).

fof(f3679,plain,
    ( spl13_173
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f1006,f930,f113,f97,f3677]) ).

fof(f3677,plain,
    ( spl13_173
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_173])]) ).

fof(f1006,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f1005,f114]) ).

fof(f1005,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(sK6(X2,X3,cartesian_product2(X1,X0)),singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_6
    | ~ spl13_10
    | ~ spl13_88 ),
    inference(forward_demodulation,[],[f985,f114]) ).

fof(f985,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))))),sK6(X2,X3,cartesian_product2(X1,X0))),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_6
    | ~ spl13_88 ),
    inference(superposition,[],[f98,f931]) ).

fof(f3459,plain,
    ( spl13_172
    | ~ spl13_50
    | ~ spl13_149 ),
    inference(avatar_split_clause,[],[f3045,f3015,f382,f3457]) ).

fof(f3015,plain,
    ( spl13_149
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_149])]) ).

fof(f3045,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) )
    | ~ spl13_50
    | ~ spl13_149 ),
    inference(duplicate_literal_removal,[],[f3030]) ).

fof(f3030,plain,
    ( ! [X0,X1] :
        ( in(sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2)
        | sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(sK1,sK2)))))
        | cartesian_product2(X0,X1) = cartesian_product2(sK1,sK2) )
    | ~ spl13_50
    | ~ spl13_149 ),
    inference(resolution,[],[f3016,f383]) ).

fof(f3016,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_149 ),
    inference(avatar_component_clause,[],[f3015]) ).

fof(f3455,plain,
    ( spl13_171
    | ~ spl13_58
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f699,f670,f453,f3453]) ).

fof(f3453,plain,
    ( spl13_171
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_171])]) ).

fof(f670,plain,
    ( spl13_76
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))))))
        | ~ in(X4,cartesian_product2(X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_76])]) ).

fof(f699,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_58
    | ~ spl13_76 ),
    inference(resolution,[],[f671,f454]) ).

fof(f671,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X4,cartesian_product2(X3,X2))
        | unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))))))
        | ~ in(X0,X1) )
    | ~ spl13_76 ),
    inference(avatar_component_clause,[],[f670]) ).

fof(f3451,plain,
    ( spl13_170
    | ~ spl13_55
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f698,f670,f416,f3449]) ).

fof(f3449,plain,
    ( spl13_170
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_170])]) ).

fof(f698,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_55
    | ~ spl13_76 ),
    inference(resolution,[],[f671,f417]) ).

fof(f3447,plain,
    ( spl13_169
    | ~ spl13_42
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f696,f670,f293,f3445]) ).

fof(f3445,plain,
    ( spl13_169
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_169])]) ).

fof(f696,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK4,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_42
    | ~ spl13_76 ),
    inference(resolution,[],[f671,f294]) ).

fof(f3443,plain,
    ( spl13_168
    | ~ spl13_41
    | ~ spl13_76 ),
    inference(avatar_split_clause,[],[f695,f670,f289,f3441]) ).

fof(f3441,plain,
    ( spl13_168
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_168])]) ).

fof(f695,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK2,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_41
    | ~ spl13_76 ),
    inference(resolution,[],[f671,f290]) ).

fof(f3439,plain,
    ( spl13_167
    | ~ spl13_58
    | ~ spl13_75 ),
    inference(avatar_split_clause,[],[f678,f664,f453,f3437]) ).

fof(f3437,plain,
    ( spl13_167
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_167])]) ).

fof(f664,plain,
    ( spl13_75
  <=> ! [X2,X4,X0,X3,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))))))
        | ~ in(X4,cartesian_product2(X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).

fof(f678,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_58
    | ~ spl13_75 ),
    inference(resolution,[],[f665,f454]) ).

fof(f665,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X4,cartesian_product2(X3,X2))
        | unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))))))
        | ~ in(X0,X1) )
    | ~ spl13_75 ),
    inference(avatar_component_clause,[],[f664]) ).

fof(f3435,plain,
    ( spl13_166
    | ~ spl13_55
    | ~ spl13_75 ),
    inference(avatar_split_clause,[],[f677,f664,f416,f3433]) ).

fof(f3433,plain,
    ( spl13_166
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_166])]) ).

fof(f677,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))) = unordered_pair(singleton(sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))),unordered_pair(sK10(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1)))))),sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X2,X1))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_55
    | ~ spl13_75 ),
    inference(resolution,[],[f665,f417]) ).

fof(f3431,plain,
    ( spl13_165
    | ~ spl13_42
    | ~ spl13_75 ),
    inference(avatar_split_clause,[],[f675,f664,f293,f3429]) ).

fof(f3429,plain,
    ( spl13_165
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_165])]) ).

fof(f675,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK3,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK2)
        | ~ in(X1,sK1) )
    | ~ spl13_42
    | ~ spl13_75 ),
    inference(resolution,[],[f665,f294]) ).

fof(f3427,plain,
    ( spl13_164
    | ~ spl13_41
    | ~ spl13_75 ),
    inference(avatar_split_clause,[],[f674,f664,f289,f3425]) ).

fof(f3425,plain,
    ( spl13_164
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_164])]) ).

fof(f674,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))) = unordered_pair(singleton(sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))),unordered_pair(sK10(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2)))))),sK9(sK1,X3,unordered_pair(singleton(X0),unordered_pair(X0,sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X2))))))))
        | ~ in(X0,X3)
        | ~ in(X2,sK4)
        | ~ in(X1,sK3) )
    | ~ spl13_41
    | ~ spl13_75 ),
    inference(resolution,[],[f665,f290]) ).

fof(f3315,plain,
    ( spl13_163
    | ~ spl13_19
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f503,f479,f165,f3313]) ).

fof(f3313,plain,
    ( spl13_163
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))))
        | in(sK7(X1,X2,sK1),X2)
        | sP0(X1,X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_163])]) ).

fof(f503,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))))
        | in(sK7(X1,X2,sK1),X2)
        | sP0(X1,X2,sK1) )
    | ~ spl13_19
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f166]) ).

fof(f3311,plain,
    ( spl13_162
    | ~ spl13_20
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f502,f479,f169,f3309]) ).

fof(f3309,plain,
    ( spl13_162
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))))
        | in(sK8(X1,X2,sK1),X1)
        | sP0(X1,X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_162])]) ).

fof(f502,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK6(X1,X2,sK1)),unordered_pair(sK6(X1,X2,sK1),X0)))))
        | in(sK8(X1,X2,sK1),X1)
        | sP0(X1,X2,sK1) )
    | ~ spl13_20
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f170]) ).

fof(f3307,plain,
    ( spl13_161
    | ~ spl13_19
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f488,f475,f165,f3305]) ).

fof(f3305,plain,
    ( spl13_161
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))))
        | in(sK7(X1,X2,sK3),X2)
        | sP0(X1,X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_161])]) ).

fof(f488,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))))
        | in(sK7(X1,X2,sK3),X2)
        | sP0(X1,X2,sK3) )
    | ~ spl13_19
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f166]) ).

fof(f3303,plain,
    ( spl13_160
    | ~ spl13_20
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f487,f475,f169,f3301]) ).

fof(f3301,plain,
    ( spl13_160
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))))
        | in(sK8(X1,X2,sK3),X1)
        | sP0(X1,X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_160])]) ).

fof(f487,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK6(X1,X2,sK3)),unordered_pair(sK6(X1,X2,sK3),X0)))))
        | in(sK8(X1,X2,sK3),X1)
        | sP0(X1,X2,sK3) )
    | ~ spl13_20
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f170]) ).

fof(f3191,plain,
    ( spl13_159
    | ~ spl13_8
    | ~ spl13_142 ),
    inference(avatar_split_clause,[],[f2872,f2778,f105,f3189]) ).

fof(f3189,plain,
    ( spl13_159
  <=> ! [X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | cartesian_product2(sK3,sK4) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK3,sK4))
        | ~ in(cartesian_product2(sK1,sK2),sK6(X0,X1,cartesian_product2(sK3,sK4))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_159])]) ).

fof(f2778,plain,
    ( spl13_142
  <=> ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | cartesian_product2(sK3,sK4) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK3,sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_142])]) ).

fof(f2872,plain,
    ( ! [X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | cartesian_product2(sK3,sK4) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK3,sK4))
        | ~ in(cartesian_product2(sK1,sK2),sK6(X0,X1,cartesian_product2(sK3,sK4))) )
    | ~ spl13_8
    | ~ spl13_142 ),
    inference(resolution,[],[f2779,f106]) ).

fof(f2779,plain,
    ( ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | cartesian_product2(sK3,sK4) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK3,sK4)) )
    | ~ spl13_142 ),
    inference(avatar_component_clause,[],[f2778]) ).

fof(f3117,plain,
    ( spl13_158
    | ~ spl13_58
    | ~ spl13_65 ),
    inference(avatar_split_clause,[],[f569,f561,f453,f3115]) ).

fof(f3115,plain,
    ( spl13_158
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))),sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_158])]) ).

fof(f561,plain,
    ( spl13_65
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | ~ in(X2,X3)
        | unordered_pair(singleton(X0),unordered_pair(X2,X0)) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).

fof(f569,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))),sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_58
    | ~ spl13_65 ),
    inference(resolution,[],[f562,f454]) ).

fof(f562,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X2,X3)
        | ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X2,X0)) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0))))) )
    | ~ spl13_65 ),
    inference(avatar_component_clause,[],[f561]) ).

fof(f3113,plain,
    ( spl13_157
    | ~ spl13_55
    | ~ spl13_65 ),
    inference(avatar_split_clause,[],[f568,f561,f416,f3111]) ).

fof(f3111,plain,
    ( spl13_157
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))),sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_157])]) ).

fof(f568,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0))),sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X3,X2)),X0)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_55
    | ~ spl13_65 ),
    inference(resolution,[],[f562,f417]) ).

fof(f3109,plain,
    ( spl13_156
    | ~ spl13_42
    | ~ spl13_65 ),
    inference(avatar_split_clause,[],[f566,f561,f293,f3107]) ).

fof(f3107,plain,
    ( spl13_156
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))),sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_156])]) ).

fof(f566,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))),sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_65 ),
    inference(resolution,[],[f562,f294]) ).

fof(f3105,plain,
    ( spl13_155
    | ~ spl13_41
    | ~ spl13_65 ),
    inference(avatar_split_clause,[],[f565,f561,f289,f3103]) ).

fof(f3103,plain,
    ( spl13_155
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))),sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_155])]) ).

fof(f565,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0))),sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_65 ),
    inference(resolution,[],[f562,f290]) ).

fof(f3101,plain,
    ( spl13_154
    | ~ spl13_45
    | ~ spl13_58 ),
    inference(avatar_split_clause,[],[f470,f453,f327,f3099]) ).

fof(f3099,plain,
    ( spl13_154
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | ~ in(X2,X3)
        | unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))),sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_154])]) ).

fof(f327,plain,
    ( spl13_45
  <=> ! [X0,X3,X2,X1] :
        ( unordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))
        | ~ in(X2,X1)
        | ~ in(X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).

fof(f470,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | ~ in(X2,X3)
        | unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))),sK9(cartesian_product2(sK3,sK4),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))))) )
    | ~ spl13_45
    | ~ spl13_58 ),
    inference(resolution,[],[f454,f328]) ).

fof(f328,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X3,X0)
        | ~ in(X2,X1)
        | unordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))))) )
    | ~ spl13_45 ),
    inference(avatar_component_clause,[],[f327]) ).

fof(f3097,plain,
    ( spl13_153
    | ~ spl13_45
    | ~ spl13_55 ),
    inference(avatar_split_clause,[],[f461,f416,f327,f3095]) ).

fof(f3095,plain,
    ( spl13_153
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | ~ in(X2,X3)
        | unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))),sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_153])]) ).

fof(f461,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | ~ in(X2,X3)
        | unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1)))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))),sK9(cartesian_product2(sK1,sK2),X3,unordered_pair(singleton(X2),unordered_pair(X2,unordered_pair(singleton(X1),unordered_pair(X0,X1))))))) )
    | ~ spl13_45
    | ~ spl13_55 ),
    inference(resolution,[],[f417,f328]) ).

fof(f3029,plain,
    ( spl13_152
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1787,f1753,f173,f3027]) ).

fof(f1787,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(superposition,[],[f174,f1754]) ).

fof(f3025,plain,
    ( spl13_151
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1786,f1753,f137,f3023]) ).

fof(f1786,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X1,X0),cartesian_product2(X2,X3)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(superposition,[],[f138,f1754]) ).

fof(f3021,plain,
    ( spl13_150
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1757,f1753,f173,f3019]) ).

fof(f1757,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_21
    | ~ spl13_112 ),
    inference(superposition,[],[f174,f1754]) ).

fof(f3017,plain,
    ( spl13_149
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(avatar_split_clause,[],[f1756,f1753,f137,f3015]) ).

fof(f1756,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0))),sK9(X3,X2,sK5(cartesian_product2(X2,X3),cartesian_product2(X1,X0)))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_14
    | ~ spl13_112 ),
    inference(superposition,[],[f138,f1754]) ).

fof(f2860,plain,
    ( spl13_148
    | ~ spl13_28
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f511,f479,f216,f2858]) ).

fof(f2858,plain,
    ( spl13_148
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0)))))
        | ~ in(X2,cartesian_product2(X1,sK1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_148])]) ).

