TSTP Solution File: SET787-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET787-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:18:56 EDT 2024
% Result : Unsatisfiable 0.16s 0.45s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 147
% Syntax : Number of formulae : 455 ( 16 unt; 0 def)
% Number of atoms : 1450 ( 245 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1842 ( 847 ~; 860 |; 0 &)
% ( 135 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 138 ( 136 usr; 136 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-2 aty)
% Number of variables : 641 ( 641 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1684,plain,
$false,
inference(avatar_sat_refutation,[],[f19,f24,f28,f32,f36,f42,f46,f51,f56,f60,f64,f68,f72,f79,f89,f93,f102,f112,f116,f126,f130,f144,f152,f161,f165,f169,f191,f195,f209,f213,f217,f242,f246,f260,f271,f275,f285,f295,f302,f306,f321,f325,f329,f360,f364,f368,f389,f393,f404,f437,f441,f460,f471,f475,f511,f523,f577,f581,f585,f589,f593,f597,f653,f657,f661,f665,f705,f709,f713,f735,f748,f752,f756,f760,f772,f800,f813,f817,f821,f825,f837,f866,f870,f874,f905,f909,f913,f935,f939,f943,f947,f951,f972,f1002,f1015,f1027,f1040,f1049,f1054,f1074,f1078,f1098,f1102,f1106,f1111,f1115,f1119,f1161,f1165,f1169,f1173,f1209,f1213,f1217,f1249,f1253,f1273,f1277,f1281,f1285,f1295,f1326,f1330,f1350,f1363,f1371,f1393,f1397,f1418,f1430,f1435,f1455,f1459,f1667,f1671,f1683]) ).
fof(f1683,plain,
( ~ spl0_2
| spl0_14
| ~ spl0_6
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1367,f1042,f40,f76,f21]) ).
fof(f21,plain,
( spl0_2
<=> member(sk2,union(cons(a,cons(b,eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f76,plain,
( spl0_14
<=> member(sk2,b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f40,plain,
( spl0_6
<=> ! [X0,X1] :
( ~ member(X0,union(X1))
| member(X0,unionE_sk1(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1042,plain,
( spl0_98
<=> b = unionE_sk1(sk2,cons(a,cons(b,eptset))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1367,plain,
( member(sk2,b)
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| ~ spl0_6
| ~ spl0_98 ),
inference(superposition,[],[f41,f1044]) ).
fof(f1044,plain,
( b = unionE_sk1(sk2,cons(a,cons(b,eptset)))
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f41,plain,
( ! [X0,X1] :
( member(X0,unionE_sk1(X0,X1))
| ~ member(X0,union(X1)) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f1671,plain,
( spl0_135
| ~ spl0_10
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f314,f304,f58,f1669]) ).
fof(f1669,plain,
( spl0_135
<=> ! [X2,X0,X1] :
( unionE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),converse(X2)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),converse(X2))),converseE_sk1(unionE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),converse(X2))))
| ~ member(pair(X1,X0),union(converse(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f58,plain,
( spl0_10
<=> ! [X4,X0,X1] :
( ~ member(pair(X0,X1),X4)
| member(pair(X1,X0),converse(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f304,plain,
( spl0_40
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1))),converseE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1))))
| ~ member(X0,converse(union(converse(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f314,plain,
( ! [X2,X0,X1] :
( unionE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),converse(X2)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),converse(X2))),converseE_sk1(unionE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),converse(X2))))
| ~ member(pair(X1,X0),union(converse(X2))) )
| ~ spl0_10
| ~ spl0_40 ),
inference(resolution,[],[f305,f59]) ).
fof(f59,plain,
( ! [X0,X1,X4] :
( member(pair(X1,X0),converse(X4))
| ~ member(pair(X0,X1),X4) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f305,plain,
( ! [X0,X1] :
( ~ member(X0,converse(union(converse(X1))))
| unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1))),converseE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)))) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f1667,plain,
( spl0_134
| ~ spl0_13
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f310,f300,f70,f1665]) ).
fof(f1665,plain,
( spl0_134
<=> ! [X0,X1] :
( unionE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),union(converse(X1))),converse(X1)) = pair(converseE_sk2(unionE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),union(converse(X1))),converse(X1))),converseE_sk1(unionE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),union(converse(X1))),converse(X1))))
| ~ member(X0,converse(union(union(converse(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f70,plain,
( spl0_13
<=> ! [X7,X8] :
( ~ member(X8,converse(X7))
| member(pair(converse_sk1(X8),converse_sk2(X8)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f300,plain,
( spl0_39
<=> ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1)) = pair(converseE_sk2(unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1))),converseE_sk1(unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1))))
| ~ member(X0,union(union(converse(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f310,plain,
( ! [X0,X1] :
( unionE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),union(converse(X1))),converse(X1)) = pair(converseE_sk2(unionE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),union(converse(X1))),converse(X1))),converseE_sk1(unionE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),union(converse(X1))),converse(X1))))
| ~ member(X0,converse(union(union(converse(X1))))) )
| ~ spl0_13
| ~ spl0_39 ),
inference(resolution,[],[f301,f71]) ).
fof(f71,plain,
( ! [X8,X7] :
( member(pair(converse_sk1(X8),converse_sk2(X8)),X7)
| ~ member(X8,converse(X7)) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f301,plain,
( ! [X0,X1] :
( ~ member(X0,union(union(converse(X1))))
| unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1)) = pair(converseE_sk2(unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1))),converseE_sk1(unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1)))) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f1459,plain,
( spl0_133
| ~ spl0_11
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f406,f402,f62,f1457]) ).
fof(f1457,plain,
( spl0_133
<=> ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(X2))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(X2)))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(X2)))))
| member(pair(converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(X2))))),converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(X2)))))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f62,plain,
( spl0_11
<=> ! [X2,X7,X3] :
( member(pair(X3,X2),X7)
| ~ member(pair(X2,X3),converse(X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f402,plain,
( spl0_49
<=> ! [X2,X0,X1] :
( member(pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,X2)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,X2))))),X2)
| pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,X2)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,X2))))) = X1
| ~ member(X0,union(converse(cons(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f406,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(X2))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(X2)))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(X2)))))
| member(pair(converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(X2))))),converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(X2)))))),X2) )
| ~ spl0_11
| ~ spl0_49 ),
inference(resolution,[],[f403,f63]) ).
fof(f63,plain,
( ! [X2,X3,X7] :
( ~ member(pair(X2,X3),converse(X7))
| member(pair(X3,X2),X7) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f403,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,X2)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,X2))))),X2)
| pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,X2)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,X2))))) = X1
| ~ member(X0,union(converse(cons(X1,X2)))) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f1455,plain,
( spl0_132
| ~ spl0_7
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f276,f273,f44,f1453]) ).
fof(f1453,plain,
( spl0_132
<=> ! [X2,X0,X1] :
( member(pair(converse_sk2(unionE_sk1(X0,converse(converse(cons(X1,X2))))),converse_sk1(unionE_sk1(X0,converse(converse(cons(X1,X2)))))),X2)
| pair(converse_sk2(unionE_sk1(X0,converse(converse(cons(X1,X2))))),converse_sk1(unionE_sk1(X0,converse(converse(cons(X1,X2)))))) = X1
| ~ member(X0,union(converse(converse(cons(X1,X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f44,plain,
( spl0_7
<=> ! [X0,X1] :
( ~ member(X0,union(X1))
| member(unionE_sk1(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f273,plain,
( spl0_36
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(converse(cons(X1,X2))))
| member(pair(converse_sk2(X0),converse_sk1(X0)),X2)
| pair(converse_sk2(X0),converse_sk1(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f276,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk2(unionE_sk1(X0,converse(converse(cons(X1,X2))))),converse_sk1(unionE_sk1(X0,converse(converse(cons(X1,X2)))))),X2)
| pair(converse_sk2(unionE_sk1(X0,converse(converse(cons(X1,X2))))),converse_sk1(unionE_sk1(X0,converse(converse(cons(X1,X2)))))) = X1
| ~ member(X0,union(converse(converse(cons(X1,X2))))) )
| ~ spl0_7
| ~ spl0_36 ),
inference(resolution,[],[f274,f45]) ).
fof(f45,plain,
( ! [X0,X1] :
( member(unionE_sk1(X0,X1),X1)
| ~ member(X0,union(X1)) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f274,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(converse(cons(X1,X2))))
| member(pair(converse_sk2(X0),converse_sk1(X0)),X2)
| pair(converse_sk2(X0),converse_sk1(X0)) = X1 )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f1435,plain,
( spl0_131
| ~ spl0_16
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f499,f473,f91,f1433]) ).
fof(f1433,plain,
( spl0_131
<=> ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,converse(eptset)))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,converse(eptset))))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,converse(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,converse(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f91,plain,
( spl0_16
<=> ! [X0] : ~ member(X0,converse(eptset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f473,plain,
( spl0_54
<=> ! [X0,X3,X2,X1] :
( member(pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,X3))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))))),X3)
| pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,X3))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,X3))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f499,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,converse(eptset)))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,converse(eptset))))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,converse(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,converse(eptset)))))) )
| ~ spl0_16
| ~ spl0_54 ),
inference(resolution,[],[f474,f92]) ).
fof(f92,plain,
( ! [X0] : ~ member(X0,converse(eptset))
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f474,plain,
( ! [X2,X3,X0,X1] :
( member(pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,X3))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))))),X3)
| pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,X3))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,X3))))) )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f1430,plain,
( spl0_130
| ~ spl0_15
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f488,f473,f87,f1428]) ).
fof(f1428,plain,
( spl0_130
<=> ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,union(eptset)))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,union(eptset))))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,union(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,union(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f87,plain,
( spl0_15
<=> ! [X0] : ~ member(X0,union(eptset)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f488,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,union(eptset)))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,union(eptset))))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,union(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,union(eptset)))))) )
| ~ spl0_15
| ~ spl0_54 ),
inference(resolution,[],[f474,f88]) ).
fof(f88,plain,
( ! [X0] : ~ member(X0,union(eptset))
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f1418,plain,
( spl0_129
| ~ spl0_7
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f286,f283,f44,f1416]) ).
