TSTP Solution File: SET685+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET685+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:11:54 EDT 2024
% Result : Theorem 1.51s 0.57s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 336
% Syntax : Number of formulae : 1201 ( 58 unt; 0 def)
% Number of atoms : 6585 ( 162 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 9608 (4224 ~;4712 |; 263 &)
% ( 322 <=>; 85 =>; 0 <=; 2 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 302 ( 300 usr; 293 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 9 con; 0-4 aty)
% Number of variables : 1902 (1788 !; 114 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2794,plain,
$false,
inference(avatar_sat_refutation,[],[f196,f201,f206,f211,f216,f225,f230,f234,f239,f243,f248,f252,f257,f261,f265,f269,f273,f277,f281,f286,f290,f294,f302,f306,f310,f315,f319,f323,f332,f336,f340,f344,f348,f361,f365,f376,f380,f385,f387,f391,f395,f399,f403,f407,f411,f439,f443,f452,f461,f463,f471,f475,f485,f492,f496,f500,f509,f522,f524,f527,f595,f606,f608,f618,f627,f631,f641,f643,f647,f651,f656,f665,f670,f683,f693,f697,f702,f707,f711,f719,f723,f729,f734,f739,f743,f749,f750,f760,f764,f768,f772,f793,f797,f801,f818,f833,f842,f846,f852,f857,f861,f877,f892,f896,f911,f915,f924,f929,f937,f942,f947,f962,f977,f983,f987,f993,f997,f1004,f1009,f1013,f1018,f1030,f1045,f1047,f1049,f1053,f1061,f1067,f1092,f1097,f1102,f1121,f1125,f1129,f1133,f1164,f1169,f1183,f1184,f1191,f1203,f1207,f1223,f1232,f1236,f1240,f1276,f1284,f1303,f1307,f1314,f1318,f1322,f1339,f1344,f1348,f1352,f1356,f1360,f1364,f1406,f1425,f1429,f1435,f1440,f1445,f1449,f1472,f1476,f1480,f1490,f1494,f1498,f1502,f1506,f1510,f1514,f1526,f1548,f1552,f1556,f1563,f1567,f1574,f1579,f1583,f1587,f1601,f1605,f1610,f1614,f1618,f1632,f1636,f1643,f1647,f1651,f1660,f1664,f1665,f1669,f1673,f1681,f1685,f1691,f1696,f1700,f1706,f1710,f1724,f1728,f1732,f1739,f1743,f1749,f1753,f1758,f1762,f1768,f1773,f1798,f1800,f1805,f1819,f1821,f1825,f1831,f1839,f1843,f1865,f1870,f1881,f1897,f1901,f1917,f1922,f1939,f1947,f1952,f1955,f1967,f1975,f1979,f1991,f1996,f2000,f2004,f2008,f2078,f2082,f2086,f2090,f2108,f2112,f2132,f2134,f2138,f2142,f2146,f2208,f2212,f2216,f2218,f2222,f2252,f2256,f2260,f2264,f2268,f2272,f2369,f2373,f2377,f2387,f2393,f2398,f2402,f2406,f2410,f2414,f2418,f2423,f2427,f2688,f2692,f2696,f2700,f2704,f2708,f2712,f2754,f2785,f2793]) ).
fof(f2793,plain,
( ~ spl21_7
| ~ spl21_223
| spl21_125
| ~ spl21_233 ),
inference(avatar_split_clause,[],[f2763,f1879,f1027,f1795,f222]) ).
fof(f222,plain,
( spl21_7
<=> member(sK9,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).
fof(f1795,plain,
( spl21_223
<=> ilf_type(sK5,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_223])]) ).
fof(f1027,plain,
( spl21_125
<=> member(sK8,image(sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_125])]) ).
fof(f1879,plain,
( spl21_233
<=> ! [X0] :
( ~ member(sK9,X0)
| ~ ilf_type(X0,set_type)
| member(sK8,image(sK7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_233])]) ).