fof(f511,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK10(sK1,X1,X2)),unordered_pair(sK10(sK1,X1,X2),X0)))))
        | ~ in(X2,cartesian_product2(X1,sK1)) )
    | ~ spl13_28
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f217]) ).

fof(f2856,plain,
    ( spl13_147
    | ~ spl13_27
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f510,f479,f212,f2854]) ).

fof(f2854,plain,
    ( spl13_147
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0)))))
        | ~ in(X2,cartesian_product2(sK1,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_147])]) ).

fof(f510,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK9(X1,sK1,X2)),unordered_pair(sK9(X1,sK1,X2),X0)))))
        | ~ in(X2,cartesian_product2(sK1,X1)) )
    | ~ spl13_27
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f213]) ).

fof(f2852,plain,
    ( spl13_146
    | ~ spl13_28
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f496,f475,f216,f2850]) ).

fof(f2850,plain,
    ( spl13_146
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0)))))
        | ~ in(X2,cartesian_product2(X1,sK3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_146])]) ).

fof(f496,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK10(sK3,X1,X2)),unordered_pair(sK10(sK3,X1,X2),X0)))))
        | ~ in(X2,cartesian_product2(X1,sK3)) )
    | ~ spl13_28
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f217]) ).

fof(f2848,plain,
    ( spl13_145
    | ~ spl13_27
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f495,f475,f212,f2846]) ).

fof(f2846,plain,
    ( spl13_145
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0)))))
        | ~ in(X2,cartesian_product2(sK3,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_145])]) ).

fof(f495,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK9(X1,sK3,X2)),unordered_pair(sK9(X1,sK3,X2),X0)))))
        | ~ in(X2,cartesian_product2(sK3,X1)) )
    | ~ spl13_27
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f213]) ).

fof(f2842,plain,
    ( spl13_144
    | ~ spl13_58
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f981,f930,f453,f2840]) ).

fof(f2840,plain,
    ( spl13_144
  <=> ! [X0,X3,X2,X1] :
        ( in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_144])]) ).

fof(f981,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK2)
        | ~ in(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK1)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_58
    | ~ spl13_88 ),
    inference(superposition,[],[f454,f931]) ).

fof(f2838,plain,
    ( spl13_143
    | ~ spl13_55
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f980,f930,f416,f2836]) ).

fof(f2836,plain,
    ( spl13_143
  <=> ! [X0,X3,X2,X1] :
        ( in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_143])]) ).

fof(f980,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK4)
        | ~ in(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK3)
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_55
    | ~ spl13_88 ),
    inference(superposition,[],[f417,f931]) ).

fof(f2780,plain,
    ( spl13_142
    | ~ spl13_25
    | ~ spl13_114 ),
    inference(avatar_split_clause,[],[f2705,f1871,f197,f2778]) ).

fof(f1871,plain,
    ( spl13_114
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_114])]) ).

fof(f2705,plain,
    ( ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | cartesian_product2(sK3,sK4) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK3,sK4)) )
    | ~ spl13_25
    | ~ spl13_114 ),
    inference(duplicate_literal_removal,[],[f2696]) ).

fof(f2696,plain,
    ( ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK3,sK4)),cartesian_product2(sK1,sK2))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4))))
        | cartesian_product2(sK3,sK4) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK3,sK4))
        | sK6(X0,X1,cartesian_product2(sK3,sK4)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK3,sK4))),unordered_pair(sK8(X0,X1,cartesian_product2(sK3,sK4)),sK7(X0,X1,cartesian_product2(sK3,sK4)))) )
    | ~ spl13_25
    | ~ spl13_114 ),
    inference(resolution,[],[f1872,f198]) ).

fof(f1872,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_114 ),
    inference(avatar_component_clause,[],[f1871]) ).

fof(f2722,plain,
    ( spl13_141
    | ~ spl13_15
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f498,f479,f141,f2720]) ).

fof(f2720,plain,
    ( spl13_141
  <=> ! [X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0)))))
        | in(sK5(sK1,X1),X1)
        | sK1 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_141])]) ).

fof(f498,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(sK1,X1)),unordered_pair(sK5(sK1,X1),X0)))))
        | in(sK5(sK1,X1),X1)
        | sK1 = X1 )
    | ~ spl13_15
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f142]) ).

fof(f2718,plain,
    ( spl13_140
    | ~ spl13_15
    | ~ spl13_60 ),
    inference(avatar_split_clause,[],[f497,f479,f141,f2716]) ).

fof(f2716,plain,
    ( spl13_140
  <=> ! [X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0)))))
        | in(sK5(X1,sK1),X1)
        | sK1 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_140])]) ).

fof(f497,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK2)
        | unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0))),sK9(sK4,sK3,unordered_pair(singleton(sK5(X1,sK1)),unordered_pair(sK5(X1,sK1),X0)))))
        | in(sK5(X1,sK1),X1)
        | sK1 = X1 )
    | ~ spl13_15
    | ~ spl13_60 ),
    inference(resolution,[],[f480,f142]) ).

fof(f2714,plain,
    ( spl13_139
    | ~ spl13_15
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f483,f475,f141,f2712]) ).

fof(f2712,plain,
    ( spl13_139
  <=> ! [X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0)))))
        | in(sK5(sK3,X1),X1)
        | sK3 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_139])]) ).

fof(f483,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(sK3,X1)),unordered_pair(sK5(sK3,X1),X0)))))
        | in(sK5(sK3,X1),X1)
        | sK3 = X1 )
    | ~ spl13_15
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f142]) ).

fof(f2710,plain,
    ( spl13_138
    | ~ spl13_15
    | ~ spl13_59 ),
    inference(avatar_split_clause,[],[f482,f475,f141,f2708]) ).

fof(f2708,plain,
    ( spl13_138
  <=> ! [X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0)))))
        | in(sK5(X1,sK3),X1)
        | sK3 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_138])]) ).

fof(f482,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK4)
        | unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0))),sK9(sK2,sK1,unordered_pair(singleton(sK5(X1,sK3)),unordered_pair(sK5(X1,sK3),X0)))))
        | in(sK5(X1,sK3),X1)
        | sK3 = X1 )
    | ~ spl13_15
    | ~ spl13_59 ),
    inference(resolution,[],[f476,f142]) ).

fof(f2679,plain,
    ( spl13_137
    | ~ spl13_8
    | ~ spl13_125 ),
    inference(avatar_split_clause,[],[f2612,f2143,f105,f2677]) ).

fof(f2677,plain,
    ( spl13_137
  <=> ! [X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | cartesian_product2(sK1,sK2) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK1,sK2))
        | ~ in(cartesian_product2(sK3,sK4),sK6(X0,X1,cartesian_product2(sK1,sK2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_137])]) ).

fof(f2143,plain,
    ( spl13_125
  <=> ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | cartesian_product2(sK1,sK2) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_125])]) ).

fof(f2612,plain,
    ( ! [X0,X1] :
        ( sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | cartesian_product2(sK1,sK2) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK1,sK2))
        | ~ in(cartesian_product2(sK3,sK4),sK6(X0,X1,cartesian_product2(sK1,sK2))) )
    | ~ spl13_8
    | ~ spl13_125 ),
    inference(resolution,[],[f2144,f106]) ).

fof(f2144,plain,
    ( ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | cartesian_product2(sK1,sK2) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK1,sK2)) )
    | ~ spl13_125 ),
    inference(avatar_component_clause,[],[f2143]) ).

fof(f2650,plain,
    ( spl13_136
    | ~ spl13_46
    | ~ spl13_54 ),
    inference(avatar_split_clause,[],[f438,f412,f344,f2648]) ).

fof(f2648,plain,
    ( spl13_136
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))))
        | sP0(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))
        | sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))) = unordered_pair(singleton(sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))))),unordered_pair(sK10(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))),sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_136])]) ).

fof(f344,plain,
    ( spl13_46
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X2,cartesian_product2(X1,X0),X3) = unordered_pair(singleton(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3))),unordered_pair(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3)),sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3))))
        | ~ in(X3,cartesian_product2(cartesian_product2(X1,X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).

fof(f438,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))))
        | sP0(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))
        | sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))) = unordered_pair(singleton(sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5))))),unordered_pair(sK10(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))),sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(cartesian_product2(X0,X1),X2,cartesian_product2(cartesian_product2(X3,X4),X5)))))) )
    | ~ spl13_46
    | ~ spl13_54 ),
    inference(resolution,[],[f413,f345]) ).

fof(f345,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X3,cartesian_product2(cartesian_product2(X1,X0),X2))
        | sK9(X2,cartesian_product2(X1,X0),X3) = unordered_pair(singleton(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3))),unordered_pair(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3)),sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3)))) )
    | ~ spl13_46 ),
    inference(avatar_component_clause,[],[f344]) ).

fof(f2646,plain,
    ( spl13_135
    | ~ spl13_47
    | ~ spl13_54 ),
    inference(avatar_split_clause,[],[f437,f412,f348,f2644]) ).

fof(f2644,plain,
    ( spl13_135
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))))
        | sP0(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))
        | sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))) = unordered_pair(singleton(sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))))),unordered_pair(sK10(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))),sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_135])]) ).

fof(f348,plain,
    ( spl13_47
  <=> ! [X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X1,X0),X2,X3) = unordered_pair(singleton(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3))),unordered_pair(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3)),sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3))))
        | ~ in(X3,cartesian_product2(X2,cartesian_product2(X1,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).

fof(f437,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))))
        | sP0(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))
        | sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))) = unordered_pair(singleton(sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5)))))),unordered_pair(sK10(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))),sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,cartesian_product2(X4,X5))))))) )
    | ~ spl13_47
    | ~ spl13_54 ),
    inference(resolution,[],[f413,f349]) ).

fof(f349,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X3,cartesian_product2(X2,cartesian_product2(X1,X0)))
        | sK10(cartesian_product2(X1,X0),X2,X3) = unordered_pair(singleton(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3))),unordered_pair(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3)),sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3)))) )
    | ~ spl13_47 ),
    inference(avatar_component_clause,[],[f348]) ).

fof(f2642,plain,
    ( spl13_134
    | ~ spl13_46
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f433,f408,f344,f2640]) ).

fof(f2640,plain,
    ( spl13_134
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))))
        | sP0(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))
        | sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))) = unordered_pair(singleton(sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))))),unordered_pair(sK10(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))),sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_134])]) ).

fof(f433,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))))
        | sP0(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))
        | sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))) = unordered_pair(singleton(sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5))))),unordered_pair(sK10(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))),sK9(X4,X3,sK9(X5,cartesian_product2(X3,X4),sK6(X0,cartesian_product2(X1,X2),cartesian_product2(cartesian_product2(X3,X4),X5)))))) )
    | ~ spl13_46
    | ~ spl13_53 ),
    inference(resolution,[],[f409,f345]) ).

fof(f2638,plain,
    ( spl13_133
    | ~ spl13_47
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f432,f408,f348,f2636]) ).

fof(f2636,plain,
    ( spl13_133
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))))
        | sP0(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))
        | sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))) = unordered_pair(singleton(sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))))),unordered_pair(sK10(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))),sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_133])]) ).

fof(f432,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))))
        | sP0(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))
        | sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))) = unordered_pair(singleton(sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5)))))),unordered_pair(sK10(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))),sK9(X5,X4,sK10(cartesian_product2(X4,X5),X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,cartesian_product2(X4,X5))))))) )
    | ~ spl13_47
    | ~ spl13_53 ),
    inference(resolution,[],[f409,f349]) ).

fof(f2634,plain,
    ( spl13_132
    | ~ spl13_46
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f428,f404,f344,f2632]) ).

fof(f2632,plain,
    ( spl13_132
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))),sK9(X5,X4,sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))))
        | sP0(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))
        | sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X2,X1,sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))))),unordered_pair(sK10(X2,X1,sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))),sK9(X2,X1,sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_132])]) ).

fof(f428,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))),sK9(X5,X4,sK6(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))))
        | sP0(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))
        | sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X2,X1,sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5))))),unordered_pair(sK10(X2,X1,sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))),sK9(X2,X1,sK9(X3,cartesian_product2(X1,X2),sK7(X0,cartesian_product2(cartesian_product2(X1,X2),X3),cartesian_product2(X4,X5)))))) )
    | ~ spl13_46
    | ~ spl13_52 ),
    inference(resolution,[],[f405,f345]) ).

fof(f2601,plain,
    ( spl13_131
    | ~ spl13_47
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f427,f404,f348,f2599]) ).

fof(f2599,plain,
    ( spl13_131
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))),sK9(X5,X4,sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))))
        | sP0(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))
        | sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X3,X2,sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))))),unordered_pair(sK10(X3,X2,sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))),sK9(X3,X2,sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_131])]) ).

fof(f427,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))),sK9(X5,X4,sK6(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))))
        | sP0(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))
        | sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X3,X2,sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5))))),unordered_pair(sK10(X3,X2,sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))),sK9(X3,X2,sK10(cartesian_product2(X2,X3),X1,sK7(X0,cartesian_product2(X1,cartesian_product2(X2,X3)),cartesian_product2(X4,X5)))))) )
    | ~ spl13_47
    | ~ spl13_52 ),
    inference(resolution,[],[f405,f349]) ).

fof(f2597,plain,
    ( spl13_130
    | ~ spl13_46
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f423,f400,f344,f2595]) ).

fof(f2595,plain,
    ( spl13_130
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))),sK9(X5,X4,sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))))
        | sP0(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))
        | sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))),sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_130])]) ).