fof(f1416,plain,
( spl0_129
<=> ! [X0,X1] :
( pair(converse_sk2(unionE_sk1(X0,converse(X1))),converse_sk1(unionE_sk1(X0,converse(X1)))) = pair(converseE_sk2(pair(converse_sk2(unionE_sk1(X0,converse(X1))),converse_sk1(unionE_sk1(X0,converse(X1))))),converseE_sk1(pair(converse_sk2(unionE_sk1(X0,converse(X1))),converse_sk1(unionE_sk1(X0,converse(X1))))))
| ~ member(X0,union(converse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f283,plain,
( spl0_37
<=> ! [X0,X1] :
( pair(converse_sk2(X0),converse_sk1(X0)) = pair(converseE_sk2(pair(converse_sk2(X0),converse_sk1(X0))),converseE_sk1(pair(converse_sk2(X0),converse_sk1(X0))))
| ~ member(X0,converse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f286,plain,
( ! [X0,X1] :
( pair(converse_sk2(unionE_sk1(X0,converse(X1))),converse_sk1(unionE_sk1(X0,converse(X1)))) = pair(converseE_sk2(pair(converse_sk2(unionE_sk1(X0,converse(X1))),converse_sk1(unionE_sk1(X0,converse(X1))))),converseE_sk1(pair(converse_sk2(unionE_sk1(X0,converse(X1))),converse_sk1(unionE_sk1(X0,converse(X1))))))
| ~ member(X0,union(converse(X1))) )
| ~ spl0_7
| ~ spl0_37 ),
inference(resolution,[],[f284,f45]) ).
fof(f284,plain,
( ! [X0,X1] :
( ~ member(X0,converse(X1))
| pair(converse_sk2(X0),converse_sk1(X0)) = pair(converseE_sk2(pair(converse_sk2(X0),converse_sk1(X0))),converseE_sk1(pair(converse_sk2(X0),converse_sk1(X0)))) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f1397,plain,
( spl0_128
| ~ spl0_3
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f493,f473,f26,f1395]) ).
fof(f1395,plain,
( spl0_128
<=> ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,eptset))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,eptset)))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,eptset)))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f26,plain,
( spl0_3
<=> ! [X6] : ~ member(X6,eptset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,eptset))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,eptset)))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,eptset)))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,eptset))))) )
| ~ spl0_3
| ~ spl0_54 ),
inference(resolution,[],[f474,f27]) ).
fof(f27,plain,
( ! [X6] : ~ member(X6,eptset)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f26]) ).
fof(f1393,plain,
( spl0_127
| ~ spl0_30
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f279,f273,f211,f1391]) ).
fof(f1391,plain,
( spl0_127
<=> ! [X2,X0,X1] :
( member(pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))),X1)
| pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))) = X2
| ~ member(X0,converse(converse(converse(converse(converse(cons(X2,X1))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f211,plain,
( spl0_30
<=> ! [X0,X1] :
( ~ member(X0,converse(converse(converse(X1))))
| member(pair(converse_sk1(X0),converse_sk2(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f279,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))),X1)
| pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))) = X2
| ~ member(X0,converse(converse(converse(converse(converse(cons(X2,X1))))))) )
| ~ spl0_30
| ~ spl0_36 ),
inference(resolution,[],[f274,f212]) ).
fof(f212,plain,
( ! [X0,X1] :
( member(pair(converse_sk1(X0),converse_sk2(X0)),X1)
| ~ member(X0,converse(converse(converse(X1)))) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f1371,plain,
( spl0_126
| ~ spl0_17
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f281,f273,f100,f1369]) ).
fof(f1369,plain,
( spl0_126
<=> ! [X2,X0,X1] :
( member(pair(converse_sk2(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk1(pair(converse_sk2(X0),converse_sk1(X0)))),X1)
| pair(converse_sk2(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk1(pair(converse_sk2(X0),converse_sk1(X0)))) = X2
| ~ member(X0,converse(converse(converse(converse(cons(X2,X1)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f100,plain,
( spl0_17
<=> ! [X0,X1] :
( ~ member(X0,converse(converse(X1)))
| member(pair(converse_sk2(X0),converse_sk1(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f281,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk2(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk1(pair(converse_sk2(X0),converse_sk1(X0)))),X1)
| pair(converse_sk2(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk1(pair(converse_sk2(X0),converse_sk1(X0)))) = X2
| ~ member(X0,converse(converse(converse(converse(cons(X2,X1)))))) )
| ~ spl0_17
| ~ spl0_36 ),
inference(resolution,[],[f274,f101]) ).
fof(f101,plain,
( ! [X0,X1] :
( member(pair(converse_sk2(X0),converse_sk1(X0)),X1)
| ~ member(X0,converse(converse(X1))) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f1363,plain,
( spl0_125
| ~ spl0_21
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f228,f211,f128,f1361]) ).
fof(f1361,plain,
( spl0_125
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(converse(converse(converse(cons(X1,X2))))))
| member(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))),X2)
| pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f128,plain,
( spl0_21
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(cons(X1,X2)))
| member(pair(converse_sk1(X0),converse_sk2(X0)),X2)
| pair(converse_sk1(X0),converse_sk2(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f228,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(converse(converse(converse(cons(X1,X2))))))
| member(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))),X2)
| pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))) = X1 )
| ~ spl0_21
| ~ spl0_30 ),
inference(resolution,[],[f212,f129]) ).
fof(f129,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(cons(X1,X2)))
| member(pair(converse_sk1(X0),converse_sk2(X0)),X2)
| pair(converse_sk1(X0),converse_sk2(X0)) = X1 )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f1350,plain,
( spl0_124
| ~ spl0_13
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f280,f273,f70,f1348]) ).
fof(f1348,plain,
( spl0_124
<=> ! [X2,X0,X1] :
( member(pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))),X1)
| pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))) = X2
| ~ member(X0,converse(converse(converse(cons(X2,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f280,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))),X1)
| pair(converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk1(pair(converse_sk1(X0),converse_sk2(X0)))) = X2
| ~ member(X0,converse(converse(converse(cons(X2,X1))))) )
| ~ spl0_13
| ~ spl0_36 ),
inference(resolution,[],[f274,f71]) ).
fof(f1330,plain,
( spl0_123
| ~ spl0_20
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f253,f244,f124,f1328]) ).
fof(f1328,plain,
( spl0_123
<=> ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(cons(X2,converse(eptset))))),cons(X2,converse(eptset))) = X2
| unionE_sk1(X0,cons(X1,union(cons(X2,converse(eptset))))) = X1
| ~ member(X0,union(cons(X1,union(cons(X2,converse(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f124,plain,
( spl0_20
<=> ! [X2,X0,X1] :
( member(unionE_sk1(X0,cons(X1,X2)),X2)
| unionE_sk1(X0,cons(X1,X2)) = X1
| ~ member(X0,union(cons(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f244,plain,
( spl0_33
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(eptset))) = X1
| ~ member(X0,union(cons(X1,converse(eptset)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f253,plain,
( ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(cons(X2,converse(eptset))))),cons(X2,converse(eptset))) = X2
| unionE_sk1(X0,cons(X1,union(cons(X2,converse(eptset))))) = X1
| ~ member(X0,union(cons(X1,union(cons(X2,converse(eptset)))))) )
| ~ spl0_20
| ~ spl0_33 ),
inference(resolution,[],[f245,f125]) ).
fof(f125,plain,
( ! [X2,X0,X1] :
( member(unionE_sk1(X0,cons(X1,X2)),X2)
| unionE_sk1(X0,cons(X1,X2)) = X1
| ~ member(X0,union(cons(X1,X2))) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f245,plain,
( ! [X0,X1] :
( ~ member(X0,union(cons(X1,converse(eptset))))
| unionE_sk1(X0,cons(X1,converse(eptset))) = X1 )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f1326,plain,
( spl0_122
| ~ spl0_20
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f248,f240,f124,f1324]) ).
fof(f1324,plain,
( spl0_122
<=> ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(cons(X2,union(eptset))))),cons(X2,union(eptset))) = X2
| unionE_sk1(X0,cons(X1,union(cons(X2,union(eptset))))) = X1
| ~ member(X0,union(cons(X1,union(cons(X2,union(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f240,plain,
( spl0_32
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,union(eptset))) = X1
| ~ member(X0,union(cons(X1,union(eptset)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f248,plain,
( ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(cons(X2,union(eptset))))),cons(X2,union(eptset))) = X2
| unionE_sk1(X0,cons(X1,union(cons(X2,union(eptset))))) = X1
| ~ member(X0,union(cons(X1,union(cons(X2,union(eptset)))))) )
| ~ spl0_20
| ~ spl0_32 ),
inference(resolution,[],[f241,f125]) ).
fof(f241,plain,
( ! [X0,X1] :
( ~ member(X0,union(cons(X1,union(eptset))))
| unionE_sk1(X0,cons(X1,union(eptset))) = X1 )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f1295,plain,
( ~ spl0_2
| spl0_8
| ~ spl0_6
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1237,f1046,f40,f48,f21]) ).
fof(f48,plain,
( spl0_8
<=> member(sk2,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1046,plain,
( spl0_99
<=> a = unionE_sk1(sk2,cons(a,cons(b,eptset))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1237,plain,
( member(sk2,a)
| ~ member(sk2,union(cons(a,cons(b,eptset))))
| ~ spl0_6
| ~ spl0_99 ),
inference(superposition,[],[f41,f1048]) ).
fof(f1048,plain,
( a = unionE_sk1(sk2,cons(a,cons(b,eptset)))
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f1285,plain,
( spl0_121
| ~ spl0_10
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f382,f366,f58,f1283]) ).
fof(f1283,plain,
( spl0_121
<=> ! [X2,X0,X1] :
( pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = pair(converseE_sk2(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))),converseE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))))
| ~ member(pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f366,plain,
( spl0_46
<=> ! [X2,X0,X1] :
( pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = pair(converseE_sk2(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))),converseE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))))
| ~ member(pair(X1,X0),converse(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f382,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = pair(converseE_sk2(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))),converseE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))))
| ~ member(pair(X0,X1),X2) )
| ~ spl0_10
| ~ spl0_46 ),
inference(resolution,[],[f367,f59]) ).
fof(f367,plain,
( ! [X2,X0,X1] :
( ~ member(pair(X1,X0),converse(X2))
| pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = pair(converseE_sk2(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))),converseE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))))) )
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f1281,plain,
( spl0_120
| ~ spl0_13
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f297,f293,f70,f1279]) ).