fof(f2763,plain,
( ~ ilf_type(sK5,set_type)
| ~ member(sK9,sK5)
| spl21_125
| ~ spl21_233 ),
inference(resolution,[],[f1880,f1029]) ).
fof(f1029,plain,
( ~ member(sK8,image(sK7,sK5))
| spl21_125 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1880,plain,
( ! [X0] :
( member(sK8,image(sK7,X0))
| ~ ilf_type(X0,set_type)
| ~ member(sK9,X0) )
| ~ spl21_233 ),
inference(avatar_component_clause,[],[f1879]) ).
fof(f2785,plain,
( ~ spl21_122
| ~ spl21_128
| spl21_292
| ~ spl21_12
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f1024,f383,f245,f2782,f1042,f1006]) ).
fof(f1006,plain,
( spl21_122
<=> sP0(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_122])]) ).
fof(f1042,plain,
( spl21_128
<=> ilf_type(ordered_pair(sK9,sK8),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_128])]) ).
fof(f2782,plain,
( spl21_292
<=> ordered_pair(sK9,sK8) = ordered_pair(sK11(ordered_pair(sK9,sK8)),sK12(ordered_pair(sK9,sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_292])]) ).
fof(f245,plain,
( spl21_12
<=> member(ordered_pair(sK9,sK8),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).
fof(f383,plain,
( spl21_41
<=> ! [X4,X0] :
( ordered_pair(sK11(X4),sK12(X4)) = X4
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_41])]) ).
fof(f1024,plain,
( ordered_pair(sK9,sK8) = ordered_pair(sK11(ordered_pair(sK9,sK8)),sK12(ordered_pair(sK9,sK8)))
| ~ ilf_type(ordered_pair(sK9,sK8),set_type)
| ~ sP0(sK7)
| ~ spl21_12
| ~ spl21_41 ),
inference(resolution,[],[f247,f384]) ).
fof(f384,plain,
( ! [X0,X4] :
( ~ member(X4,X0)
| ordered_pair(sK11(X4),sK12(X4)) = X4
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) )
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f247,plain,
( member(ordered_pair(sK9,sK8),sK7)
| ~ spl21_12 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f2754,plain,
( ~ spl21_223
| ~ spl21_37
| ~ spl21_75
| ~ spl21_125
| ~ spl21_51
| spl21_275 ),
inference(avatar_split_clause,[],[f2419,f2380,f459,f1027,f659,f358,f1795]) ).
fof(f358,plain,
( spl21_37
<=> ilf_type(sK8,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_37])]) ).
fof(f659,plain,
( spl21_75
<=> ilf_type(sK7,binary_relation_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_75])]) ).
fof(f459,plain,
( spl21_51
<=> ! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_51])]) ).
fof(f2380,plain,
( spl21_275
<=> member(sK16(sK5,sK8,sK7),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_275])]) ).
fof(f2419,plain,
( ~ member(sK8,image(sK7,sK5))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK5,set_type)
| ~ spl21_51
| spl21_275 ),
inference(resolution,[],[f2382,f460]) ).
fof(f460,plain,
( ! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_51 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f2382,plain,
( ~ member(sK16(sK5,sK8,sK7),sK5)
| spl21_275 ),
inference(avatar_component_clause,[],[f2380]) ).
fof(f2712,plain,
( spl21_291
| ~ spl21_9
| ~ spl21_178 ),
inference(avatar_split_clause,[],[f1527,f1508,f232,f2710]) ).
fof(f2710,plain,
( spl21_291
<=> ! [X0,X1] :
( member(sK13(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| empty(sK14(power_set(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_291])]) ).
fof(f232,plain,
( spl21_9
<=> ! [X0] : ilf_type(X0,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).
fof(f1508,plain,
( spl21_178
<=> ! [X0,X1] :
( ~ ilf_type(sK13(sK14(power_set(X0),X1)),set_type)
| member(sK13(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| empty(sK14(power_set(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_178])]) ).