fof(f423,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))),sK9(X5,X4,sK6(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))))
        | sP0(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))
        | sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))),sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK8(cartesian_product2(cartesian_product2(X0,X1),X2),X3,cartesian_product2(X4,X5)))))) )
    | ~ spl13_46
    | ~ spl13_51 ),
    inference(resolution,[],[f401,f345]) ).

fof(f2593,plain,
    ( spl13_129
    | ~ spl13_47
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f422,f400,f348,f2591]) ).

fof(f2591,plain,
    ( spl13_129
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))),sK9(X5,X4,sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))))
        | sP0(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))
        | sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))),sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_129])]) ).

fof(f422,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)) = unordered_pair(singleton(sK9(X5,X4,sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))),unordered_pair(sK10(X5,X4,sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))),sK9(X5,X4,sK6(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))))
        | sP0(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))
        | sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))) = unordered_pair(singleton(sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5))))),unordered_pair(sK10(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))),sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK8(cartesian_product2(X0,cartesian_product2(X1,X2)),X3,cartesian_product2(X4,X5)))))) )
    | ~ spl13_47
    | ~ spl13_51 ),
    inference(resolution,[],[f401,f349]) ).

fof(f2157,plain,
    ( spl13_128
    | ~ spl13_46
    | ~ spl13_50 ),
    inference(avatar_split_clause,[],[f397,f382,f344,f2155]) ).

fof(f397,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))))
        | cartesian_product2(X0,X1) = cartesian_product2(cartesian_product2(X2,X3),X4)
        | sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))) = unordered_pair(singleton(sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4))))),unordered_pair(sK10(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))),sK9(X3,X2,sK9(X4,cartesian_product2(X2,X3),sK5(cartesian_product2(X0,X1),cartesian_product2(cartesian_product2(X2,X3),X4)))))) )
    | ~ spl13_46
    | ~ spl13_50 ),
    inference(resolution,[],[f383,f345]) ).

fof(f2153,plain,
    ( spl13_127
    | ~ spl13_47
    | ~ spl13_50 ),
    inference(avatar_split_clause,[],[f396,f382,f348,f2151]) ).

fof(f396,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))))
        | cartesian_product2(X0,X1) = cartesian_product2(X2,cartesian_product2(X3,X4))
        | sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))) = unordered_pair(singleton(sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4)))))),unordered_pair(sK10(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))),sK9(X4,X3,sK10(cartesian_product2(X3,X4),X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,cartesian_product2(X3,X4))))))) )
    | ~ spl13_47
    | ~ spl13_50 ),
    inference(resolution,[],[f383,f349]) ).

fof(f2149,plain,
    ( spl13_126
    | ~ spl13_46
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f390,f378,f344,f2147]) ).

fof(f390,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))))
        | cartesian_product2(X3,X4) = cartesian_product2(cartesian_product2(X0,X1),X2)
        | sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4))))),unordered_pair(sK10(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))),sK9(X1,X0,sK9(X2,cartesian_product2(X0,X1),sK5(cartesian_product2(cartesian_product2(X0,X1),X2),cartesian_product2(X3,X4)))))) )
    | ~ spl13_46
    | ~ spl13_49 ),
    inference(resolution,[],[f379,f345]) ).

fof(f2145,plain,
    ( spl13_125
    | ~ spl13_25
    | ~ spl13_110 ),
    inference(avatar_split_clause,[],[f1983,f1542,f197,f2143]) ).

fof(f1542,plain,
    ( spl13_110
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_110])]) ).

fof(f1983,plain,
    ( ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | cartesian_product2(sK1,sK2) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK1,sK2)) )
    | ~ spl13_25
    | ~ spl13_110 ),
    inference(duplicate_literal_removal,[],[f1974]) ).

fof(f1974,plain,
    ( ! [X0,X1] :
        ( in(sK6(X0,X1,cartesian_product2(sK1,sK2)),cartesian_product2(sK3,sK4))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2))))
        | cartesian_product2(sK1,sK2) = cartesian_product2(X1,X0)
        | sP0(X0,X1,cartesian_product2(sK1,sK2))
        | sK6(X0,X1,cartesian_product2(sK1,sK2)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(sK1,sK2))),unordered_pair(sK8(X0,X1,cartesian_product2(sK1,sK2)),sK7(X0,X1,cartesian_product2(sK1,sK2)))) )
    | ~ spl13_25
    | ~ spl13_110 ),
    inference(resolution,[],[f1543,f198]) ).

fof(f1543,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_110 ),
    inference(avatar_component_clause,[],[f1542]) ).

fof(f2141,plain,
    ( spl13_124
    | ~ spl13_47
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f389,f378,f348,f2139]) ).

fof(f389,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))),sK9(X4,X3,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))))
        | cartesian_product2(X3,X4) = cartesian_product2(X0,cartesian_product2(X1,X2))
        | sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))) = unordered_pair(singleton(sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4))))),unordered_pair(sK10(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))),sK9(X2,X1,sK10(cartesian_product2(X1,X2),X0,sK5(cartesian_product2(X0,cartesian_product2(X1,X2)),cartesian_product2(X3,X4)))))) )
    | ~ spl13_47
    | ~ spl13_49 ),
    inference(resolution,[],[f379,f349]) ).

fof(f2127,plain,
    ( spl13_123
    | ~ spl13_25
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f370,f348,f197,f2125]) ).

fof(f2125,plain,
    ( spl13_123
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | sP0(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))
        | sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))) = unordered_pair(singleton(sK7(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))),unordered_pair(sK8(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))),sK7(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_123])]) ).

fof(f370,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | sP0(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))
        | sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))) = unordered_pair(singleton(sK7(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))),unordered_pair(sK8(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))),sK7(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))) )
    | ~ spl13_25
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f198]) ).

fof(f2123,plain,
    ( spl13_122
    | ~ spl13_25
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f359,f344,f197,f2121]) ).

fof(f2121,plain,
    ( spl13_122
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | sP0(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))
        | sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)) = unordered_pair(singleton(sK7(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))),unordered_pair(sK8(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)),sK7(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_122])]) ).

fof(f359,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | sP0(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))
        | sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)) = unordered_pair(singleton(sK7(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))),unordered_pair(sK8(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)),sK7(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))) )
    | ~ spl13_25
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f198]) ).

fof(f1987,plain,
    ( spl13_121
    | ~ spl13_45
    | ~ spl13_54 ),
    inference(avatar_split_clause,[],[f434,f412,f327,f1985]) ).

fof(f1985,plain,
    ( spl13_121
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK8(cartesian_product2(X0,X1),X2,X3) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3)),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))))
        | sP0(cartesian_product2(X0,X1),X2,X3)
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3))) = unordered_pair(singleton(sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3))))),unordered_pair(sK10(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3)))),sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_121])]) ).

fof(f434,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK8(cartesian_product2(X0,X1),X2,X3) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3)),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))))
        | sP0(cartesian_product2(X0,X1),X2,X3)
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3))) = unordered_pair(singleton(sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3))))),unordered_pair(sK10(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3)))),sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(cartesian_product2(X0,X1),X2,X3)))))) )
    | ~ spl13_45
    | ~ spl13_54 ),
    inference(resolution,[],[f413,f328]) ).

fof(f1973,plain,
    ( spl13_120
    | ~ spl13_45
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f429,f408,f327,f1971]) ).

fof(f1971,plain,
    ( spl13_120
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK7(X0,cartesian_product2(X1,X2),X3) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3)),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))))
        | sP0(X0,cartesian_product2(X1,X2),X3)
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3))) = unordered_pair(singleton(sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3))))),unordered_pair(sK10(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3)))),sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_120])]) ).

fof(f429,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK7(X0,cartesian_product2(X1,X2),X3) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3)),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))))
        | sP0(X0,cartesian_product2(X1,X2),X3)
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3))) = unordered_pair(singleton(sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3))))),unordered_pair(sK10(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3)))),sK9(X3,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK6(X0,cartesian_product2(X1,X2),X3)))))) )
    | ~ spl13_45
    | ~ spl13_53 ),
    inference(resolution,[],[f409,f328]) ).

fof(f1969,plain,
    ( spl13_119
    | ~ spl13_45
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f424,f404,f327,f1967]) ).

fof(f1967,plain,
    ( spl13_119
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3)))) = unordered_pair(singleton(sK9(X1,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3)))))),unordered_pair(sK10(X1,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3))))),sK9(X1,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_119])]) ).

fof(f424,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3)))) = unordered_pair(singleton(sK9(X1,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3)))))),unordered_pair(sK10(X1,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3))))),sK9(X1,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK7(X0,X1,cartesian_product2(X2,X3))))))) )
    | ~ spl13_45
    | ~ spl13_52 ),
    inference(resolution,[],[f405,f328]) ).

fof(f1965,plain,
    ( spl13_118
    | ~ spl13_45
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f419,f400,f327,f1963]) ).

fof(f1963,plain,
    ( spl13_118
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3)))) = unordered_pair(singleton(sK9(X0,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3)))))),unordered_pair(sK10(X0,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3))))),sK9(X0,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_118])]) ).

fof(f419,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X4,X5)
        | unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3)))) = unordered_pair(singleton(sK9(X0,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3)))))),unordered_pair(sK10(X0,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3))))),sK9(X0,X5,unordered_pair(singleton(X4),unordered_pair(X4,sK8(X0,X1,cartesian_product2(X2,X3))))))) )
    | ~ spl13_45
    | ~ spl13_51 ),
    inference(resolution,[],[f401,f328]) ).

fof(f1951,plain,
    ( spl13_117
    | ~ spl13_38
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f426,f404,f265,f1949]) ).

fof(f1949,plain,
    ( spl13_117
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)))))
        | sP0(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))
        | sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_117])]) ).

fof(f265,plain,
    ( spl13_38
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | unordered_pair(singleton(sK9(X2,X1,X0)),unordered_pair(sK10(X2,X1,X0),sK9(X2,X1,X0))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).

fof(f426,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))),sK9(X4,X3,sK6(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)))))
        | sP0(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))
        | sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4)))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),cartesian_product2(X3,X4))))) )
    | ~ spl13_38
    | ~ spl13_52 ),
    inference(resolution,[],[f405,f266]) ).

fof(f266,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | unordered_pair(singleton(sK9(X2,X1,X0)),unordered_pair(sK10(X2,X1,X0),sK9(X2,X1,X0))) = X0 )
    | ~ spl13_38 ),
    inference(avatar_component_clause,[],[f265]) ).

fof(f1947,plain,
    ( spl13_116
    | ~ spl13_38
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f421,f400,f265,f1945]) ).

fof(f1945,plain,
    ( spl13_116
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)))))
        | sP0(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))
        | sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_116])]) ).

fof(f421,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X4,X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X4,X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))),sK9(X4,X3,sK6(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)))))
        | sP0(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))
        | sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4)))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,cartesian_product2(X3,X4))))) )
    | ~ spl13_38
    | ~ spl13_51 ),
    inference(resolution,[],[f401,f266]) ).

fof(f1877,plain,
    ( spl13_115
    | ~ spl13_45
    | ~ spl13_50 ),
    inference(avatar_split_clause,[],[f393,f382,f327,f1875]) ).

fof(f1875,plain,
    ( spl13_115
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK5(cartesian_product2(X0,X1),X2) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),X2)),sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))))
        | cartesian_product2(X0,X1) = X2
        | ~ in(X3,X4)
        | unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2))) = unordered_pair(singleton(sK9(X2,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2))))),unordered_pair(sK10(X2,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2)))),sK9(X2,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_115])]) ).

fof(f393,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK5(cartesian_product2(X0,X1),X2) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),X2)),sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))))
        | cartesian_product2(X0,X1) = X2
        | ~ in(X3,X4)
        | unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2))) = unordered_pair(singleton(sK9(X2,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2))))),unordered_pair(sK10(X2,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2)))),sK9(X2,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(cartesian_product2(X0,X1),X2)))))) )
    | ~ spl13_45
    | ~ spl13_50 ),
    inference(resolution,[],[f383,f328]) ).

fof(f1873,plain,
    ( spl13_114
    | ~ spl13_21
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f976,f930,f173,f1871]) ).

fof(f976,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_21
    | ~ spl13_88 ),
    inference(superposition,[],[f174,f931]) ).

fof(f1869,plain,
    ( spl13_113
    | ~ spl13_45
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f386,f378,f327,f1867]) ).

fof(f1867,plain,
    ( spl13_113
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK5(X0,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(X0,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))))
        | cartesian_product2(X1,X2) = X0
        | ~ in(X3,X4)
        | unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2)))) = unordered_pair(singleton(sK9(X0,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2)))))),unordered_pair(sK10(X0,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2))))),sK9(X0,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_113])]) ).

fof(f386,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK5(X0,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(X0,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))))
        | cartesian_product2(X1,X2) = X0
        | ~ in(X3,X4)
        | unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2)))) = unordered_pair(singleton(sK9(X0,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2)))))),unordered_pair(sK10(X0,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2))))),sK9(X0,X4,unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,cartesian_product2(X1,X2))))))) )
    | ~ spl13_45
    | ~ spl13_49 ),
    inference(resolution,[],[f379,f328]) ).

fof(f1755,plain,
    ( spl13_112
    | ~ spl13_38
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f388,f378,f265,f1753]) ).

fof(f388,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),sK9(X3,X2,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))))
        | cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
        | sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3)))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))),sK9(X1,X0,sK5(cartesian_product2(X0,X1),cartesian_product2(X2,X3))))) )
    | ~ spl13_38
    | ~ spl13_49 ),
    inference(resolution,[],[f379,f266]) ).