fof(f1279,plain,
( spl0_120
<=> ! [X2,X0,X1] :
( pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))) = X1
| member(pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))),X2)
| ~ member(X0,converse(cons(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f293,plain,
( spl0_38
<=> ! [X0,X3,X2,X1] :
( member(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),X2)
| pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = X3
| ~ member(pair(X1,X0),cons(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f297,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))) = X1
| member(pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))),X2)
| ~ member(X0,converse(cons(X1,X2))) )
| ~ spl0_13
| ~ spl0_38 ),
inference(resolution,[],[f294,f71]) ).
fof(f294,plain,
( ! [X2,X3,X0,X1] :
( ~ member(pair(X1,X0),cons(X3,X2))
| pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = X3
| member(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),X2) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f1277,plain,
( spl0_119
| ~ spl0_10
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f288,f283,f58,f1275]) ).
fof(f1275,plain,
( spl0_119
<=> ! [X2,X0,X1] :
( pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1))) = pair(converseE_sk2(pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1)))),converseE_sk1(pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1)))))
| ~ member(pair(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f288,plain,
( ! [X2,X0,X1] :
( pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1))) = pair(converseE_sk2(pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1)))),converseE_sk1(pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1)))))
| ~ member(pair(X1,X0),X2) )
| ~ spl0_10
| ~ spl0_37 ),
inference(resolution,[],[f284,f59]) ).
fof(f1273,plain,
( spl0_118
| ~ spl0_22
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f221,f211,f142,f1271]) ).
fof(f1271,plain,
( spl0_118
<=> ! [X0,X1] :
( ~ member(X0,converse(converse(converse(union(converse(X1))))))
| unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1))),converseE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f142,plain,
( spl0_22
<=> ! [X0,X1] :
( unionE_sk1(X0,converse(X1)) = pair(converseE_sk2(unionE_sk1(X0,converse(X1))),converseE_sk1(unionE_sk1(X0,converse(X1))))
| ~ member(X0,union(converse(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f221,plain,
( ! [X0,X1] :
( ~ member(X0,converse(converse(converse(union(converse(X1))))))
| unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1))),converseE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)))) )
| ~ spl0_22
| ~ spl0_30 ),
inference(resolution,[],[f212,f143]) ).
fof(f143,plain,
( ! [X0,X1] :
( ~ member(X0,union(converse(X1)))
| unionE_sk1(X0,converse(X1)) = pair(converseE_sk2(unionE_sk1(X0,converse(X1))),converseE_sk1(unionE_sk1(X0,converse(X1)))) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f1253,plain,
( spl0_117
| ~ spl0_28
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f349,f323,f193,f1251]) ).
fof(f1251,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(converse(converse(eptset)))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(converse(eptset)))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(converse(eptset)))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f193,plain,
( spl0_28
<=> ! [X0] : ~ member(X0,converse(converse(converse(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f323,plain,
( spl0_42
<=> ! [X0,X3,X2,X1] :
( unionE_sk1(X0,cons(X1,cons(X2,X3))) = X1
| ~ member(X0,union(cons(X1,cons(X2,X3))))
| member(unionE_sk1(X0,cons(X1,cons(X2,X3))),X3)
| unionE_sk1(X0,cons(X1,cons(X2,X3))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f349,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(converse(converse(eptset)))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(converse(eptset)))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(converse(eptset)))))) = X2 )
| ~ spl0_28
| ~ spl0_42 ),
inference(resolution,[],[f324,f194]) ).
fof(f194,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(eptset))))
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f324,plain,
( ! [X2,X3,X0,X1] :
( member(unionE_sk1(X0,cons(X1,cons(X2,X3))),X3)
| ~ member(X0,union(cons(X1,cons(X2,X3))))
| unionE_sk1(X0,cons(X1,cons(X2,X3))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,X3))) = X2 )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f1249,plain,
( spl0_116
| ~ spl0_27
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f346,f323,f189,f1247]) ).
fof(f1247,plain,
( spl0_116
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(converse(union(eptset)))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(union(eptset)))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(union(eptset)))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f189,plain,
( spl0_27
<=> ! [X0] : ~ member(X0,converse(converse(union(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f346,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(converse(union(eptset)))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(union(eptset)))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(union(eptset)))))) = X2 )
| ~ spl0_27
| ~ spl0_42 ),
inference(resolution,[],[f324,f190]) ).
fof(f190,plain,
( ! [X0] : ~ member(X0,converse(converse(union(eptset))))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f1217,plain,
( spl0_115
| ~ spl0_28
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f432,f402,f193,f1215]) ).
fof(f1215,plain,
( spl0_115
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(converse(converse(eptset))))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(converse(converse(eptset)))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(converse(converse(eptset))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f432,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(converse(converse(eptset))))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(converse(converse(eptset)))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(converse(converse(eptset))))))) )
| ~ spl0_28
| ~ spl0_49 ),
inference(resolution,[],[f403,f194]) ).
fof(f1213,plain,
( spl0_114
| ~ spl0_27
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f427,f402,f189,f1211]) ).
fof(f1211,plain,
( spl0_114
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(converse(union(eptset))))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(converse(union(eptset)))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(converse(union(eptset))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f427,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(converse(union(eptset))))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(converse(union(eptset)))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(converse(union(eptset))))))) )
| ~ spl0_27
| ~ spl0_49 ),
inference(resolution,[],[f403,f190]) ).
fof(f1209,plain,
( spl0_113
| ~ spl0_20
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f235,f215,f124,f1207]) ).
fof(f1207,plain,
( spl0_113
<=> ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(cons(X2,eptset)))),cons(X2,eptset)) = X2
| unionE_sk1(X0,cons(X1,union(cons(X2,eptset)))) = X1
| ~ member(X0,union(cons(X1,union(cons(X2,eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f215,plain,
( spl0_31
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,eptset)) = X1
| ~ member(X0,union(cons(X1,eptset))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f235,plain,
( ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(cons(X2,eptset)))),cons(X2,eptset)) = X2
| unionE_sk1(X0,cons(X1,union(cons(X2,eptset)))) = X1
| ~ member(X0,union(cons(X1,union(cons(X2,eptset))))) )
| ~ spl0_20
| ~ spl0_31 ),
inference(resolution,[],[f216,f125]) ).
fof(f216,plain,
( ! [X0,X1] :
( ~ member(X0,union(cons(X1,eptset)))
| unionE_sk1(X0,cons(X1,eptset)) = X1 )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f1173,plain,
( spl0_112
| ~ spl0_26
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f348,f323,f167,f1171]) ).
fof(f1171,plain,
( spl0_112
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(converse(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(eptset))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f167,plain,
( spl0_26
<=> ! [X0] : ~ member(X0,converse(converse(eptset))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f348,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(converse(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(converse(eptset))))) = X2 )
| ~ spl0_26
| ~ spl0_42 ),
inference(resolution,[],[f324,f168]) ).
fof(f168,plain,
( ! [X0] : ~ member(X0,converse(converse(eptset)))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f1169,plain,
( spl0_111
| ~ spl0_24
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f342,f323,f159,f1167]) ).
fof(f1167,plain,
( spl0_111
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(union(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(union(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(union(eptset))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f159,plain,
( spl0_24
<=> ! [X0] : ~ member(X0,converse(union(eptset))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f342,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(union(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(union(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(union(eptset))))) = X2 )
| ~ spl0_24
| ~ spl0_42 ),
inference(resolution,[],[f324,f160]) ).
fof(f160,plain,
( ! [X0] : ~ member(X0,converse(union(eptset)))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f1165,plain,
( spl0_110
| ~ spl0_25
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f337,f323,f163,f1163]) ).
fof(f1163,plain,
( spl0_110
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,union(converse(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,union(converse(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,union(converse(eptset))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f163,plain,
( spl0_25
<=> ! [X0] : ~ member(X0,union(converse(eptset))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f337,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,union(converse(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,union(converse(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,union(converse(eptset))))) = X2 )
| ~ spl0_25
| ~ spl0_42 ),
inference(resolution,[],[f324,f164]) ).
fof(f164,plain,
( ! [X0] : ~ member(X0,union(converse(eptset)))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f1161,plain,
( spl0_109
| ~ spl0_18
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f330,f323,f110,f1159]) ).
fof(f1159,plain,
( spl0_109
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,union(union(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,union(union(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,union(union(eptset))))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f110,plain,
( spl0_18
<=> ! [X0] : ~ member(X0,union(union(eptset))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f330,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,union(union(eptset))))))
| unionE_sk1(X0,cons(X1,cons(X2,union(union(eptset))))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,union(union(eptset))))) = X2 )
| ~ spl0_18
| ~ spl0_42 ),
inference(resolution,[],[f324,f111]) ).
fof(f111,plain,
( ! [X0] : ~ member(X0,union(union(eptset)))
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f110]) ).
fof(f1119,plain,
( spl0_108
| ~ spl0_26
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f431,f402,f167,f1117]) ).
fof(f1117,plain,
( spl0_108
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(converse(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(converse(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(converse(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f431,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(converse(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(converse(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(converse(eptset)))))) )
| ~ spl0_26
| ~ spl0_49 ),
inference(resolution,[],[f403,f168]) ).
fof(f1115,plain,
( spl0_107
| ~ spl0_24
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f423,f402,f159,f1113]) ).
fof(f1113,plain,
( spl0_107
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(union(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(union(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(union(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f423,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(union(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(union(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(union(eptset)))))) )
| ~ spl0_24
| ~ spl0_49 ),
inference(resolution,[],[f403,f160]) ).
fof(f1111,plain,
( ~ spl0_106
| spl0_98
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1050,f1046,f1042,f1108]) ).
fof(f1108,plain,
( spl0_106
<=> a = b ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1050,plain,
( a != b
| spl0_98
| ~ spl0_99 ),
inference(forward_demodulation,[],[f1043,f1048]) ).
fof(f1043,plain,
( b != unionE_sk1(sk2,cons(a,cons(b,eptset)))
| spl0_98 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f1106,plain,
( spl0_105
| ~ spl0_25
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f418,f402,f163,f1104]) ).
