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