fof(f1718,plain,
    ( spl13_111
    | ~ spl13_23
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f443,f440,f186,f1716]) ).

fof(f186,plain,
    ( spl13_23
  <=> ! [X0,X8,X2,X1] :
        ( unordered_pair(singleton(sK9(X0,X1,X8)),unordered_pair(sK10(X0,X1,X8),sK9(X0,X1,X8))) = X8
        | ~ in(X8,X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).

fof(f440,plain,
    ( spl13_56
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | sP0(X2,X3,cartesian_product2(X1,X0))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).

fof(f443,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,cartesian_product2(X2,X3))
        | unordered_pair(singleton(sK9(X0,X1,X4)),unordered_pair(sK10(X0,X1,X4),sK9(X0,X1,X4))) = X4 )
    | ~ spl13_23
    | ~ spl13_56 ),
    inference(resolution,[],[f441,f187]) ).

fof(f187,plain,
    ( ! [X2,X0,X1,X8] :
        ( ~ sP0(X0,X1,X2)
        | ~ in(X8,X2)
        | unordered_pair(singleton(sK9(X0,X1,X8)),unordered_pair(sK10(X0,X1,X8),sK9(X0,X1,X8))) = X8 )
    | ~ spl13_23 ),
    inference(avatar_component_clause,[],[f186]) ).

fof(f441,plain,
    ( ! [X2,X3,X0,X1] :
        ( sP0(X2,X3,cartesian_product2(X1,X0))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0)))) )
    | ~ spl13_56 ),
    inference(avatar_component_clause,[],[f440]) ).

fof(f1544,plain,
    ( spl13_110
    | ~ spl13_14
    | ~ spl13_88 ),
    inference(avatar_split_clause,[],[f975,f930,f137,f1542]) ).

fof(f975,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK1,sK2))
        | in(sK6(X2,X3,cartesian_product2(X1,X0)),cartesian_product2(sK3,sK4))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0))))
        | cartesian_product2(X1,X0) = cartesian_product2(X3,X2) )
    | ~ spl13_14
    | ~ spl13_88 ),
    inference(superposition,[],[f138,f931]) ).

fof(f1438,plain,
    ( spl13_109
    | ~ spl13_20
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f374,f348,f169,f1436]) ).

fof(f1436,plain,
    ( spl13_109
  <=> ! [X2,X4,X0,X3,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))))
        | in(sK6(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4),X4)
        | sP0(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_109])]) ).

fof(f374,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK8(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))))
        | in(sK6(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4),X4)
        | sP0(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4) )
    | ~ spl13_20
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f170]) ).

fof(f1434,plain,
    ( spl13_108
    | ~ spl13_19
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f373,f348,f165,f1432]) ).

fof(f1432,plain,
    ( spl13_108
  <=> ! [X2,X4,X0,X3,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))))
        | in(sK6(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4),X4)
        | sP0(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_108])]) ).

fof(f373,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK7(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))))
        | in(sK6(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4),X4)
        | sP0(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4) )
    | ~ spl13_19
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f166]) ).

fof(f1430,plain,
    ( spl13_107
    | ~ spl13_19
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f372,f348,f165,f1428]) ).

fof(f1428,plain,
    ( spl13_107
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | in(sK7(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))),X4)
        | sP0(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_107])]) ).

fof(f372,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | in(sK7(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))),X4)
        | sP0(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))) )
    | ~ spl13_19
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f166]) ).

fof(f1426,plain,
    ( spl13_106
    | ~ spl13_20
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f371,f348,f169,f1424]) ).

fof(f1424,plain,
    ( spl13_106
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | in(sK8(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))),X3)
        | sP0(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_106])]) ).

fof(f371,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK6(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | in(sK8(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))),X3)
        | sP0(X3,X4,cartesian_product2(X2,cartesian_product2(X0,X1))) )
    | ~ spl13_20
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f170]) ).

fof(f1422,plain,
    ( spl13_105
    | ~ spl13_20
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f363,f344,f169,f1420]) ).

fof(f1420,plain,
    ( spl13_105
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))))
        | in(sK6(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4),X4)
        | sP0(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_105])]) ).

fof(f363,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK8(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))))
        | in(sK6(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4),X4)
        | sP0(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4) )
    | ~ spl13_20
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f170]) ).

fof(f1418,plain,
    ( spl13_104
    | ~ spl13_19
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f362,f344,f165,f1416]) ).

fof(f1416,plain,
    ( spl13_104
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))))
        | in(sK6(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4),X4)
        | sP0(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_104])]) ).

fof(f362,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK7(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))))
        | in(sK6(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4),X4)
        | sP0(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4) )
    | ~ spl13_19
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f166]) ).

fof(f1414,plain,
    ( spl13_103
    | ~ spl13_19
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f361,f344,f165,f1412]) ).

fof(f1412,plain,
    ( spl13_103
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | in(sK7(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)),X4)
        | sP0(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_103])]) ).

fof(f361,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | in(sK7(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)),X4)
        | sP0(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)) )
    | ~ spl13_19
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f166]) ).

fof(f1391,plain,
    ( spl13_102
    | ~ spl13_20
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f360,f344,f169,f1389]) ).

fof(f1389,plain,
    ( spl13_102
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | in(sK8(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)),X3)
        | sP0(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_102])]) ).

fof(f360,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK6(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | in(sK8(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)),X3)
        | sP0(X3,X4,cartesian_product2(cartesian_product2(X1,X2),X0)) )
    | ~ spl13_20
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f170]) ).

fof(f1362,plain,
    ( spl13_101
    | ~ spl13_22
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f444,f440,f181,f1360]) ).

fof(f181,plain,
    ( spl13_22
  <=> ! [X10,X0,X9,X2,X1] :
        ( in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),X2)
        | ~ in(X10,X0)
        | ~ in(X9,X1)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).

fof(f444,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,X0)
        | ~ in(X5,X1)
        | in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),cartesian_product2(X2,X3)) )
    | ~ spl13_22
    | ~ spl13_56 ),
    inference(resolution,[],[f441,f182]) ).

fof(f182,plain,
    ( ! [X2,X10,X0,X1,X9] :
        ( ~ sP0(X0,X1,X2)
        | ~ in(X10,X0)
        | ~ in(X9,X1)
        | in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),X2) )
    | ~ spl13_22 ),
    inference(avatar_component_clause,[],[f181]) ).

fof(f1222,plain,
    ( spl13_100
    | ~ spl13_15
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f369,f348,f141,f1220]) ).

fof(f1220,plain,
    ( spl13_100
  <=> ! [X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)))))
        | in(sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3),X3)
        | cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_100])]) ).

fof(f369,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)))))
        | in(sK5(cartesian_product2(X2,cartesian_product2(X0,X1)),X3),X3)
        | cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
    | ~ spl13_15
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f142]) ).

fof(f1218,plain,
    ( spl13_99
    | ~ spl13_15
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f368,f348,f141,f1216]) ).

fof(f1216,plain,
    ( spl13_99
  <=> ! [X0,X3,X2,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | in(sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1))),X3)
        | cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_99])]) ).

fof(f368,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1))))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))))))
        | in(sK5(X3,cartesian_product2(X2,cartesian_product2(X0,X1))),X3)
        | cartesian_product2(X2,cartesian_product2(X0,X1)) = X3 )
    | ~ spl13_15
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f142]) ).

fof(f1214,plain,
    ( spl13_98
    | ~ spl13_15
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f358,f344,f141,f1212]) ).

fof(f1212,plain,
    ( spl13_98
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3)))))
        | in(sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3),X3)
        | cartesian_product2(cartesian_product2(X1,X2),X0) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_98])]) ).

fof(f358,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3)))))
        | in(sK5(cartesian_product2(cartesian_product2(X1,X2),X0),X3),X3)
        | cartesian_product2(cartesian_product2(X1,X2),X0) = X3 )
    | ~ spl13_15
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f142]) ).

fof(f1195,plain,
    ( spl13_97
    | ~ spl13_15
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f357,f344,f141,f1193]) ).

fof(f1193,plain,
    ( spl13_97
  <=> ! [X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | in(sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0)),X3)
        | cartesian_product2(cartesian_product2(X1,X2),X0) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_97])]) ).

fof(f357,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0))))))
        | in(sK5(X3,cartesian_product2(cartesian_product2(X1,X2),X0)),X3)
        | cartesian_product2(cartesian_product2(X1,X2),X0) = X3 )
    | ~ spl13_15
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f142]) ).

fof(f1128,plain,
    ( spl13_96
    | ~ spl13_17
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f446,f440,f149,f1126]) ).

fof(f149,plain,
    ( spl13_17
  <=> ! [X0,X8,X2,X1] :
        ( in(sK9(X0,X1,X8),X1)
        | ~ in(X8,X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).

fof(f446,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,cartesian_product2(X2,X3))
        | in(sK9(X0,X1,X4),X1) )
    | ~ spl13_17
    | ~ spl13_56 ),
    inference(resolution,[],[f441,f150]) ).

fof(f150,plain,
    ( ! [X2,X0,X1,X8] :
        ( ~ sP0(X0,X1,X2)
        | ~ in(X8,X2)
        | in(sK9(X0,X1,X8),X1) )
    | ~ spl13_17 ),
    inference(avatar_component_clause,[],[f149]) ).

fof(f1124,plain,
    ( spl13_95
    | ~ spl13_18
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f445,f440,f153,f1122]) ).

fof(f153,plain,
    ( spl13_18
  <=> ! [X0,X8,X2,X1] :
        ( in(sK10(X0,X1,X8),X0)
        | ~ in(X8,X2)
        | ~ sP0(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).

fof(f445,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | ~ in(X4,cartesian_product2(X2,X3))
        | in(sK10(X0,X1,X4),X0) )
    | ~ spl13_18
    | ~ spl13_56 ),
    inference(resolution,[],[f441,f154]) ).

fof(f154,plain,
    ( ! [X2,X0,X1,X8] :
        ( ~ sP0(X0,X1,X2)
        | ~ in(X8,X2)
        | in(sK10(X0,X1,X8),X0) )
    | ~ spl13_18 ),
    inference(avatar_component_clause,[],[f153]) ).

fof(f1120,plain,
    ( spl13_94
    | ~ spl13_25
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f336,f327,f197,f1118]) ).

fof(f336,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | sP0(X2,X3,X4)
        | sK6(X2,X3,X4) = unordered_pair(singleton(sK7(X2,X3,X4)),unordered_pair(sK8(X2,X3,X4),sK7(X2,X3,X4))) )
    | ~ spl13_25
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f198]) ).

fof(f1065,plain,
    ( spl13_93
    | ~ spl13_38
    | ~ spl13_58 ),
    inference(avatar_split_clause,[],[f469,f453,f265,f1063]) ).

fof(f1063,plain,
    ( spl13_93
  <=> ! [X0,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | unordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X0,X1)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X0,X1))),sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X0,X1))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_93])]) ).

fof(f469,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | unordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X0,X1)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X0,X1))),sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X0,X1))))) )
    | ~ spl13_38
    | ~ spl13_58 ),
    inference(resolution,[],[f454,f266]) ).

fof(f1044,plain,
    ( spl13_92
    | ~ spl13_28
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f376,f348,f216,f1042]) ).

fof(f1042,plain,
    ( spl13_92
  <=> ! [X2,X4,X0,X3,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))))
        | ~ in(X4,cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_92])]) ).

fof(f376,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK10(cartesian_product2(X2,cartesian_product2(X0,X1)),X3,X4)))))
        | ~ in(X4,cartesian_product2(X3,cartesian_product2(X2,cartesian_product2(X0,X1)))) )
    | ~ spl13_28
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f217]) ).

fof(f1040,plain,
    ( spl13_91
    | ~ spl13_27
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f375,f348,f212,f1038]) ).

fof(f1038,plain,
    ( spl13_91
  <=> ! [X2,X4,X0,X3,X1] :
        ( sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))))
        | ~ in(X4,cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_91])]) ).

fof(f375,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,sK9(X3,cartesian_product2(X2,cartesian_product2(X0,X1)),X4)))))
        | ~ in(X4,cartesian_product2(cartesian_product2(X2,cartesian_product2(X0,X1)),X3)) )
    | ~ spl13_27
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f213]) ).

fof(f1036,plain,
    ( spl13_90
    | ~ spl13_28
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f365,f344,f216,f1034]) ).

fof(f1034,plain,
    ( spl13_90
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))))
        | ~ in(X4,cartesian_product2(X3,cartesian_product2(cartesian_product2(X1,X2),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_90])]) ).

fof(f365,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK10(cartesian_product2(cartesian_product2(X1,X2),X0),X3,X4)))))
        | ~ in(X4,cartesian_product2(X3,cartesian_product2(cartesian_product2(X1,X2),X0))) )
    | ~ spl13_28
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f217]) ).

fof(f1032,plain,
    ( spl13_89
    | ~ spl13_27
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f364,f344,f212,f1030]) ).

fof(f1030,plain,
    ( spl13_89
  <=> ! [X4,X0,X3,X2,X1] :
        ( sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))))
        | ~ in(X4,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_89])]) ).

fof(f364,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),sK9(X3,cartesian_product2(cartesian_product2(X1,X2),X0),X4)))))
        | ~ in(X4,cartesian_product2(cartesian_product2(cartesian_product2(X1,X2),X0),X3)) )
    | ~ spl13_27
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f213]) ).