fof(f1104,plain,
( spl0_105
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,union(converse(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,union(converse(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,union(converse(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f418,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,union(converse(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,union(converse(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,union(converse(eptset)))))) )
| ~ spl0_25
| ~ spl0_49 ),
inference(resolution,[],[f403,f164]) ).
fof(f1102,plain,
( spl0_104
| ~ spl0_18
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f410,f402,f110,f1100]) ).
fof(f1100,plain,
( spl0_104
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,union(union(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,union(union(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,union(union(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f410,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,union(union(eptset)))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,union(union(eptset))))))) = X1
| ~ member(X0,union(converse(cons(X1,union(union(eptset)))))) )
| ~ spl0_18
| ~ spl0_49 ),
inference(resolution,[],[f403,f111]) ).
fof(f1098,plain,
( spl0_103
| ~ spl0_10
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f278,f273,f58,f1096]) ).
fof(f1096,plain,
( spl0_103
<=> ! [X0,X3,X2,X1] :
( member(pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1))),X2)
| pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1))) = X3
| ~ member(pair(X1,X0),converse(cons(X3,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f278,plain,
( ! [X2,X3,X0,X1] :
( member(pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1))),X2)
| pair(converse_sk2(pair(X0,X1)),converse_sk1(pair(X0,X1))) = X3
| ~ member(pair(X1,X0),converse(cons(X3,X2))) )
| ~ spl0_10
| ~ spl0_36 ),
inference(resolution,[],[f274,f59]) ).
fof(f1078,plain,
( spl0_102
| ~ spl0_16
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f345,f323,f91,f1076]) ).
fof(f1076,plain,
( spl0_102
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(eptset)))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(eptset)))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(eptset)))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f345,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,converse(eptset)))))
| unionE_sk1(X0,cons(X1,cons(X2,converse(eptset)))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,converse(eptset)))) = X2 )
| ~ spl0_16
| ~ spl0_42 ),
inference(resolution,[],[f324,f92]) ).
fof(f1074,plain,
( spl0_101
| ~ spl0_15
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f335,f323,f87,f1072]) ).
fof(f1072,plain,
( spl0_101
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,union(eptset)))))
| unionE_sk1(X0,cons(X1,cons(X2,union(eptset)))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,union(eptset)))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f335,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,union(eptset)))))
| unionE_sk1(X0,cons(X1,cons(X2,union(eptset)))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,union(eptset)))) = X2 )
| ~ spl0_15
| ~ spl0_42 ),
inference(resolution,[],[f324,f88]) ).
fof(f1054,plain,
( spl0_100
| ~ spl0_16
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f426,f402,f91,f1052]) ).
fof(f1052,plain,
( spl0_100
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(eptset))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(eptset)))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f426,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,converse(eptset))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,converse(eptset)))))) = X1
| ~ member(X0,union(converse(cons(X1,converse(eptset))))) )
| ~ spl0_16
| ~ spl0_49 ),
inference(resolution,[],[f403,f92]) ).
fof(f1049,plain,
( spl0_98
| spl0_99
| ~ spl0_2
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1036,f1025,f21,f1046,f1042]) ).
fof(f1025,plain,
( spl0_96
<=> ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,eptset))))
| unionE_sk1(X0,cons(X1,cons(X2,eptset))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,eptset))) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1036,plain,
( a = unionE_sk1(sk2,cons(a,cons(b,eptset)))
| b = unionE_sk1(sk2,cons(a,cons(b,eptset)))
| ~ spl0_2
| ~ spl0_96 ),
inference(resolution,[],[f1026,f23]) ).
fof(f23,plain,
( member(sk2,union(cons(a,cons(b,eptset))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f1026,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,eptset))))
| unionE_sk1(X0,cons(X1,cons(X2,eptset))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,eptset))) = X2 )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f1040,plain,
( spl0_97
| ~ spl0_15
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f416,f402,f87,f1038]) ).
fof(f1038,plain,
( spl0_97
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,union(eptset))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,union(eptset)))))) = X1
| ~ member(X0,union(converse(cons(X1,union(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f416,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,union(eptset))))),converse_sk2(unionE_sk1(X0,converse(cons(X1,union(eptset)))))) = X1
| ~ member(X0,union(converse(cons(X1,union(eptset))))) )
| ~ spl0_15
| ~ spl0_49 ),
inference(resolution,[],[f403,f88]) ).
fof(f1027,plain,
( spl0_96
| ~ spl0_3
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f339,f323,f26,f1025]) ).
fof(f339,plain,
( ! [X2,X0,X1] :
( ~ member(X0,union(cons(X1,cons(X2,eptset))))
| unionE_sk1(X0,cons(X1,cons(X2,eptset))) = X1
| unionE_sk1(X0,cons(X1,cons(X2,eptset))) = X2 )
| ~ spl0_3
| ~ spl0_42 ),
inference(resolution,[],[f324,f27]) ).
fof(f1015,plain,
( spl0_95
| ~ spl0_3
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f420,f402,f26,f1013]) ).
fof(f1013,plain,
( spl0_95
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,eptset)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,eptset))))) = X1
| ~ member(X0,union(converse(cons(X1,eptset)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f420,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,eptset)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,eptset))))) = X1
| ~ member(X0,union(converse(cons(X1,eptset)))) )
| ~ spl0_3
| ~ spl0_49 ),
inference(resolution,[],[f403,f27]) ).
fof(f1002,plain,
( spl0_94
| ~ spl0_13
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f263,f258,f70,f1000]) ).
fof(f1000,plain,
( spl0_94
<=> ! [X0,X1] :
( pair(converse_sk1(X0),converse_sk2(X0)) = pair(converseE_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converseE_sk1(pair(converse_sk1(X0),converse_sk2(X0))))
| ~ member(X0,converse(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f258,plain,
( spl0_34
<=> ! [X2,X0,X1] :
( pair(X0,X1) = pair(converseE_sk2(pair(X0,X1)),converseE_sk1(pair(X0,X1)))
| ~ member(pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f263,plain,
( ! [X0,X1] :
( pair(converse_sk1(X0),converse_sk2(X0)) = pair(converseE_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converseE_sk1(pair(converse_sk1(X0),converse_sk2(X0))))
| ~ member(X0,converse(X1)) )
| ~ spl0_13
| ~ spl0_34 ),
inference(resolution,[],[f259,f71]) ).
fof(f259,plain,
( ! [X2,X0,X1] :
( ~ member(pair(X0,X1),X2)
| pair(X0,X1) = pair(converseE_sk2(pair(X0,X1)),converseE_sk1(pair(X0,X1))) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f972,plain,
( spl0_93
| ~ spl0_13
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f545,f319,f70,f970]) ).
fof(f970,plain,
( spl0_93
<=> ! [X0] : ~ member(X0,converse(union(converse(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f319,plain,
( spl0_41
<=> ! [X0] : ~ member(X0,union(converse(union(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f545,plain,
( ! [X0] : ~ member(X0,converse(union(converse(union(eptset)))))
| ~ spl0_13
| ~ spl0_41 ),
inference(resolution,[],[f320,f71]) ).
fof(f320,plain,
( ! [X0] : ~ member(X0,union(converse(union(eptset))))
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f951,plain,
( spl0_92
| ~ spl0_30
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f254,f244,f211,f949]) ).
fof(f949,plain,
( spl0_92
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,converse(eptset))) = X1
| ~ member(X0,converse(converse(converse(union(cons(X1,converse(eptset))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f254,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,converse(eptset))) = X1
| ~ member(X0,converse(converse(converse(union(cons(X1,converse(eptset))))))) )
| ~ spl0_30
| ~ spl0_33 ),
inference(resolution,[],[f245,f212]) ).
fof(f947,plain,
( spl0_91
| ~ spl0_7
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f252,f244,f44,f945]) ).
fof(f945,plain,
( spl0_91
<=> ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(cons(X1,converse(eptset)))),cons(X1,converse(eptset))) = X1
| ~ member(X0,union(union(cons(X1,converse(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f252,plain,
( ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(cons(X1,converse(eptset)))),cons(X1,converse(eptset))) = X1
| ~ member(X0,union(union(cons(X1,converse(eptset))))) )
| ~ spl0_7
| ~ spl0_33 ),
inference(resolution,[],[f245,f45]) ).
fof(f943,plain,
( spl0_90
| ~ spl0_30
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f249,f240,f211,f941]) ).
fof(f941,plain,
( spl0_90
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,union(eptset))) = X1
| ~ member(X0,converse(converse(converse(union(cons(X1,union(eptset))))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f249,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,union(eptset))) = X1
| ~ member(X0,converse(converse(converse(union(cons(X1,union(eptset))))))) )
| ~ spl0_30
| ~ spl0_32 ),
inference(resolution,[],[f241,f212]) ).
fof(f939,plain,
( spl0_89
| ~ spl0_7
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f247,f240,f44,f937]) ).
fof(f937,plain,
( spl0_89
<=> ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(cons(X1,union(eptset)))),cons(X1,union(eptset))) = X1
| ~ member(X0,union(union(cons(X1,union(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f247,plain,
( ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(cons(X1,union(eptset)))),cons(X1,union(eptset))) = X1
| ~ member(X0,union(union(cons(X1,union(eptset))))) )
| ~ spl0_7
| ~ spl0_32 ),
inference(resolution,[],[f241,f45]) ).
fof(f935,plain,
( spl0_88
| ~ spl0_9
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f224,f211,f54,f933]) ).
fof(f933,plain,
( spl0_88
<=> ! [X2,X0,X1] :
( ~ member(X0,converse(converse(converse(cons(X1,X2)))))
| member(pair(converse_sk1(X0),converse_sk2(X0)),X2)
| pair(converse_sk1(X0),converse_sk2(X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f54,plain,
( spl0_9
<=> ! [X4,X0,X1] :
( X0 = X1
| member(X0,X4)
| ~ member(X0,cons(X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f224,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(converse(converse(cons(X1,X2)))))
| member(pair(converse_sk1(X0),converse_sk2(X0)),X2)
| pair(converse_sk1(X0),converse_sk2(X0)) = X1 )
| ~ spl0_9
| ~ spl0_30 ),
inference(resolution,[],[f212,f55]) ).
fof(f55,plain,
( ! [X0,X1,X4] :
( ~ member(X0,cons(X1,X4))
| member(X0,X4)
| X0 = X1 )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f913,plain,
( spl0_87
| ~ spl0_17
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f256,f244,f100,f911]) ).