fof(f932,plain,
    ( spl13_88
    | ~ spl13_13
    | ~ spl13_56 ),
    inference(avatar_split_clause,[],[f447,f440,f132,f930]) ).

fof(f132,plain,
    ( spl13_13
  <=> ! [X2,X0,X1] :
        ( cartesian_product2(X0,X1) = X2
        | ~ sP0(X1,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).

fof(f447,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK7(X0,X1,cartesian_product2(X2,X3))),unordered_pair(sK8(X0,X1,cartesian_product2(X2,X3)),sK7(X0,X1,cartesian_product2(X2,X3))))
        | cartesian_product2(X2,X3) = cartesian_product2(X1,X0) )
    | ~ spl13_13
    | ~ spl13_56 ),
    inference(resolution,[],[f441,f133]) ).

fof(f133,plain,
    ( ! [X2,X0,X1] :
        ( ~ sP0(X1,X0,X2)
        | cartesian_product2(X0,X1) = X2 )
    | ~ spl13_13 ),
    inference(avatar_component_clause,[],[f132]) ).

fof(f928,plain,
    ( spl13_87
    | ~ spl13_44
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f333,f327,f313,f926]) ).

fof(f313,plain,
    ( spl13_44
  <=> ! [X0,X3,X2,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
        | ~ in(X0,X2)
        | ~ in(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).

fof(f333,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))),unordered_pair(sK10(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2))))),sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X3,X2)))))))
        | ~ in(X2,X4)
        | ~ in(X3,X5) )
    | ~ spl13_44
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f314]) ).

fof(f314,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
        | ~ in(X0,X2)
        | ~ in(X1,X3) )
    | ~ spl13_44 ),
    inference(avatar_component_clause,[],[f313]) ).

fof(f924,plain,
    ( spl13_86
    | ~ spl13_38
    | ~ spl13_55 ),
    inference(avatar_split_clause,[],[f460,f416,f265,f922]) ).

fof(f922,plain,
    ( spl13_86
  <=> ! [X0,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | unordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X0,X1)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X0,X1))),sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X0,X1))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_86])]) ).

fof(f460,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | unordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X0,X1)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X0,X1))),sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X0,X1))))) )
    | ~ spl13_38
    | ~ spl13_55 ),
    inference(resolution,[],[f417,f266]) ).

fof(f920,plain,
    ( spl13_85
    | ~ spl13_36
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f330,f327,f250,f918]) ).

fof(f250,plain,
    ( spl13_36
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | ~ in(X2,X3)
        | in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).

fof(f330,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(X4,X5),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X2,X4)
        | ~ in(X3,X5) )
    | ~ spl13_36
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f251]) ).

fof(f251,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1))
        | ~ in(X2,X3)
        | ~ in(X0,X1) )
    | ~ spl13_36 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f832,plain,
    ( spl13_84
    | ~ spl13_44
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f367,f348,f313,f830]) ).

fof(f367,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3)))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X4,X3))))))
        | ~ in(X3,X2)
        | ~ in(X4,cartesian_product2(X0,X1)) )
    | ~ spl13_44
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f314]) ).

fof(f828,plain,
    ( spl13_83
    | ~ spl13_36
    | ~ spl13_47 ),
    inference(avatar_split_clause,[],[f366,f348,f250,f826]) ).

fof(f366,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))) = unordered_pair(singleton(sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))))),unordered_pair(sK10(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4)))),sK9(X1,X0,sK10(cartesian_product2(X0,X1),X2,unordered_pair(singleton(X3),unordered_pair(X3,X4))))))
        | ~ in(X3,X2)
        | ~ in(X4,cartesian_product2(X0,X1)) )
    | ~ spl13_36
    | ~ spl13_47 ),
    inference(resolution,[],[f349,f251]) ).

fof(f824,plain,
    ( spl13_82
    | ~ spl13_44
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f356,f344,f313,f822]) ).

fof(f356,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X4,X3))))))
        | ~ in(X3,cartesian_product2(X1,X2))
        | ~ in(X4,X0) )
    | ~ spl13_44
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f314]) ).

fof(f820,plain,
    ( spl13_81
    | ~ spl13_36
    | ~ spl13_46 ),
    inference(avatar_split_clause,[],[f355,f344,f250,f818]) ).

fof(f355,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))) = unordered_pair(singleton(sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))))),unordered_pair(sK10(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4)))),sK9(X2,X1,sK9(X0,cartesian_product2(X1,X2),unordered_pair(singleton(X3),unordered_pair(X3,X4))))))
        | ~ in(X3,cartesian_product2(X1,X2))
        | ~ in(X4,X0) )
    | ~ spl13_36
    | ~ spl13_46 ),
    inference(resolution,[],[f345,f251]) ).

fof(f730,plain,
    ( spl13_80
    | ~ spl13_20
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f340,f327,f169,f728]) ).

fof(f340,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK8(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4) )
    | ~ spl13_20
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f170]) ).

fof(f726,plain,
    ( spl13_79
    | ~ spl13_19
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f339,f327,f165,f724]) ).

fof(f339,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK7(X2,X3,X4))))))
        | in(sK6(X2,X3,X4),X4)
        | sP0(X2,X3,X4) )
    | ~ spl13_19
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f166]) ).

fof(f722,plain,
    ( spl13_78
    | ~ spl13_19
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f338,f327,f165,f720]) ).

fof(f338,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | in(sK7(X2,X3,X4),X3)
        | sP0(X2,X3,X4) )
    | ~ spl13_19
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f166]) ).

fof(f718,plain,
    ( spl13_77
    | ~ spl13_20
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f337,f327,f169,f716]) ).

fof(f337,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))) = unordered_pair(singleton(sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))),unordered_pair(sK10(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4)))),sK9(X4,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK6(X2,X3,X4))))))
        | in(sK8(X2,X3,X4),X2)
        | sP0(X2,X3,X4) )
    | ~ spl13_20
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f170]) ).

fof(f672,plain,
    ( spl13_76
    | ~ spl13_28
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f342,f327,f216,f670]) ).

fof(f342,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK10(X2,X3,X4))))))
        | ~ in(X4,cartesian_product2(X3,X2)) )
    | ~ spl13_28
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f217]) ).

fof(f666,plain,
    ( spl13_75
    | ~ spl13_27
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f341,f327,f212,f664]) ).

fof(f341,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK9(X2,X3,X4))))))
        | ~ in(X4,cartesian_product2(X3,X2)) )
    | ~ spl13_27
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f213]) ).

fof(f620,plain,
    ( spl13_74
    | ~ spl13_15
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f335,f327,f141,f618]) ).

fof(f335,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))) = unordered_pair(singleton(sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))),unordered_pair(sK10(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3)))),sK9(X2,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))))
        | in(sK5(X2,X3),X3)
        | X2 = X3 )
    | ~ spl13_15
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f142]) ).

fof(f616,plain,
    ( spl13_73
    | ~ spl13_15
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f334,f327,f141,f614]) ).

fof(f334,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3)))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X0,sK5(X2,X3))))))
        | in(sK5(X2,X3),X2)
        | X2 = X3 )
    | ~ spl13_15
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f142]) ).

fof(f612,plain,
    ( spl13_72
    | ~ spl13_8
    | ~ spl13_54 ),
    inference(avatar_split_clause,[],[f435,f412,f105,f610]) ).

fof(f610,plain,
    ( spl13_72
  <=> ! [X0,X3,X2,X1] :
        ( sK8(cartesian_product2(X0,X1),X2,X3) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3)),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))))
        | sP0(cartesian_product2(X0,X1),X2,X3)
        | ~ in(X3,sK6(cartesian_product2(X0,X1),X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).

fof(f435,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK8(cartesian_product2(X0,X1),X2,X3) = unordered_pair(singleton(sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))),unordered_pair(sK10(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3)),sK9(X1,X0,sK8(cartesian_product2(X0,X1),X2,X3))))
        | sP0(cartesian_product2(X0,X1),X2,X3)
        | ~ in(X3,sK6(cartesian_product2(X0,X1),X2,X3)) )
    | ~ spl13_8
    | ~ spl13_54 ),
    inference(resolution,[],[f413,f106]) ).

fof(f608,plain,
    ( spl13_71
    | ~ spl13_10
    | ~ spl13_57 ),
    inference(avatar_split_clause,[],[f465,f449,f113,f606]) ).

fof(f606,plain,
    ( spl13_71
  <=> ! [X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
        | ~ in(X0,sK1)
        | ~ in(X1,sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).

fof(f465,plain,
    ( ! [X0,X1] :
        ( ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
        | ~ in(X0,sK1)
        | ~ in(X1,sK2) )
    | ~ spl13_10
    | ~ spl13_57 ),
    inference(superposition,[],[f450,f114]) ).

fof(f604,plain,
    ( spl13_70
    | ~ spl13_8
    | ~ spl13_53 ),
    inference(avatar_split_clause,[],[f430,f408,f105,f602]) ).

fof(f602,plain,
    ( spl13_70
  <=> ! [X0,X3,X2,X1] :
        ( sK7(X0,cartesian_product2(X1,X2),X3) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3)),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))))
        | sP0(X0,cartesian_product2(X1,X2),X3)
        | ~ in(X3,sK6(X0,cartesian_product2(X1,X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_70])]) ).

fof(f430,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK7(X0,cartesian_product2(X1,X2),X3) = unordered_pair(singleton(sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))),unordered_pair(sK10(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3)),sK9(X2,X1,sK7(X0,cartesian_product2(X1,X2),X3))))
        | sP0(X0,cartesian_product2(X1,X2),X3)
        | ~ in(X3,sK6(X0,cartesian_product2(X1,X2),X3)) )
    | ~ spl13_8
    | ~ spl13_53 ),
    inference(resolution,[],[f409,f106]) ).

fof(f600,plain,
    ( spl13_69
    | ~ spl13_8
    | ~ spl13_52 ),
    inference(avatar_split_clause,[],[f425,f404,f105,f598]) ).

fof(f598,plain,
    ( spl13_69
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X1,sK7(X0,X1,cartesian_product2(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_69])]) ).

fof(f425,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X1,sK7(X0,X1,cartesian_product2(X2,X3))) )
    | ~ spl13_8
    | ~ spl13_52 ),
    inference(resolution,[],[f405,f106]) ).

fof(f596,plain,
    ( spl13_68
    | ~ spl13_8
    | ~ spl13_51 ),
    inference(avatar_split_clause,[],[f420,f400,f105,f594]) ).

fof(f594,plain,
    ( spl13_68
  <=> ! [X0,X3,X2,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X0,sK8(X0,X1,cartesian_product2(X2,X3))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_68])]) ).

fof(f420,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X0,X1,cartesian_product2(X2,X3)) = unordered_pair(singleton(sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))),unordered_pair(sK10(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3))),sK9(X3,X2,sK6(X0,X1,cartesian_product2(X2,X3)))))
        | sP0(X0,X1,cartesian_product2(X2,X3))
        | ~ in(X0,sK8(X0,X1,cartesian_product2(X2,X3))) )
    | ~ spl13_8
    | ~ spl13_51 ),
    inference(resolution,[],[f401,f106]) ).

fof(f592,plain,
    ( spl13_67
    | ~ spl13_8
    | ~ spl13_50 ),
    inference(avatar_split_clause,[],[f394,f382,f105,f590]) ).

fof(f590,plain,
    ( spl13_67
  <=> ! [X2,X0,X1] :
        ( sK5(cartesian_product2(X0,X1),X2) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),X2)),sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))))
        | cartesian_product2(X0,X1) = X2
        | ~ in(X2,sK5(cartesian_product2(X0,X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_67])]) ).

fof(f394,plain,
    ( ! [X2,X0,X1] :
        ( sK5(cartesian_product2(X0,X1),X2) = unordered_pair(singleton(sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))),unordered_pair(sK10(X1,X0,sK5(cartesian_product2(X0,X1),X2)),sK9(X1,X0,sK5(cartesian_product2(X0,X1),X2))))
        | cartesian_product2(X0,X1) = X2
        | ~ in(X2,sK5(cartesian_product2(X0,X1),X2)) )
    | ~ spl13_8
    | ~ spl13_50 ),
    inference(resolution,[],[f383,f106]) ).

fof(f588,plain,
    ( spl13_66
    | ~ spl13_8
    | ~ spl13_49 ),
    inference(avatar_split_clause,[],[f387,f378,f105,f586]) ).

fof(f586,plain,
    ( spl13_66
  <=> ! [X2,X0,X1] :
        ( sK5(X0,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(X0,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))))
        | cartesian_product2(X1,X2) = X0
        | ~ in(X0,sK5(X0,cartesian_product2(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_66])]) ).

fof(f387,plain,
    ( ! [X2,X0,X1] :
        ( sK5(X0,cartesian_product2(X1,X2)) = unordered_pair(singleton(sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))),unordered_pair(sK10(X2,X1,sK5(X0,cartesian_product2(X1,X2))),sK9(X2,X1,sK5(X0,cartesian_product2(X1,X2)))))
        | cartesian_product2(X1,X2) = X0
        | ~ in(X0,sK5(X0,cartesian_product2(X1,X2))) )
    | ~ spl13_8
    | ~ spl13_49 ),
    inference(resolution,[],[f379,f106]) ).

fof(f563,plain,
    ( spl13_65
    | ~ spl13_38
    | ~ spl13_44 ),
    inference(avatar_split_clause,[],[f322,f313,f265,f561]) ).