fof(f911,plain,
( spl0_87
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),cons(X1,converse(eptset))) = X1
| ~ member(X0,converse(converse(union(cons(X1,converse(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f256,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),cons(X1,converse(eptset))) = X1
| ~ member(X0,converse(converse(union(cons(X1,converse(eptset)))))) )
| ~ spl0_17
| ~ spl0_33 ),
inference(resolution,[],[f245,f101]) ).
fof(f909,plain,
( spl0_86
| ~ spl0_7
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f541,f319,f44,f907]) ).
fof(f907,plain,
( spl0_86
<=> ! [X0] : ~ member(X0,union(union(converse(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f541,plain,
( ! [X0] : ~ member(X0,union(union(converse(union(eptset)))))
| ~ spl0_7
| ~ spl0_41 ),
inference(resolution,[],[f320,f45]) ).
fof(f905,plain,
( spl0_85
| ~ spl0_17
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f251,f240,f100,f903]) ).
fof(f903,plain,
( spl0_85
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),cons(X1,union(eptset))) = X1
| ~ member(X0,converse(converse(union(cons(X1,union(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f251,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),cons(X1,union(eptset))) = X1
| ~ member(X0,converse(converse(union(cons(X1,union(eptset)))))) )
| ~ spl0_17
| ~ spl0_32 ),
inference(resolution,[],[f241,f101]) ).
fof(f874,plain,
( spl0_84
| ~ spl0_13
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f255,f244,f70,f872]) ).
fof(f872,plain,
( spl0_84
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,converse(eptset))) = X1
| ~ member(X0,converse(union(cons(X1,converse(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f255,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,converse(eptset))) = X1
| ~ member(X0,converse(union(cons(X1,converse(eptset))))) )
| ~ spl0_13
| ~ spl0_33 ),
inference(resolution,[],[f245,f71]) ).
fof(f870,plain,
( spl0_83
| ~ spl0_13
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f250,f240,f70,f868]) ).
fof(f868,plain,
( spl0_83
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,union(eptset))) = X1
| ~ member(X0,converse(union(cons(X1,union(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f250,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,union(eptset))) = X1
| ~ member(X0,converse(union(cons(X1,union(eptset))))) )
| ~ spl0_13
| ~ spl0_32 ),
inference(resolution,[],[f241,f71]) ).
fof(f866,plain,
( spl0_82
| ~ spl0_30
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f236,f215,f211,f864]) ).
fof(f864,plain,
( spl0_82
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,eptset)) = X1
| ~ member(X0,converse(converse(converse(union(cons(X1,eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f236,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,eptset)) = X1
| ~ member(X0,converse(converse(converse(union(cons(X1,eptset)))))) )
| ~ spl0_30
| ~ spl0_31 ),
inference(resolution,[],[f216,f212]) ).
fof(f837,plain,
( spl0_81
| ~ spl0_7
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f532,f269,f44,f835]) ).
fof(f835,plain,
( spl0_81
<=> ! [X0] : ~ member(X0,union(converse(union(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f269,plain,
( spl0_35
<=> ! [X0] : ~ member(X0,converse(union(union(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f532,plain,
( ! [X0] : ~ member(X0,union(converse(union(union(eptset)))))
| ~ spl0_7
| ~ spl0_35 ),
inference(resolution,[],[f270,f45]) ).
fof(f270,plain,
( ! [X0] : ~ member(X0,converse(union(union(eptset))))
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f825,plain,
( spl0_80
| ~ spl0_17
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f238,f215,f100,f823]) ).
fof(f823,plain,
( spl0_80
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),cons(X1,eptset)) = X1
| ~ member(X0,converse(converse(union(cons(X1,eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f238,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),cons(X1,eptset)) = X1
| ~ member(X0,converse(converse(union(cons(X1,eptset))))) )
| ~ spl0_17
| ~ spl0_31 ),
inference(resolution,[],[f216,f101]) ).
fof(f821,plain,
( spl0_79
| ~ spl0_7
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f234,f215,f44,f819]) ).
fof(f819,plain,
( spl0_79
<=> ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(cons(X1,eptset))),cons(X1,eptset)) = X1
| ~ member(X0,union(union(cons(X1,eptset)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f234,plain,
( ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(cons(X1,eptset))),cons(X1,eptset)) = X1
| ~ member(X0,union(union(cons(X1,eptset)))) )
| ~ spl0_7
| ~ spl0_31 ),
inference(resolution,[],[f216,f45]) ).
fof(f817,plain,
( spl0_78
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f202,f193,f124,f815]) ).
fof(f815,plain,
( spl0_78
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(converse(converse(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(converse(converse(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f202,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(converse(converse(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(converse(converse(eptset)))))) )
| ~ spl0_20
| ~ spl0_28 ),
inference(resolution,[],[f194,f125]) ).
fof(f813,plain,
( spl0_77
| ~ spl0_20
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f197,f189,f124,f811]) ).
fof(f811,plain,
( spl0_77
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(converse(union(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(converse(union(eptset)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f197,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(converse(union(eptset))))) = X1
| ~ member(X0,union(cons(X1,converse(converse(union(eptset)))))) )
| ~ spl0_20
| ~ spl0_27 ),
inference(resolution,[],[f190,f125]) ).
fof(f800,plain,
( spl0_76
| ~ spl0_13
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f237,f215,f70,f798]) ).
fof(f798,plain,
( spl0_76
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,eptset)) = X1
| ~ member(X0,converse(union(cons(X1,eptset)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f237,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),cons(X1,eptset)) = X1
| ~ member(X0,converse(union(cons(X1,eptset)))) )
| ~ spl0_13
| ~ spl0_31 ),
inference(resolution,[],[f216,f71]) ).
fof(f772,plain,
( spl0_75
| ~ spl0_13
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f528,f207,f70,f770]) ).
fof(f770,plain,
( spl0_75
<=> ! [X0] : ~ member(X0,converse(union(union(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f207,plain,
( spl0_29
<=> ! [X0] : ~ member(X0,union(union(union(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f528,plain,
( ! [X0] : ~ member(X0,converse(union(union(union(eptset)))))
| ~ spl0_13
| ~ spl0_29 ),
inference(resolution,[],[f208,f71]) ).
fof(f208,plain,
( ! [X0] : ~ member(X0,union(union(union(eptset))))
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f760,plain,
( spl0_74
| ~ spl0_20
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f184,f167,f124,f758]) ).
fof(f758,plain,
( spl0_74
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(converse(eptset)))) = X1
| ~ member(X0,union(cons(X1,converse(converse(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f184,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(converse(eptset)))) = X1
| ~ member(X0,union(cons(X1,converse(converse(eptset))))) )
| ~ spl0_20
| ~ spl0_26 ),
inference(resolution,[],[f168,f125]) ).
fof(f756,plain,
( spl0_73
| ~ spl0_20
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f180,f163,f124,f754]) ).
fof(f754,plain,
( spl0_73
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,union(converse(eptset)))) = X1
| ~ member(X0,union(cons(X1,union(converse(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f180,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,union(converse(eptset)))) = X1
| ~ member(X0,union(cons(X1,union(converse(eptset))))) )
| ~ spl0_20
| ~ spl0_25 ),
inference(resolution,[],[f164,f125]) ).
fof(f752,plain,
( spl0_72
| ~ spl0_20
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f175,f159,f124,f750]) ).
fof(f750,plain,
( spl0_72
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(union(eptset)))) = X1
| ~ member(X0,union(cons(X1,converse(union(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f175,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(union(eptset)))) = X1
| ~ member(X0,union(cons(X1,converse(union(eptset))))) )
| ~ spl0_20
| ~ spl0_24 ),
inference(resolution,[],[f160,f125]) ).
fof(f748,plain,
( spl0_71
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f171,f124,f110,f746]) ).
fof(f746,plain,
( spl0_71
<=> ! [X0,X1] :
( unionE_sk1(X0,cons(X1,union(union(eptset)))) = X1
| ~ member(X0,union(cons(X1,union(union(eptset))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f171,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,union(union(eptset)))) = X1
| ~ member(X0,union(cons(X1,union(union(eptset))))) )
| ~ spl0_18
| ~ spl0_20 ),
inference(resolution,[],[f111,f125]) ).
fof(f735,plain,
( spl0_70
| ~ spl0_11
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f218,f211,f62,f733]) ).
fof(f733,plain,
( spl0_70
<=> ! [X0,X1] :
( ~ member(X0,converse(converse(converse(converse(X1)))))
| member(pair(converse_sk2(X0),converse_sk1(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f218,plain,
( ! [X0,X1] :
( ~ member(X0,converse(converse(converse(converse(X1)))))
| member(pair(converse_sk2(X0),converse_sk1(X0)),X1) )
| ~ spl0_11
| ~ spl0_30 ),
inference(resolution,[],[f212,f63]) ).
fof(f713,plain,
( spl0_69
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f233,f211,f193,f711]) ).
fof(f711,plain,
( spl0_69
<=> ! [X0] : ~ member(X0,converse(converse(converse(converse(converse(converse(eptset))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f233,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(converse(converse(converse(eptset)))))))
| ~ spl0_28
| ~ spl0_30 ),
inference(resolution,[],[f212,f194]) ).
fof(f709,plain,
( spl0_68
| ~ spl0_7
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f524,f207,f44,f707]) ).
fof(f707,plain,
( spl0_68
<=> ! [X0] : ~ member(X0,union(union(union(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f524,plain,
( ! [X0] : ~ member(X0,union(union(union(union(eptset)))))
| ~ spl0_7
| ~ spl0_29 ),
inference(resolution,[],[f208,f45]) ).
fof(f705,plain,
( spl0_67
| ~ spl0_27
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f231,f211,f189,f703]) ).
fof(f703,plain,
( spl0_67
<=> ! [X0] : ~ member(X0,converse(converse(converse(converse(converse(union(eptset))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f231,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(converse(converse(union(eptset)))))))
| ~ spl0_27
| ~ spl0_30 ),
inference(resolution,[],[f212,f190]) ).
fof(f665,plain,
( spl0_66
| ~ spl0_18
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f223,f211,f110,f663]) ).
fof(f663,plain,
( spl0_66
<=> ! [X0] : ~ member(X0,converse(converse(converse(union(union(eptset)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f223,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(union(union(eptset))))))
| ~ spl0_18
| ~ spl0_30 ),
inference(resolution,[],[f212,f111]) ).
fof(f661,plain,
( spl0_65
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f222,f211,f163,f659]) ).
fof(f659,plain,
( spl0_65
<=> ! [X0] : ~ member(X0,converse(converse(converse(union(converse(eptset)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f222,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(union(converse(eptset))))))
| ~ spl0_25
| ~ spl0_30 ),
inference(resolution,[],[f212,f164]) ).
fof(f657,plain,
( spl0_64
| ~ spl0_17
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f205,f193,f100,f655]) ).
fof(f655,plain,
( spl0_64
<=> ! [X0] : ~ member(X0,converse(converse(converse(converse(converse(eptset)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f205,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(converse(converse(eptset))))))
| ~ spl0_17
| ~ spl0_28 ),
inference(resolution,[],[f194,f101]) ).
fof(f653,plain,
( spl0_63
| ~ spl0_17
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f200,f189,f100,f651]) ).
fof(f651,plain,
( spl0_63
<=> ! [X0] : ~ member(X0,converse(converse(converse(converse(union(eptset)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f200,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(converse(union(eptset))))))
| ~ spl0_17
| ~ spl0_27 ),
inference(resolution,[],[f190,f101]) ).
fof(f597,plain,
( spl0_62
| ~ spl0_7
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f201,f193,f44,f595]) ).
fof(f595,plain,
( spl0_62
<=> ! [X0] : ~ member(X0,union(converse(converse(converse(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f201,plain,
( ! [X0] : ~ member(X0,union(converse(converse(converse(eptset)))))
| ~ spl0_7
| ~ spl0_28 ),
inference(resolution,[],[f194,f45]) ).
fof(f593,plain,
( spl0_61
| ~ spl0_7
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f196,f189,f44,f591]) ).
fof(f591,plain,
( spl0_61
<=> ! [X0] : ~ member(X0,union(converse(converse(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f196,plain,
( ! [X0] : ~ member(X0,union(converse(converse(union(eptset)))))
| ~ spl0_7
| ~ spl0_27 ),
inference(resolution,[],[f190,f45]) ).
fof(f589,plain,
( spl0_60
| ~ spl0_17
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f187,f167,f100,f587]) ).
fof(f587,plain,
( spl0_60
<=> ! [X0] : ~ member(X0,converse(converse(converse(converse(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f187,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(converse(eptset)))))
| ~ spl0_17
| ~ spl0_26 ),
inference(resolution,[],[f168,f101]) ).
fof(f585,plain,
( spl0_59
| ~ spl0_17
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f182,f163,f100,f583]) ).
fof(f583,plain,
( spl0_59
<=> ! [X0] : ~ member(X0,converse(converse(union(converse(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f182,plain,
( ! [X0] : ~ member(X0,converse(converse(union(converse(eptset)))))
| ~ spl0_17
| ~ spl0_25 ),
inference(resolution,[],[f164,f101]) ).
fof(f581,plain,
( spl0_58
| ~ spl0_17
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f178,f159,f100,f579]) ).
fof(f579,plain,
( spl0_58
<=> ! [X0] : ~ member(X0,converse(converse(converse(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f178,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(union(eptset)))))
| ~ spl0_17
| ~ spl0_24 ),
inference(resolution,[],[f160,f101]) ).
fof(f577,plain,
( spl0_57
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f173,f110,f100,f575]) ).
fof(f575,plain,
( spl0_57
<=> ! [X0] : ~ member(X0,converse(converse(union(union(eptset))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f173,plain,
( ! [X0] : ~ member(X0,converse(converse(union(union(eptset)))))
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f111,f101]) ).
fof(f523,plain,
( spl0_56
| ~ spl0_7
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f183,f167,f44,f521]) ).
fof(f521,plain,
( spl0_56
<=> ! [X0] : ~ member(X0,union(converse(converse(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f183,plain,
( ! [X0] : ~ member(X0,union(converse(converse(eptset))))
| ~ spl0_7
| ~ spl0_26 ),
inference(resolution,[],[f168,f45]) ).
fof(f511,plain,
( spl0_55
| ~ spl0_20
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f154,f150,f124,f509]) ).
fof(f509,plain,
( spl0_55
<=> ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(converse(X2))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(converse(X2)))))) = pair(converseE_sk2(pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(converse(X2))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(converse(X2))))))),converseE_sk1(pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(converse(X2))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(converse(X2))))))))
| unionE_sk1(X0,cons(X1,converse(converse(X2)))) = X1
| ~ member(X0,union(cons(X1,converse(converse(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f150,plain,
( spl0_23
<=> ! [X0,X1] :
( ~ member(X0,converse(converse(X1)))
| pair(converse_sk1(X0),converse_sk2(X0)) = pair(converseE_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converseE_sk1(pair(converse_sk1(X0),converse_sk2(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f154,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(converse(X2))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(converse(X2)))))) = pair(converseE_sk2(pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(converse(X2))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(converse(X2))))))),converseE_sk1(pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(converse(X2))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(converse(X2))))))))
| unionE_sk1(X0,cons(X1,converse(converse(X2)))) = X1
| ~ member(X0,union(cons(X1,converse(converse(X2))))) )
| ~ spl0_20
| ~ spl0_23 ),
inference(resolution,[],[f151,f125]) ).
fof(f151,plain,
( ! [X0,X1] :
( ~ member(X0,converse(converse(X1)))
| pair(converse_sk1(X0),converse_sk2(X0)) = pair(converseE_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converseE_sk1(pair(converse_sk1(X0),converse_sk2(X0)))) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f475,plain,
( spl0_54
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f137,f128,f124,f473]) ).
fof(f137,plain,
( ! [X2,X3,X0,X1] :
( member(pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,X3))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))))),X3)
| pair(converse_sk1(unionE_sk1(X0,cons(X1,converse(cons(X2,X3))))),converse_sk2(unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))))) = X2
| unionE_sk1(X0,cons(X1,converse(cons(X2,X3)))) = X1
| ~ member(X0,union(cons(X1,converse(cons(X2,X3))))) )
| ~ spl0_20
| ~ spl0_21 ),
inference(resolution,[],[f129,f125]) ).
fof(f471,plain,
( spl0_53
| ~ spl0_13
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f181,f163,f70,f469]) ).
fof(f469,plain,
( spl0_53
<=> ! [X0] : ~ member(X0,converse(union(converse(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f181,plain,
( ! [X0] : ~ member(X0,converse(union(converse(eptset))))
| ~ spl0_13
| ~ spl0_25 ),
inference(resolution,[],[f164,f71]) ).
fof(f460,plain,
( spl0_52
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f146,f142,f124,f458]) ).
fof(f458,plain,
( spl0_52
<=> ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(converse(X2)))),converse(X2)) = pair(converseE_sk2(unionE_sk1(unionE_sk1(X0,cons(X1,union(converse(X2)))),converse(X2))),converseE_sk1(unionE_sk1(unionE_sk1(X0,cons(X1,union(converse(X2)))),converse(X2))))
| unionE_sk1(X0,cons(X1,union(converse(X2)))) = X1
| ~ member(X0,union(cons(X1,union(converse(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f146,plain,
( ! [X2,X0,X1] :
( unionE_sk1(unionE_sk1(X0,cons(X1,union(converse(X2)))),converse(X2)) = pair(converseE_sk2(unionE_sk1(unionE_sk1(X0,cons(X1,union(converse(X2)))),converse(X2))),converseE_sk1(unionE_sk1(unionE_sk1(X0,cons(X1,union(converse(X2)))),converse(X2))))
| unionE_sk1(X0,cons(X1,union(converse(X2)))) = X1
| ~ member(X0,union(cons(X1,union(converse(X2))))) )
| ~ spl0_20
| ~ spl0_22 ),
inference(resolution,[],[f143,f125]) ).
fof(f441,plain,
( spl0_51
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f156,f150,f70,f439]) ).
fof(f439,plain,
( spl0_51
<=> ! [X0,X1] :
( pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))) = pair(converseE_sk2(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))))),converseE_sk1(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))))))
| ~ member(X0,converse(converse(converse(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f156,plain,
( ! [X0,X1] :
( pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))) = pair(converseE_sk2(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))))),converseE_sk1(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0))))))
| ~ member(X0,converse(converse(converse(X1)))) )
| ~ spl0_13
| ~ spl0_23 ),
inference(resolution,[],[f151,f71]) ).
fof(f437,plain,
( spl0_50
| ~ spl0_7
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f153,f150,f44,f435]) ).
fof(f435,plain,
( spl0_50
<=> ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(converse(X1)))),converse_sk2(unionE_sk1(X0,converse(converse(X1))))) = pair(converseE_sk2(pair(converse_sk1(unionE_sk1(X0,converse(converse(X1)))),converse_sk2(unionE_sk1(X0,converse(converse(X1)))))),converseE_sk1(pair(converse_sk1(unionE_sk1(X0,converse(converse(X1)))),converse_sk2(unionE_sk1(X0,converse(converse(X1)))))))
| ~ member(X0,union(converse(converse(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f153,plain,
( ! [X0,X1] :
( pair(converse_sk1(unionE_sk1(X0,converse(converse(X1)))),converse_sk2(unionE_sk1(X0,converse(converse(X1))))) = pair(converseE_sk2(pair(converse_sk1(unionE_sk1(X0,converse(converse(X1)))),converse_sk2(unionE_sk1(X0,converse(converse(X1)))))),converseE_sk1(pair(converse_sk1(unionE_sk1(X0,converse(converse(X1)))),converse_sk2(unionE_sk1(X0,converse(converse(X1)))))))
| ~ member(X0,union(converse(converse(X1)))) )
| ~ spl0_7
| ~ spl0_23 ),
inference(resolution,[],[f151,f45]) ).
fof(f404,plain,
( spl0_49
| ~ spl0_7
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f136,f128,f44,f402]) ).
fof(f136,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,X2)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,X2))))),X2)
| pair(converse_sk1(unionE_sk1(X0,converse(cons(X1,X2)))),converse_sk2(unionE_sk1(X0,converse(cons(X1,X2))))) = X1
| ~ member(X0,union(converse(cons(X1,X2)))) )
| ~ spl0_7
| ~ spl0_21 ),
inference(resolution,[],[f129,f45]) ).