fof(f322,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X2,X3)
        | unordered_pair(singleton(X0),unordered_pair(X2,X0)) = unordered_pair(singleton(sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0)))),unordered_pair(sK10(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0))),sK9(X3,X1,unordered_pair(singleton(X0),unordered_pair(X2,X0))))) )
    | ~ spl13_38
    | ~ spl13_44 ),
    inference(resolution,[],[f314,f266]) ).

fof(f544,plain,
    ( spl13_64
    | ~ spl13_10
    | ~ spl13_48 ),
    inference(avatar_split_clause,[],[f456,f352,f113,f542]) ).

fof(f542,plain,
    ( spl13_64
  <=> ! [X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
        | ~ in(X0,sK3)
        | ~ in(X1,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_64])]) ).

fof(f456,plain,
    ( ! [X0,X1] :
        ( ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
        | ~ in(X0,sK3)
        | ~ in(X1,sK4) )
    | ~ spl13_10
    | ~ spl13_48 ),
    inference(superposition,[],[f353,f114]) ).

fof(f525,plain,
    ( spl13_63
    | ~ spl13_42
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f332,f327,f293,f523]) ).

fof(f332,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(sK3,sK4),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X3,sK2)
        | ~ in(X2,sK1) )
    | ~ spl13_42
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f294]) ).

fof(f521,plain,
    ( spl13_62
    | ~ spl13_41
    | ~ spl13_45 ),
    inference(avatar_split_clause,[],[f331,f327,f289,f519]) ).

fof(f331,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))) = unordered_pair(singleton(sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))),unordered_pair(sK10(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3))))),sK9(cartesian_product2(sK1,sK2),X1,unordered_pair(singleton(X0),unordered_pair(X0,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))))
        | ~ in(X3,sK4)
        | ~ in(X2,sK3) )
    | ~ spl13_41
    | ~ spl13_45 ),
    inference(resolution,[],[f328,f290]) ).

fof(f515,plain,
    ( spl13_61
    | ~ spl13_10
    | ~ spl13_43 ),
    inference(avatar_split_clause,[],[f316,f309,f113,f513]) ).

fof(f513,plain,
    ( spl13_61
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(cartesian_product2(X2,X3),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
        | ~ in(X1,X3)
        | ~ in(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).

fof(f309,plain,
    ( spl13_43
  <=> ! [X0,X3,X2,X1] :
        ( ~ in(X0,X1)
        | ~ in(X2,X3)
        | ~ in(cartesian_product2(X1,X3),unordered_pair(singleton(X0),unordered_pair(X0,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).

fof(f316,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(X2,X3),unordered_pair(singleton(X0),unordered_pair(X1,X0)))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
    | ~ spl13_10
    | ~ spl13_43 ),
    inference(superposition,[],[f310,f114]) ).

fof(f310,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(cartesian_product2(X1,X3),unordered_pair(singleton(X0),unordered_pair(X0,X2)))
        | ~ in(X2,X3)
        | ~ in(X0,X1) )
    | ~ spl13_43 ),
    inference(avatar_component_clause,[],[f309]) ).

fof(f481,plain,
    ( spl13_60
    | ~ spl13_38
    | ~ spl13_42 ),
    inference(avatar_split_clause,[],[f304,f293,f265,f479]) ).

fof(f304,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | unordered_pair(singleton(X1),unordered_pair(X1,X0)) = unordered_pair(singleton(sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0)))),unordered_pair(sK10(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0))),sK9(sK4,sK3,unordered_pair(singleton(X1),unordered_pair(X1,X0))))) )
    | ~ spl13_38
    | ~ spl13_42 ),
    inference(resolution,[],[f294,f266]) ).

fof(f477,plain,
    ( spl13_59
    | ~ spl13_38
    | ~ spl13_41 ),
    inference(avatar_split_clause,[],[f298,f289,f265,f475]) ).

fof(f298,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | unordered_pair(singleton(X1),unordered_pair(X1,X0)) = unordered_pair(singleton(sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0)))),unordered_pair(sK10(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0))),sK9(sK2,sK1,unordered_pair(singleton(X1),unordered_pair(X1,X0))))) )
    | ~ spl13_38
    | ~ spl13_41 ),
    inference(resolution,[],[f290,f266]) ).

fof(f455,plain,
    ( spl13_58
    | ~ spl13_10
    | ~ spl13_42 ),
    inference(avatar_split_clause,[],[f306,f293,f113,f453]) ).

fof(f306,plain,
    ( ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4))
        | ~ in(X1,sK2)
        | ~ in(X0,sK1) )
    | ~ spl13_10
    | ~ spl13_42 ),
    inference(superposition,[],[f294,f114]) ).

fof(f451,plain,
    ( spl13_57
    | ~ spl13_8
    | ~ spl13_42 ),
    inference(avatar_split_clause,[],[f305,f293,f105,f449]) ).

fof(f305,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK2)
        | ~ in(X1,sK1)
        | ~ in(cartesian_product2(sK3,sK4),unordered_pair(singleton(X1),unordered_pair(X1,X0))) )
    | ~ spl13_8
    | ~ spl13_42 ),
    inference(resolution,[],[f294,f106]) ).

fof(f442,plain,
    ( spl13_56
    | ~ spl13_25
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f271,f265,f197,f440]) ).

fof(f271,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | sP0(X2,X3,cartesian_product2(X1,X0))
        | sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK7(X2,X3,cartesian_product2(X1,X0))),unordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK7(X2,X3,cartesian_product2(X1,X0)))) )
    | ~ spl13_25
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f198]) ).

fof(f418,plain,
    ( spl13_55
    | ~ spl13_10
    | ~ spl13_41 ),
    inference(avatar_split_clause,[],[f300,f289,f113,f416]) ).

fof(f300,plain,
    ( ! [X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2))
        | ~ in(X1,sK4)
        | ~ in(X0,sK3) )
    | ~ spl13_10
    | ~ spl13_41 ),
    inference(superposition,[],[f290,f114]) ).

fof(f414,plain,
    ( spl13_54
    | ~ spl13_20
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f275,f265,f169,f412]) ).

fof(f275,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK8(cartesian_product2(X1,X0),X2,X3) = unordered_pair(singleton(sK9(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3))),unordered_pair(sK10(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3)),sK9(X0,X1,sK8(cartesian_product2(X1,X0),X2,X3))))
        | in(sK6(cartesian_product2(X1,X0),X2,X3),X3)
        | sP0(cartesian_product2(X1,X0),X2,X3) )
    | ~ spl13_20
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f170]) ).

fof(f410,plain,
    ( spl13_53
    | ~ spl13_19
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f274,f265,f165,f408]) ).

fof(f274,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK7(X2,cartesian_product2(X1,X0),X3) = unordered_pair(singleton(sK9(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3))),unordered_pair(sK10(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3)),sK9(X0,X1,sK7(X2,cartesian_product2(X1,X0),X3))))
        | in(sK6(X2,cartesian_product2(X1,X0),X3),X3)
        | sP0(X2,cartesian_product2(X1,X0),X3) )
    | ~ spl13_19
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f166]) ).

fof(f406,plain,
    ( spl13_52
    | ~ spl13_19
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f273,f265,f165,f404]) ).

fof(f273,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | in(sK7(X2,X3,cartesian_product2(X1,X0)),X3)
        | sP0(X2,X3,cartesian_product2(X1,X0)) )
    | ~ spl13_19
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f166]) ).

fof(f402,plain,
    ( spl13_51
    | ~ spl13_20
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f272,f265,f169,f400]) ).

fof(f272,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK6(X2,X3,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0))),sK9(X0,X1,sK6(X2,X3,cartesian_product2(X1,X0)))))
        | in(sK8(X2,X3,cartesian_product2(X1,X0)),X2)
        | sP0(X2,X3,cartesian_product2(X1,X0)) )
    | ~ spl13_20
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f170]) ).

fof(f384,plain,
    ( spl13_50
    | ~ spl13_15
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f270,f265,f141,f382]) ).

fof(f270,plain,
    ( ! [X2,X0,X1] :
        ( sK5(cartesian_product2(X1,X0),X2) = unordered_pair(singleton(sK9(X0,X1,sK5(cartesian_product2(X1,X0),X2))),unordered_pair(sK10(X0,X1,sK5(cartesian_product2(X1,X0),X2)),sK9(X0,X1,sK5(cartesian_product2(X1,X0),X2))))
        | in(sK5(cartesian_product2(X1,X0),X2),X2)
        | cartesian_product2(X1,X0) = X2 )
    | ~ spl13_15
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f142]) ).

fof(f380,plain,
    ( spl13_49
    | ~ spl13_15
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f269,f265,f141,f378]) ).

fof(f269,plain,
    ( ! [X2,X0,X1] :
        ( sK5(X2,cartesian_product2(X1,X0)) = unordered_pair(singleton(sK9(X0,X1,sK5(X2,cartesian_product2(X1,X0)))),unordered_pair(sK10(X0,X1,sK5(X2,cartesian_product2(X1,X0))),sK9(X0,X1,sK5(X2,cartesian_product2(X1,X0)))))
        | in(sK5(X2,cartesian_product2(X1,X0)),X2)
        | cartesian_product2(X1,X0) = X2 )
    | ~ spl13_15
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f142]) ).

fof(f354,plain,
    ( spl13_48
    | ~ spl13_8
    | ~ spl13_41 ),
    inference(avatar_split_clause,[],[f299,f289,f105,f352]) ).

fof(f299,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK4)
        | ~ in(X1,sK3)
        | ~ in(cartesian_product2(sK1,sK2),unordered_pair(singleton(X1),unordered_pair(X1,X0))) )
    | ~ spl13_8
    | ~ spl13_41 ),
    inference(resolution,[],[f290,f106]) ).

fof(f350,plain,
    ( spl13_47
    | ~ spl13_28
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f277,f265,f216,f348]) ).

fof(f277,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK10(cartesian_product2(X1,X0),X2,X3) = unordered_pair(singleton(sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3))),unordered_pair(sK10(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3)),sK9(X0,X1,sK10(cartesian_product2(X1,X0),X2,X3))))
        | ~ in(X3,cartesian_product2(X2,cartesian_product2(X1,X0))) )
    | ~ spl13_28
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f217]) ).

fof(f346,plain,
    ( spl13_46
    | ~ spl13_27
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f276,f265,f212,f344]) ).

fof(f276,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK9(X2,cartesian_product2(X1,X0),X3) = unordered_pair(singleton(sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3))),unordered_pair(sK10(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3)),sK9(X0,X1,sK9(X2,cartesian_product2(X1,X0),X3))))
        | ~ in(X3,cartesian_product2(cartesian_product2(X1,X0),X2)) )
    | ~ spl13_27
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f213]) ).

fof(f329,plain,
    ( spl13_45
    | ~ spl13_36
    | ~ spl13_38 ),
    inference(avatar_split_clause,[],[f268,f265,f250,f327]) ).

fof(f268,plain,
    ( ! [X2,X3,X0,X1] :
        ( unordered_pair(singleton(X2),unordered_pair(X2,X3)) = unordered_pair(singleton(sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))),unordered_pair(sK10(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3))),sK9(X0,X1,unordered_pair(singleton(X2),unordered_pair(X2,X3)))))
        | ~ in(X2,X1)
        | ~ in(X3,X0) )
    | ~ spl13_36
    | ~ spl13_38 ),
    inference(resolution,[],[f266,f251]) ).

fof(f315,plain,
    ( spl13_44
    | ~ spl13_10
    | ~ spl13_36 ),
    inference(avatar_split_clause,[],[f262,f250,f113,f313]) ).

fof(f262,plain,
    ( ! [X2,X3,X0,X1] :
        ( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
        | ~ in(X0,X2)
        | ~ in(X1,X3) )
    | ~ spl13_10
    | ~ spl13_36 ),
    inference(superposition,[],[f251,f114]) ).

fof(f311,plain,
    ( spl13_43
    | ~ spl13_8
    | ~ spl13_36 ),
    inference(avatar_split_clause,[],[f261,f250,f105,f309]) ).

fof(f261,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X2,X3)
        | ~ in(cartesian_product2(X1,X3),unordered_pair(singleton(X0),unordered_pair(X0,X2))) )
    | ~ spl13_8
    | ~ spl13_36 ),
    inference(resolution,[],[f251,f106]) ).

fof(f295,plain,
    ( spl13_42
    | ~ spl13_7
    | ~ spl13_36 ),
    inference(avatar_split_clause,[],[f258,f250,f101,f293]) ).

fof(f258,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK1)
        | ~ in(X1,sK2)
        | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK3,sK4)) )
    | ~ spl13_7
    | ~ spl13_36 ),
    inference(resolution,[],[f251,f102]) ).

fof(f291,plain,
    ( spl13_41
    | ~ spl13_6
    | ~ spl13_36 ),
    inference(avatar_split_clause,[],[f257,f250,f97,f289]) ).

fof(f257,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,sK3)
        | ~ in(X1,sK4)
        | in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(sK1,sK2)) )
    | ~ spl13_6
    | ~ spl13_36 ),
    inference(resolution,[],[f251,f98]) ).

fof(f287,plain,
    ( spl13_40
    | ~ spl13_8
    | ~ spl13_25 ),
    inference(avatar_split_clause,[],[f200,f197,f105,f285]) ).

fof(f285,plain,
    ( spl13_40
  <=> ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | sK6(X0,X1,X2) = unordered_pair(singleton(sK7(X0,X1,X2)),unordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2)))
        | ~ in(X2,sK6(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).