fof(f393,plain,
( spl0_48
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f140,f128,f100,f391]) ).
fof(f391,plain,
( spl0_48
<=> ! [X2,X0,X1] :
( member(pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))),X1)
| pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))) = X2
| ~ member(X0,converse(converse(converse(cons(X2,X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f140,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))),X1)
| pair(converse_sk1(pair(converse_sk2(X0),converse_sk1(X0))),converse_sk2(pair(converse_sk2(X0),converse_sk1(X0)))) = X2
| ~ member(X0,converse(converse(converse(cons(X2,X1))))) )
| ~ spl0_17
| ~ spl0_21 ),
inference(resolution,[],[f129,f101]) ).
fof(f389,plain,
( spl0_47
| ~ spl0_7
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f179,f163,f44,f387]) ).
fof(f387,plain,
( spl0_47
<=> ! [X0] : ~ member(X0,union(union(converse(eptset)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f179,plain,
( ! [X0] : ~ member(X0,union(union(converse(eptset))))
| ~ spl0_7
| ~ spl0_25 ),
inference(resolution,[],[f164,f45]) ).
fof(f368,plain,
( spl0_46
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f155,f150,f58,f366]) ).
fof(f155,plain,
( ! [X2,X0,X1] :
( pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = pair(converseE_sk2(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))),converseE_sk1(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1)))))
| ~ member(pair(X1,X0),converse(X2)) )
| ~ spl0_10
| ~ spl0_23 ),
inference(resolution,[],[f151,f59]) ).
fof(f364,plain,
( spl0_45
| ~ spl0_13
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f139,f128,f70,f362]) ).
fof(f362,plain,
( spl0_45
<=> ! [X2,X0,X1] :
( member(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))),X1)
| pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))) = X2
| ~ member(X0,converse(converse(cons(X2,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f139,plain,
( ! [X2,X0,X1] :
( member(pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))),X1)
| pair(converse_sk1(pair(converse_sk1(X0),converse_sk2(X0))),converse_sk2(pair(converse_sk1(X0),converse_sk2(X0)))) = X2
| ~ member(X0,converse(converse(cons(X2,X1)))) )
| ~ spl0_13
| ~ spl0_21 ),
inference(resolution,[],[f129,f71]) ).
fof(f360,plain,
( spl0_44
| ~ spl0_12
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f134,f124,f66,f358]) ).
fof(f358,plain,
( spl0_44
<=> ! [X2,X0,X1] :
( unionE_sk1(X0,cons(X1,converse(X2))) = X1
| ~ member(X0,union(cons(X1,converse(X2))))
| unionE_sk1(X0,cons(X1,converse(X2))) = pair(converseE_sk2(unionE_sk1(X0,cons(X1,converse(X2)))),converseE_sk1(unionE_sk1(X0,cons(X1,converse(X2))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f66,plain,
( spl0_12
<=> ! [X7,X8] :
( ~ member(X8,converse(X7))
| pair(converseE_sk2(X8),converseE_sk1(X8)) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f134,plain,
( ! [X2,X0,X1] :
( unionE_sk1(X0,cons(X1,converse(X2))) = X1
| ~ member(X0,union(cons(X1,converse(X2))))
| unionE_sk1(X0,cons(X1,converse(X2))) = pair(converseE_sk2(unionE_sk1(X0,cons(X1,converse(X2)))),converseE_sk1(unionE_sk1(X0,cons(X1,converse(X2))))) )
| ~ spl0_12
| ~ spl0_20 ),
inference(resolution,[],[f125,f67]) ).
fof(f67,plain,
( ! [X8,X7] :
( ~ member(X8,converse(X7))
| pair(converseE_sk2(X8),converseE_sk1(X8)) = X8 )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f329,plain,
( spl0_43
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f148,f142,f100,f327]) ).
fof(f327,plain,
( spl0_43
<=> ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),converse(X1)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),converse(X1))),converseE_sk1(unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),converse(X1))))
| ~ member(X0,converse(converse(union(converse(X1))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f148,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),converse(X1)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),converse(X1))),converseE_sk1(unionE_sk1(pair(converse_sk2(X0),converse_sk1(X0)),converse(X1))))
| ~ member(X0,converse(converse(union(converse(X1))))) )
| ~ spl0_17
| ~ spl0_22 ),
inference(resolution,[],[f143,f101]) ).
fof(f325,plain,
( spl0_42
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f132,f124,f54,f323]) ).
fof(f132,plain,
( ! [X2,X3,X0,X1] :
( unionE_sk1(X0,cons(X1,cons(X2,X3))) = X1
| ~ member(X0,union(cons(X1,cons(X2,X3))))
| member(unionE_sk1(X0,cons(X1,cons(X2,X3))),X3)
| unionE_sk1(X0,cons(X1,cons(X2,X3))) = X2 )
| ~ spl0_9
| ~ spl0_20 ),
inference(resolution,[],[f125,f55]) ).
fof(f321,plain,
( spl0_41
| ~ spl0_7
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f174,f159,f44,f319]) ).
fof(f174,plain,
( ! [X0] : ~ member(X0,union(converse(union(eptset))))
| ~ spl0_7
| ~ spl0_24 ),
inference(resolution,[],[f160,f45]) ).
fof(f306,plain,
( spl0_40
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f147,f142,f70,f304]) ).
fof(f147,plain,
( ! [X0,X1] :
( unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1)) = pair(converseE_sk2(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1))),converseE_sk1(unionE_sk1(pair(converse_sk1(X0),converse_sk2(X0)),converse(X1))))
| ~ member(X0,converse(union(converse(X1)))) )
| ~ spl0_13
| ~ spl0_22 ),
inference(resolution,[],[f143,f71]) ).
fof(f302,plain,
( spl0_39
| ~ spl0_7
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f145,f142,f44,f300]) ).
fof(f145,plain,
( ! [X0,X1] :
( unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1)) = pair(converseE_sk2(unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1))),converseE_sk1(unionE_sk1(unionE_sk1(X0,union(converse(X1))),converse(X1))))
| ~ member(X0,union(union(converse(X1)))) )
| ~ spl0_7
| ~ spl0_22 ),
inference(resolution,[],[f143,f45]) ).
fof(f295,plain,
( spl0_38
| ~ spl0_10
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f138,f128,f58,f293]) ).
fof(f138,plain,
( ! [X2,X3,X0,X1] :
( member(pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))),X2)
| pair(converse_sk1(pair(X0,X1)),converse_sk2(pair(X0,X1))) = X3
| ~ member(pair(X1,X0),cons(X3,X2)) )
| ~ spl0_10
| ~ spl0_21 ),
inference(resolution,[],[f129,f59]) ).
fof(f285,plain,
( spl0_37
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f118,f114,f70,f283]) ).
fof(f114,plain,
( spl0_19
<=> ! [X2,X0,X1] :
( pair(X0,X1) = pair(converseE_sk2(pair(X0,X1)),converseE_sk1(pair(X0,X1)))
| ~ member(pair(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f118,plain,
( ! [X0,X1] :
( pair(converse_sk2(X0),converse_sk1(X0)) = pair(converseE_sk2(pair(converse_sk2(X0),converse_sk1(X0))),converseE_sk1(pair(converse_sk2(X0),converse_sk1(X0))))
| ~ member(X0,converse(X1)) )
| ~ spl0_13
| ~ spl0_19 ),
inference(resolution,[],[f115,f71]) ).
fof(f115,plain,
( ! [X2,X0,X1] :
( ~ member(pair(X1,X0),X2)
| pair(X0,X1) = pair(converseE_sk2(pair(X0,X1)),converseE_sk1(pair(X0,X1))) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f275,plain,
( spl0_36
| ~ spl0_9
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f105,f100,f54,f273]) ).
fof(f105,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(converse(cons(X1,X2))))
| member(pair(converse_sk2(X0),converse_sk1(X0)),X2)
| pair(converse_sk2(X0),converse_sk1(X0)) = X1 )
| ~ spl0_9
| ~ spl0_17 ),
inference(resolution,[],[f101,f55]) ).
fof(f271,plain,
( spl0_35
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f172,f110,f70,f269]) ).
fof(f172,plain,
( ! [X0] : ~ member(X0,converse(union(union(eptset))))
| ~ spl0_13
| ~ spl0_18 ),
inference(resolution,[],[f111,f71]) ).
fof(f260,plain,
( spl0_34
| ~ spl0_10
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f117,f114,f58,f258]) ).
fof(f117,plain,
( ! [X2,X0,X1] :
( pair(X0,X1) = pair(converseE_sk2(pair(X0,X1)),converseE_sk1(pair(X0,X1)))
| ~ member(pair(X0,X1),X2) )
| ~ spl0_10
| ~ spl0_19 ),
inference(resolution,[],[f115,f59]) ).
fof(f246,plain,
( spl0_33
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f135,f124,f91,f244]) ).
fof(f135,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,converse(eptset))) = X1
| ~ member(X0,union(cons(X1,converse(eptset)))) )
| ~ spl0_16
| ~ spl0_20 ),
inference(resolution,[],[f125,f92]) ).
fof(f242,plain,
( spl0_32
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f131,f124,f87,f240]) ).
fof(f131,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,union(eptset))) = X1
| ~ member(X0,union(cons(X1,union(eptset)))) )
| ~ spl0_15
| ~ spl0_20 ),
inference(resolution,[],[f125,f88]) ).
fof(f217,plain,
( spl0_31
| ~ spl0_3
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f133,f124,f26,f215]) ).
fof(f133,plain,
( ! [X0,X1] :
( unionE_sk1(X0,cons(X1,eptset)) = X1
| ~ member(X0,union(cons(X1,eptset))) )
| ~ spl0_3
| ~ spl0_20 ),
inference(resolution,[],[f125,f27]) ).
fof(f213,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f103,f100,f62,f211]) ).
fof(f103,plain,
( ! [X0,X1] :
( ~ member(X0,converse(converse(converse(X1))))
| member(pair(converse_sk1(X0),converse_sk2(X0)),X1) )
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f101,f63]) ).
fof(f209,plain,
( spl0_29
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f170,f110,f44,f207]) ).
fof(f170,plain,
( ! [X0] : ~ member(X0,union(union(union(eptset))))
| ~ spl0_7
| ~ spl0_18 ),
inference(resolution,[],[f111,f45]) ).
fof(f195,plain,
( spl0_28
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f100,f91,f193]) ).
fof(f108,plain,
( ! [X0] : ~ member(X0,converse(converse(converse(eptset))))
| ~ spl0_16
| ~ spl0_17 ),
inference(resolution,[],[f101,f92]) ).
fof(f191,plain,
( spl0_27
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f104,f100,f87,f189]) ).
fof(f104,plain,
( ! [X0] : ~ member(X0,converse(converse(union(eptset))))
| ~ spl0_15
| ~ spl0_17 ),
inference(resolution,[],[f101,f88]) ).
fof(f169,plain,
( spl0_26
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f91,f70,f167]) ).
fof(f98,plain,
( ! [X0] : ~ member(X0,converse(converse(eptset)))
| ~ spl0_13
| ~ spl0_16 ),
inference(resolution,[],[f92,f71]) ).
fof(f165,plain,
( spl0_25
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f96,f91,f44,f163]) ).
fof(f96,plain,
( ! [X0] : ~ member(X0,union(converse(eptset)))
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f92,f45]) ).
fof(f161,plain,
( spl0_24
| ~ spl0_13
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f95,f87,f70,f159]) ).
fof(f95,plain,
( ! [X0] : ~ member(X0,converse(union(eptset)))
| ~ spl0_13
| ~ spl0_15 ),
inference(resolution,[],[f88,f71]) ).
fof(f152,plain,
( spl0_23
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f85,f70,f66,f150]) ).
fof(f85,plain,
( ! [X0,X1] :
( ~ member(X0,converse(converse(X1)))
| pair(converse_sk1(X0),converse_sk2(X0)) = pair(converseE_sk2(pair(converse_sk1(X0),converse_sk2(X0))),converseE_sk1(pair(converse_sk1(X0),converse_sk2(X0)))) )
| ~ spl0_12
| ~ spl0_13 ),
inference(resolution,[],[f71,f67]) ).
fof(f144,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f80,f66,f44,f142]) ).
fof(f80,plain,
( ! [X0,X1] :
( unionE_sk1(X0,converse(X1)) = pair(converseE_sk2(unionE_sk1(X0,converse(X1))),converseE_sk1(unionE_sk1(X0,converse(X1))))
| ~ member(X0,union(converse(X1))) )
| ~ spl0_7
| ~ spl0_12 ),
inference(resolution,[],[f67,f45]) ).
fof(f130,plain,
( spl0_21
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f84,f70,f54,f128]) ).
fof(f84,plain,
( ! [X2,X0,X1] :
( ~ member(X0,converse(cons(X1,X2)))
| member(pair(converse_sk1(X0),converse_sk2(X0)),X2)
| pair(converse_sk1(X0),converse_sk2(X0)) = X1 )
| ~ spl0_9
| ~ spl0_13 ),
inference(resolution,[],[f71,f55]) ).
fof(f126,plain,
( spl0_20
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f73,f54,f44,f124]) ).
fof(f73,plain,
( ! [X2,X0,X1] :
( member(unionE_sk1(X0,cons(X1,X2)),X2)
| unionE_sk1(X0,cons(X1,X2)) = X1
| ~ member(X0,union(cons(X1,X2))) )
| ~ spl0_7
| ~ spl0_9 ),
inference(resolution,[],[f55,f45]) ).
fof(f116,plain,
( spl0_19
| ~ spl0_10
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f81,f66,f58,f114]) ).
fof(f81,plain,
( ! [X2,X0,X1] :
( pair(X0,X1) = pair(converseE_sk2(pair(X0,X1)),converseE_sk1(pair(X0,X1)))
| ~ member(pair(X1,X0),X2) )
| ~ spl0_10
| ~ spl0_12 ),
inference(resolution,[],[f67,f59]) ).
fof(f112,plain,
( spl0_18
| ~ spl0_7
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f94,f87,f44,f110]) ).
fof(f94,plain,
( ! [X0] : ~ member(X0,union(union(eptset)))
| ~ spl0_7
| ~ spl0_15 ),
inference(resolution,[],[f88,f45]) ).
fof(f102,plain,
( spl0_17
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f82,f70,f62,f100]) ).
fof(f82,plain,
( ! [X0,X1] :
( ~ member(X0,converse(converse(X1)))
| member(pair(converse_sk2(X0),converse_sk1(X0)),X1) )
| ~ spl0_11
| ~ spl0_13 ),
inference(resolution,[],[f71,f63]) ).
fof(f93,plain,
( spl0_16
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f83,f70,f26,f91]) ).
fof(f83,plain,
( ! [X0] : ~ member(X0,converse(eptset))
| ~ spl0_3
| ~ spl0_13 ),
inference(resolution,[],[f71,f27]) ).
fof(f89,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f52,f44,f26,f87]) ).
fof(f52,plain,
( ! [X0] : ~ member(X0,union(eptset))
| ~ spl0_3
| ~ spl0_7 ),
inference(resolution,[],[f45,f27]) ).
fof(f79,plain,
( ~ spl0_14
| spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f38,f34,f16,f76]) ).
fof(f16,plain,
( spl0_1
<=> member(sk2,un(a,b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f34,plain,
( spl0_5
<=> ! [X2,X5,X3] :
( ~ member(X5,X3)
| member(X5,un(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f38,plain,
( ~ member(sk2,b)
| spl0_1
| ~ spl0_5 ),
inference(resolution,[],[f35,f18]) ).
fof(f18,plain,
( ~ member(sk2,un(a,b))
| spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f35,plain,
( ! [X2,X3,X5] :
( member(X5,un(X2,X3))
| ~ member(X5,X3) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f72,plain,
spl0_13,
inference(avatar_split_clause,[],[f12,f70]) ).
fof(f12,axiom,
! [X8,X7] :
( ~ member(X8,converse(X7))
| member(pair(converse_sk1(X8),converse_sk2(X8)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converseE_2) ).
fof(f68,plain,
spl0_12,
inference(avatar_split_clause,[],[f11,f66]) ).
fof(f11,axiom,
! [X8,X7] :
( ~ member(X8,converse(X7))
| pair(converseE_sk2(X8),converseE_sk1(X8)) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converseE_1) ).
fof(f64,plain,
spl0_11,
inference(avatar_split_clause,[],[f10,f62]) ).
fof(f10,axiom,
! [X2,X3,X7] :
( member(pair(X3,X2),X7)
| ~ member(pair(X2,X3),converse(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converseD) ).
fof(f60,plain,
spl0_10,
inference(avatar_split_clause,[],[f9,f58]) ).
fof(f9,axiom,
! [X0,X1,X4] :
( ~ member(pair(X0,X1),X4)
| member(pair(X1,X0),converse(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause10) ).
fof(f56,plain,
spl0_9,
inference(avatar_split_clause,[],[f5,f54]) ).
fof(f5,axiom,
! [X0,X1,X4] :
( X0 = X1
| member(X0,X4)
| ~ member(X0,cons(X1,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
fof(f51,plain,
( ~ spl0_8
| spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f37,f30,f16,f48]) ).
fof(f30,plain,
( spl0_4
<=> ! [X2,X5,X3] :
( ~ member(X5,X2)
| member(X5,un(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f37,plain,
( ~ member(sk2,a)
| spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f31,f18]) ).
fof(f31,plain,
( ! [X2,X3,X5] :
( member(X5,un(X2,X3))
| ~ member(X5,X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f46,plain,
spl0_7,
inference(avatar_split_clause,[],[f2,f44]) ).
fof(f2,axiom,
! [X0,X1] :
( ~ member(X0,union(X1))
| member(unionE_sk1(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f42,plain,
spl0_6,
inference(avatar_split_clause,[],[f1,f40]) ).
fof(f1,axiom,
! [X0,X1] :
( ~ member(X0,union(X1))
| member(X0,unionE_sk1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
fof(f36,plain,
spl0_5,
inference(avatar_split_clause,[],[f7,f34]) ).
fof(f7,axiom,
! [X2,X3,X5] :
( ~ member(X5,X3)
| member(X5,un(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI2) ).
fof(f32,plain,
spl0_4,
inference(avatar_split_clause,[],[f6,f30]) ).
fof(f6,axiom,
! [X2,X3,X5] :
( ~ member(X5,X2)
| member(X5,un(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI1) ).
fof(f28,plain,
spl0_3,
inference(avatar_split_clause,[],[f8,f26]) ).
fof(f8,axiom,
! [X6] : ~ member(X6,eptset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
fof(f24,plain,
spl0_2,
inference(avatar_split_clause,[],[f13,f21]) ).
fof(f13,axiom,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
fof(f19,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f14,f16]) ).
fof(f14,axiom,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SET787-1 : TPTP v8.1.2. Released v2.7.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n007.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 16:29:22 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (3442)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (3445)WARNING: value z3 for option sas not known
% 0.11/0.33 % (3449)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.33 % (3446)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33 % (3447)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.33 % (3443)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33 % (3448)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.33 % (3444)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33 % (3445)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [3]
% 0.11/0.34 TRYING [1]
% 0.11/0.34 TRYING [2]
% 0.11/0.34 TRYING [4]
% 0.11/0.35 TRYING [3]
% 0.16/0.35 TRYING [5]
% 0.16/0.36 TRYING [4]
% 0.16/0.37 TRYING [6]
% 0.16/0.41 TRYING [7]
% 0.16/0.44 TRYING [5]
% 0.16/0.44 % (3447)First to succeed.
% 0.16/0.45 % (3447)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3442"
% 0.16/0.45 % (3447)Refutation found. Thanks to Tanya!
% 0.16/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (3447)------------------------------
% 0.16/0.46 % (3447)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.46 % (3447)Termination reason: Refutation
% 0.16/0.46
% 0.16/0.46 % (3447)Memory used [KB]: 2809
% 0.16/0.46 % (3447)Time elapsed: 0.117 s
% 0.16/0.46 % (3447)Instructions burned: 226 (million)
% 0.16/0.46 % (3442)Success in time 0.131 s
%------------------------------------------------------------------------------