fof(f200,plain,
    ( ! [X2,X0,X1] :
        ( sP0(X0,X1,X2)
        | sK6(X0,X1,X2) = unordered_pair(singleton(sK7(X0,X1,X2)),unordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2)))
        | ~ in(X2,sK6(X0,X1,X2)) )
    | ~ spl13_8
    | ~ spl13_25 ),
    inference(resolution,[],[f198,f106]) ).

fof(f281,plain,
    ( spl13_39
    | ~ spl13_10
    | ~ spl13_24 ),
    inference(avatar_split_clause,[],[f194,f191,f113,f279]) ).

fof(f279,plain,
    ( spl13_39
  <=> ! [X4,X0,X3,X2,X1] :
        ( unordered_pair(singleton(X0),unordered_pair(X1,X0)) != sK6(X2,X3,X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,X2)
        | ~ in(X0,X3)
        | ~ in(sK6(X2,X3,X4),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).

fof(f191,plain,
    ( spl13_24
  <=> ! [X4,X0,X5,X2,X1] :
        ( sK6(X0,X1,X2) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
        | sP0(X0,X1,X2)
        | ~ in(X5,X0)
        | ~ in(X4,X1)
        | ~ in(sK6(X0,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).

fof(f194,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( unordered_pair(singleton(X0),unordered_pair(X1,X0)) != sK6(X2,X3,X4)
        | sP0(X2,X3,X4)
        | ~ in(X1,X2)
        | ~ in(X0,X3)
        | ~ in(sK6(X2,X3,X4),X4) )
    | ~ spl13_10
    | ~ spl13_24 ),
    inference(superposition,[],[f192,f114]) ).

fof(f192,plain,
    ( ! [X2,X0,X1,X4,X5] :
        ( sK6(X0,X1,X2) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
        | sP0(X0,X1,X2)
        | ~ in(X5,X0)
        | ~ in(X4,X1)
        | ~ in(sK6(X0,X1,X2),X2) )
    | ~ spl13_24 ),
    inference(avatar_component_clause,[],[f191]) ).

fof(f267,plain,
    ( spl13_38
    | ~ spl13_9
    | ~ spl13_23 ),
    inference(avatar_split_clause,[],[f189,f186,f109,f265]) ).

fof(f109,plain,
    ( spl13_9
  <=> ! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).

fof(f189,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | unordered_pair(singleton(sK9(X2,X1,X0)),unordered_pair(sK10(X2,X1,X0),sK9(X2,X1,X0))) = X0 )
    | ~ spl13_9
    | ~ spl13_23 ),
    inference(resolution,[],[f187,f110]) ).

fof(f110,plain,
    ( ! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1))
    | ~ spl13_9 ),
    inference(avatar_component_clause,[],[f109]) ).

fof(f256,plain,
    ( spl13_37
    | ~ spl13_8
    | ~ spl13_28 ),
    inference(avatar_split_clause,[],[f220,f216,f105,f254]) ).

fof(f254,plain,
    ( spl13_37
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | ~ in(X2,sK10(X2,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).

fof(f220,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | ~ in(X2,sK10(X2,X1,X0)) )
    | ~ spl13_8
    | ~ spl13_28 ),
    inference(resolution,[],[f217,f106]) ).

fof(f252,plain,
    ( spl13_36
    | ~ spl13_9
    | ~ spl13_22 ),
    inference(avatar_split_clause,[],[f184,f181,f109,f250]) ).

fof(f184,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ in(X0,X1)
        | ~ in(X2,X3)
        | in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1)) )
    | ~ spl13_9
    | ~ spl13_22 ),
    inference(resolution,[],[f182,f110]) ).

fof(f248,plain,
    ( spl13_35
    | ~ spl13_8
    | ~ spl13_20 ),
    inference(avatar_split_clause,[],[f179,f169,f105,f246]) ).

fof(f246,plain,
    ( spl13_35
  <=> ! [X2,X0,X1] :
        ( in(sK8(X0,X1,X2),X0)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK6(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).

fof(f179,plain,
    ( ! [X2,X0,X1] :
        ( in(sK8(X0,X1,X2),X0)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK6(X0,X1,X2)) )
    | ~ spl13_8
    | ~ spl13_20 ),
    inference(resolution,[],[f170,f106]) ).

fof(f244,plain,
    ( spl13_34
    | ~ spl13_8
    | ~ spl13_20 ),
    inference(avatar_split_clause,[],[f178,f169,f105,f242]) ).

fof(f242,plain,
    ( spl13_34
  <=> ! [X2,X0,X1] :
        ( in(sK6(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X0,sK8(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).

fof(f178,plain,
    ( ! [X2,X0,X1] :
        ( in(sK6(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X0,sK8(X0,X1,X2)) )
    | ~ spl13_8
    | ~ spl13_20 ),
    inference(resolution,[],[f170,f106]) ).

fof(f240,plain,
    ( spl13_33
    | ~ spl13_8
    | ~ spl13_19 ),
    inference(avatar_split_clause,[],[f177,f165,f105,f238]) ).

fof(f238,plain,
    ( spl13_33
  <=> ! [X2,X0,X1] :
        ( in(sK7(X0,X1,X2),X1)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK6(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).

fof(f177,plain,
    ( ! [X2,X0,X1] :
        ( in(sK7(X0,X1,X2),X1)
        | sP0(X0,X1,X2)
        | ~ in(X2,sK6(X0,X1,X2)) )
    | ~ spl13_8
    | ~ spl13_19 ),
    inference(resolution,[],[f166,f106]) ).

fof(f236,plain,
    ( spl13_32
    | ~ spl13_8
    | ~ spl13_19 ),
    inference(avatar_split_clause,[],[f176,f165,f105,f234]) ).

fof(f234,plain,
    ( spl13_32
  <=> ! [X2,X0,X1] :
        ( in(sK6(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X1,sK7(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).

fof(f176,plain,
    ( ! [X2,X0,X1] :
        ( in(sK6(X0,X1,X2),X2)
        | sP0(X0,X1,X2)
        | ~ in(X1,sK7(X0,X1,X2)) )
    | ~ spl13_8
    | ~ spl13_19 ),
    inference(resolution,[],[f166,f106]) ).

fof(f232,plain,
    ( spl13_31
    | ~ spl13_8
    | ~ spl13_27 ),
    inference(avatar_split_clause,[],[f219,f212,f105,f230]) ).

fof(f230,plain,
    ( spl13_31
  <=> ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | ~ in(X1,sK9(X2,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).

fof(f219,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | ~ in(X1,sK9(X2,X1,X0)) )
    | ~ spl13_8
    | ~ spl13_27 ),
    inference(resolution,[],[f213,f106]) ).

fof(f228,plain,
    ( spl13_30
    | ~ spl13_8
    | ~ spl13_15 ),
    inference(avatar_split_clause,[],[f157,f141,f105,f226]) ).

fof(f226,plain,
    ( spl13_30
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1),X1)
        | X0 = X1
        | ~ in(X0,sK5(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).

fof(f157,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1),X1)
        | X0 = X1
        | ~ in(X0,sK5(X0,X1)) )
    | ~ spl13_8
    | ~ spl13_15 ),
    inference(resolution,[],[f142,f106]) ).

fof(f224,plain,
    ( spl13_29
    | ~ spl13_8
    | ~ spl13_15 ),
    inference(avatar_split_clause,[],[f156,f141,f105,f222]) ).

fof(f222,plain,
    ( spl13_29
  <=> ! [X0,X1] :
        ( in(sK5(X0,X1),X0)
        | X0 = X1
        | ~ in(X1,sK5(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).

fof(f156,plain,
    ( ! [X0,X1] :
        ( in(sK5(X0,X1),X0)
        | X0 = X1
        | ~ in(X1,sK5(X0,X1)) )
    | ~ spl13_8
    | ~ spl13_15 ),
    inference(resolution,[],[f142,f106]) ).

fof(f218,plain,
    ( spl13_28
    | ~ spl13_9
    | ~ spl13_18 ),
    inference(avatar_split_clause,[],[f163,f153,f109,f216]) ).

fof(f163,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | in(sK10(X2,X1,X0),X2) )
    | ~ spl13_9
    | ~ spl13_18 ),
    inference(resolution,[],[f154,f110]) ).

fof(f214,plain,
    ( spl13_27
    | ~ spl13_9
    | ~ spl13_17 ),
    inference(avatar_split_clause,[],[f162,f149,f109,f212]) ).

fof(f162,plain,
    ( ! [X2,X0,X1] :
        ( ~ in(X0,cartesian_product2(X1,X2))
        | in(sK9(X2,X1,X0),X1) )
    | ~ spl13_9
    | ~ spl13_17 ),
    inference(resolution,[],[f150,f110]) ).

fof(f208,plain,
    ( spl13_26
    | ~ spl13_10
    | ~ spl13_12 ),
    inference(avatar_split_clause,[],[f129,f126,f113,f206]) ).

fof(f129,plain,
    ( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0)))
    | ~ spl13_10
    | ~ spl13_12 ),
    inference(superposition,[],[f127,f114]) ).

fof(f199,plain,
    spl13_25,
    inference(avatar_split_clause,[],[f65,f197]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( sK6(X0,X1,X2) = unordered_pair(singleton(sK7(X0,X1,X2)),unordered_pair(sK8(X0,X1,X2),sK7(X0,X1,X2)))
      | sP0(X0,X1,X2)
      | in(sK6(X0,X1,X2),X2) ),
    inference(forward_demodulation,[],[f64,f37]) ).

fof(f37,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( sK6(X0,X1,X2) = unordered_pair(singleton(sK7(X0,X1,X2)),unordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)))
      | sP0(X0,X1,X2)
      | in(sK6(X0,X1,X2),X2) ),
    inference(forward_demodulation,[],[f58,f37]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | sK6(X0,X1,X2) = unordered_pair(unordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)),singleton(sK7(X0,X1,X2)))
      | in(sK6(X0,X1,X2),X2) ),
    inference(definition_unfolding,[],[f48,f38]) ).

fof(f38,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | sK6(X0,X1,X2) = ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2))
      | in(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != sK6(X0,X1,X2)
                | ~ in(X5,X0)
                | ~ in(X4,X1) )
            | ~ in(sK6(X0,X1,X2),X2) )
          & ( ( sK6(X0,X1,X2) = ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2))
              & in(sK8(X0,X1,X2),X0)
              & in(sK7(X0,X1,X2),X1) )
            | in(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X0)
                  | ~ in(X9,X1) ) )
            & ( ( ordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
                & in(sK10(X0,X1,X8),X0)
                & in(sK9(X0,X1,X8),X1) )
              | ~ in(X8,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f23,f26,f25,f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ! [X4,X5] :
                ( ordered_pair(X4,X5) != X3
                | ~ in(X5,X0)
                | ~ in(X4,X1) )
            | ~ in(X3,X2) )
          & ( ? [X6,X7] :
                ( ordered_pair(X6,X7) = X3
                & in(X7,X0)
                & in(X6,X1) )
            | in(X3,X2) ) )
     => ( ( ! [X5,X4] :
              ( ordered_pair(X4,X5) != sK6(X0,X1,X2)
              | ~ in(X5,X0)
              | ~ in(X4,X1) )
          | ~ in(sK6(X0,X1,X2),X2) )
        & ( ? [X7,X6] :
              ( ordered_pair(X6,X7) = sK6(X0,X1,X2)
              & in(X7,X0)
              & in(X6,X1) )
          | in(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ? [X7,X6] :
          ( ordered_pair(X6,X7) = sK6(X0,X1,X2)
          & in(X7,X0)
          & in(X6,X1) )
     => ( sK6(X0,X1,X2) = ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2))
        & in(sK8(X0,X1,X2),X0)
        & in(sK7(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1,X8] :
      ( ? [X11,X12] :
          ( ordered_pair(X11,X12) = X8
          & in(X12,X0)
          & in(X11,X1) )
     => ( ordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
        & in(sK10(X0,X1,X8),X0)
        & in(sK9(X0,X1,X8),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X0)
                  | ~ in(X4,X1) )
              | ~ in(X3,X2) )
            & ( ? [X6,X7] :
                  ( ordered_pair(X6,X7) = X3
                  & in(X7,X0)
                  & in(X6,X1) )
              | in(X3,X2) ) ) )
      & ( ! [X8] :
            ( ( in(X8,X2)
              | ! [X9,X10] :
                  ( ordered_pair(X9,X10) != X8
                  | ~ in(X10,X0)
                  | ~ in(X9,X1) ) )
            & ( ? [X11,X12] :
                  ( ordered_pair(X11,X12) = X8
                  & in(X12,X0)
                  & in(X11,X1) )
              | ~ in(X8,X2) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ? [X3] :
            ( ( ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) )
              | ~ in(X3,X2) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ! [X4,X5] :
                  ( ordered_pair(X4,X5) != X3
                  | ~ in(X5,X1)
                  | ~ in(X4,X0) ) )
            & ( ? [X4,X5] :
                  ( ordered_pair(X4,X5) = X3
                  & in(X5,X1)
                  & in(X4,X0) )
              | ~ in(X3,X2) ) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f193,plain,
    spl13_24,
    inference(avatar_split_clause,[],[f63,f191]) ).

fof(f63,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sK6(X0,X1,X2) != unordered_pair(singleton(X4),unordered_pair(X4,X5))
      | sP0(X0,X1,X2)
      | ~ in(X5,X0)
      | ~ in(X4,X1)
      | ~ in(sK6(X0,X1,X2),X2) ),
    inference(forward_demodulation,[],[f57,f37]) ).

fof(f57,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP0(X0,X1,X2)
      | sK6(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),singleton(X4))
      | ~ in(X5,X0)
      | ~ in(X4,X1)
      | ~ in(sK6(X0,X1,X2),X2) ),
    inference(definition_unfolding,[],[f49,f38]) ).

fof(f49,plain,
    ! [X2,X0,X1,X4,X5] :
      ( sP0(X0,X1,X2)
      | ordered_pair(X4,X5) != sK6(X0,X1,X2)
      | ~ in(X5,X0)
      | ~ in(X4,X1)
      | ~ in(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f188,plain,
    spl13_23,
    inference(avatar_split_clause,[],[f68,f186]) ).

fof(f68,plain,
    ! [X2,X0,X1,X8] :
      ( unordered_pair(singleton(sK9(X0,X1,X8)),unordered_pair(sK10(X0,X1,X8),sK9(X0,X1,X8))) = X8
      | ~ in(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(forward_demodulation,[],[f67,f37]) ).

fof(f67,plain,
    ! [X2,X0,X1,X8] :
      ( unordered_pair(singleton(sK9(X0,X1,X8)),unordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8))) = X8
      | ~ in(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(forward_demodulation,[],[f60,f37]) ).

fof(f60,plain,
    ! [X2,X0,X1,X8] :
      ( unordered_pair(unordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)),singleton(sK9(X0,X1,X8))) = X8
      | ~ in(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(definition_unfolding,[],[f44,f38]) ).

fof(f44,plain,
    ! [X2,X0,X1,X8] :
      ( ordered_pair(sK9(X0,X1,X8),sK10(X0,X1,X8)) = X8
      | ~ in(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f183,plain,
    spl13_22,
    inference(avatar_split_clause,[],[f66,f181]) ).

fof(f66,plain,
    ! [X2,X10,X0,X1,X9] :
      ( in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),X2)
      | ~ in(X10,X0)
      | ~ in(X9,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(forward_demodulation,[],[f61,f37]) ).

fof(f61,plain,
    ! [X2,X10,X0,X1,X9] :
      ( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
      | ~ in(X10,X0)
      | ~ in(X9,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(equality_resolution,[],[f59]) ).

fof(f59,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( in(X8,X2)
      | unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
      | ~ in(X10,X0)
      | ~ in(X9,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(definition_unfolding,[],[f45,f38]) ).

fof(f45,plain,
    ! [X2,X10,X0,X1,X8,X9] :
      ( in(X8,X2)
      | ordered_pair(X9,X10) != X8
      | ~ in(X10,X0)
      | ~ in(X9,X1)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f175,plain,
    ( spl13_21
    | ~ spl13_6
    | ~ spl13_10 ),
    inference(avatar_split_clause,[],[f122,f113,f97,f173]) ).

fof(f122,plain,
    ( ! [X0,X1] :
        ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2)) )
    | ~ spl13_6
    | ~ spl13_10 ),
    inference(superposition,[],[f98,f114]) ).

fof(f171,plain,
    spl13_20,
    inference(avatar_split_clause,[],[f47,f169]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | in(sK8(X0,X1,X2),X0)
      | in(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f167,plain,
    spl13_19,
    inference(avatar_split_clause,[],[f46,f165]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( sP0(X0,X1,X2)
      | in(sK7(X0,X1,X2),X1)
      | in(sK6(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f155,plain,
    spl13_18,
    inference(avatar_split_clause,[],[f43,f153]) ).

fof(f43,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK10(X0,X1,X8),X0)
      | ~ in(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f151,plain,
    spl13_17,
    inference(avatar_split_clause,[],[f42,f149]) ).

fof(f42,plain,
    ! [X2,X0,X1,X8] :
      ( in(sK9(X0,X1,X8),X1)
      | ~ in(X8,X2)
      | ~ sP0(X0,X1,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f147,plain,
    spl13_16,
    inference(avatar_split_clause,[],[f41,f145]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ in(sK5(X0,X1),X1)
      | ~ in(sK5(X0,X1),X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK5(X0,X1),X1)
          | ~ in(sK5(X0,X1),X0) )
        & ( in(sK5(X0,X1),X1)
          | in(sK5(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f19,f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK5(X0,X1),X1)
          | ~ in(sK5(X0,X1),X0) )
        & ( in(sK5(X0,X1),X1)
          | in(sK5(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).

fof(f143,plain,
    spl13_15,
    inference(avatar_split_clause,[],[f40,f141]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( X0 = X1
      | in(sK5(X0,X1),X1)
      | in(sK5(X0,X1),X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f139,plain,
    ( spl13_14
    | ~ spl13_7
    | ~ spl13_10 ),
    inference(avatar_split_clause,[],[f121,f113,f101,f137]) ).

fof(f121,plain,
    ( ! [X0,X1] :
        ( ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(sK3,sK4)) )
    | ~ spl13_7
    | ~ spl13_10 ),
    inference(superposition,[],[f102,f114]) ).

fof(f134,plain,
    spl13_13,
    inference(avatar_split_clause,[],[f51,f132]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( cartesian_product2(X0,X1) = X2
      | ~ sP0(X1,X0,X2) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( cartesian_product2(X0,X1) = X2
        | ~ sP0(X1,X0,X2) )
      & ( sP0(X1,X0,X2)
        | cartesian_product2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> sP0(X1,X0,X2) ),
    inference(definition_folding,[],[f3,f14]) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ? [X4,X5] :
              ( ordered_pair(X4,X5) = X3
              & in(X5,X1)
              & in(X4,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).

fof(f128,plain,
    ( spl13_12
    | ~ spl13_10
    | ~ spl13_11 ),
    inference(avatar_split_clause,[],[f120,f117,f113,f126]) ).

fof(f117,plain,
    ( spl13_11
  <=> ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).

fof(f120,plain,
    ( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
    | ~ spl13_10
    | ~ spl13_11 ),
    inference(forward_demodulation,[],[f118,f114]) ).

fof(f118,plain,
    ( ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0)))
    | ~ spl13_11 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f119,plain,
    spl13_11,
    inference(avatar_split_clause,[],[f56,f117]) ).

fof(f56,plain,
    ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))),
    inference(definition_unfolding,[],[f36,f38]) ).

fof(f36,plain,
    ! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).

fof(f115,plain,
    spl13_10,
    inference(avatar_split_clause,[],[f37,f113]) ).

fof(f111,plain,
    spl13_9,
    inference(avatar_split_clause,[],[f62,f109]) ).

fof(f62,plain,
    ! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)),
    inference(equality_resolution,[],[f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X0,X2)
      | cartesian_product2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f107,plain,
    spl13_8,
    inference(avatar_split_clause,[],[f39,f105]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f103,plain,
    ( spl13_7
    | ~ spl13_5 ),
    inference(avatar_split_clause,[],[f95,f91,f101]) ).

fof(f91,plain,
    ( spl13_5
  <=> ! [X4,X5] :
        ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK1,sK2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).

fof(f95,plain,
    ( ! [X4,X5] :
        ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK1,sK2))
        | in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK3,sK4)) )
    | ~ spl13_5 ),
    inference(forward_demodulation,[],[f94,f37]) ).

fof(f94,plain,
    ( ! [X4,X5] :
        ( in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK1,sK2)) )
    | ~ spl13_5 ),
    inference(forward_demodulation,[],[f92,f37]) ).

fof(f92,plain,
    ( ! [X4,X5] :
        ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK3,sK4))
        | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK1,sK2)) )
    | ~ spl13_5 ),
    inference(avatar_component_clause,[],[f91]) ).

fof(f99,plain,
    ( spl13_6
    | ~ spl13_4 ),
    inference(avatar_split_clause,[],[f89,f85,f97]) ).

fof(f85,plain,
    ( spl13_4
  <=> ! [X4,X5] :
        ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK3,sK4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).

fof(f89,plain,
    ( ! [X4,X5] :
        ( ~ in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK3,sK4))
        | in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK1,sK2)) )
    | ~ spl13_4 ),
    inference(forward_demodulation,[],[f88,f37]) ).

fof(f88,plain,
    ( ! [X4,X5] :
        ( in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK3,sK4)) )
    | ~ spl13_4 ),
    inference(forward_demodulation,[],[f86,f37]) ).

fof(f86,plain,
    ( ! [X4,X5] :
        ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK1,sK2))
        | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK3,sK4)) )
    | ~ spl13_4 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f93,plain,
    spl13_5,
    inference(avatar_split_clause,[],[f55,f91]) ).

fof(f55,plain,
    ! [X4,X5] :
      ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK3,sK4))
      | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK1,sK2)) ),
    inference(definition_unfolding,[],[f33,f38,f38]) ).

fof(f33,plain,
    ! [X4,X5] :
      ( in(ordered_pair(X4,X5),cartesian_product2(sK3,sK4))
      | ~ in(ordered_pair(X4,X5),cartesian_product2(sK1,sK2)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( cartesian_product2(sK1,sK2) != cartesian_product2(sK3,sK4)
    & ! [X4,X5] :
        ( ( in(ordered_pair(X4,X5),cartesian_product2(sK1,sK2))
          | ~ in(ordered_pair(X4,X5),cartesian_product2(sK3,sK4)) )
        & ( in(ordered_pair(X4,X5),cartesian_product2(sK3,sK4))
          | ~ in(ordered_pair(X4,X5),cartesian_product2(sK1,sK2)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0,X1,X2,X3] :
        ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
        & ! [X4,X5] :
            ( ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
              | ~ in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
            & ( in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
              | ~ in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) ) ) )
   => ( cartesian_product2(sK1,sK2) != cartesian_product2(sK3,sK4)
      & ! [X5,X4] :
          ( ( in(ordered_pair(X4,X5),cartesian_product2(sK1,sK2))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(sK3,sK4)) )
          & ( in(ordered_pair(X4,X5),cartesian_product2(sK3,sK4))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(sK1,sK2)) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
      & ! [X4,X5] :
          ( ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
          & ( in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
            | ~ in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) ) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ? [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
      & ! [X4,X5] :
          ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
        <=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) ) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ! [X4,X5] :
            ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
          <=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
       => cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0,X1,X2,X3] :
      ( ! [X4,X5] :
          ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
        <=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
     => cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t108_zfmisc_1) ).

fof(f87,plain,
    spl13_4,
    inference(avatar_split_clause,[],[f54,f85]) ).

fof(f54,plain,
    ! [X4,X5] :
      ( in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK1,sK2))
      | ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),cartesian_product2(sK3,sK4)) ),
    inference(definition_unfolding,[],[f34,f38,f38]) ).

fof(f34,plain,
    ! [X4,X5] :
      ( in(ordered_pair(X4,X5),cartesian_product2(sK1,sK2))
      | ~ in(ordered_pair(X4,X5),cartesian_product2(sK3,sK4)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f83,plain,
    spl13_3,
    inference(avatar_split_clause,[],[f53,f80]) ).

fof(f80,plain,
    ( spl13_3
  <=> empty(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).

fof(f53,plain,
    empty(sK12),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    empty(sK12),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f6,f31]) ).

fof(f31,plain,
    ( ? [X0] : empty(X0)
   => empty(sK12) ),
    introduced(choice_axiom,[]) ).

fof(f6,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f78,plain,
    ~ spl13_2,
    inference(avatar_split_clause,[],[f52,f75]) ).

fof(f75,plain,
    ( spl13_2
  <=> empty(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).

fof(f52,plain,
    ~ empty(sK11),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ~ empty(sK11),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f7,f29]) ).

fof(f29,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK11) ),
    introduced(choice_axiom,[]) ).

fof(f7,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f73,plain,
    ~ spl13_1,
    inference(avatar_split_clause,[],[f35,f70]) ).

fof(f35,plain,
    cartesian_product2(sK1,sK2) != cartesian_product2(sK3,sK4),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : SET955+1 : TPTP v8.2.0. Bugfixed v4.0.0.
% 0.13/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n019.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Mon May 20 12:50:08 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (20428)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (20431)WARNING: value z3 for option sas not known
% 0.15/0.39  % (20432)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (20430)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (20429)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (20433)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)
% 0.15/0.39  % (20431)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)
% 0.15/0.39  % (20434)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)
% 0.15/0.39  % (20435)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)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.40  TRYING [1]
% 0.15/0.40  TRYING [3]
% 0.15/0.40  TRYING [2]
% 0.22/0.42  TRYING [3]
% 0.22/0.51  TRYING [4]
% 0.22/0.51  TRYING [4]
% 5.64/1.19  TRYING [5]
% 7.65/1.49  TRYING [1]
% 7.65/1.49  TRYING [2]
% 7.96/1.49  TRYING [3]
% 7.96/1.51  TRYING [4]
% 8.32/1.61  TRYING [5]
% 13.47/2.30  % (20433)First to succeed.
% 13.47/2.34  % (20433)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20428"
% 13.47/2.34  % (20433)Refutation found. Thanks to Tanya!
% 13.47/2.34  % SZS status Theorem for theBenchmark
% 13.47/2.34  % SZS output start Proof for theBenchmark
% See solution above
% 13.47/2.35  % (20433)------------------------------
% 13.47/2.35  % (20433)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 13.47/2.35  % (20433)Termination reason: Refutation
% 13.47/2.35  
% 13.47/2.35  % (20433)Memory used [KB]: 18953
% 13.47/2.35  % (20433)Time elapsed: 1.951 s
% 13.47/2.35  % (20433)Instructions burned: 6902 (million)
% 13.47/2.35  % (20428)Success in time 1.96 s
%------------------------------------------------------------------------------