fof(f1527,plain,
( ! [X0,X1] :
( member(sK13(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| empty(sK14(power_set(X0),X1)) )
| ~ spl21_9
| ~ spl21_178 ),
inference(resolution,[],[f1509,f233]) ).
fof(f233,plain,
( ! [X0] : ilf_type(X0,set_type)
| ~ spl21_9 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f1509,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK14(power_set(X0),X1)),set_type)
| member(sK13(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| empty(sK14(power_set(X0),X1)) )
| ~ spl21_178 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f2708,plain,
( spl21_290
| ~ spl21_9
| ~ spl21_177 ),
inference(avatar_split_clause,[],[f1522,f1504,f232,f2706]) ).
fof(f2706,plain,
( spl21_290
<=> ! [X0,X1] :
( member(sK10(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| sP0(sK14(power_set(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_290])]) ).
fof(f1504,plain,
( spl21_177
<=> ! [X0,X1] :
( ~ ilf_type(sK10(sK14(power_set(X0),X1)),set_type)
| member(sK10(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| sP0(sK14(power_set(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_177])]) ).
fof(f1522,plain,
( ! [X0,X1] :
( member(sK10(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| sP0(sK14(power_set(X0),X1)) )
| ~ spl21_9
| ~ spl21_177 ),
inference(resolution,[],[f1505,f233]) ).
fof(f1505,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(sK14(power_set(X0),X1)),set_type)
| member(sK10(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| sP0(sK14(power_set(X0),X1)) )
| ~ spl21_177 ),
inference(avatar_component_clause,[],[f1504]) ).
fof(f2704,plain,
( spl21_289
| ~ spl21_9
| ~ spl21_176 ),
inference(avatar_split_clause,[],[f1521,f1500,f232,f2702]) ).
fof(f2702,plain,
( spl21_289
<=> ! [X0,X1] :
( member(sK13(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| empty(sK14(X0,power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_289])]) ).
fof(f1500,plain,
( spl21_176
<=> ! [X0,X1] :
( ~ ilf_type(sK13(sK14(X0,power_set(X1))),set_type)
| member(sK13(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| empty(sK14(X0,power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_176])]) ).
fof(f1521,plain,
( ! [X0,X1] :
( member(sK13(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| empty(sK14(X0,power_set(X1))) )
| ~ spl21_9
| ~ spl21_176 ),
inference(resolution,[],[f1501,f233]) ).
fof(f1501,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK14(X0,power_set(X1))),set_type)
| member(sK13(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| empty(sK14(X0,power_set(X1))) )
| ~ spl21_176 ),
inference(avatar_component_clause,[],[f1500]) ).
fof(f2700,plain,
( spl21_288
| ~ spl21_9
| ~ spl21_175 ),
inference(avatar_split_clause,[],[f1520,f1496,f232,f2698]) ).
fof(f2698,plain,
( spl21_288
<=> ! [X0,X1] :
( member(sK10(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| sP0(sK14(X0,power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_288])]) ).
fof(f1496,plain,
( spl21_175
<=> ! [X0,X1] :
( ~ ilf_type(sK10(sK14(X0,power_set(X1))),set_type)
| member(sK10(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| sP0(sK14(X0,power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_175])]) ).
fof(f1520,plain,
( ! [X0,X1] :
( member(sK10(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| sP0(sK14(X0,power_set(X1))) )
| ~ spl21_9
| ~ spl21_175 ),
inference(resolution,[],[f1497,f233]) ).
fof(f1497,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(sK14(X0,power_set(X1))),set_type)
| member(sK10(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| sP0(sK14(X0,power_set(X1))) )
| ~ spl21_175 ),
inference(avatar_component_clause,[],[f1496]) ).
fof(f2696,plain,
( spl21_287
| ~ spl21_9
| ~ spl21_174 ),
inference(avatar_split_clause,[],[f1519,f1492,f232,f2694]) ).
fof(f2694,plain,
( spl21_287
<=> ! [X0,X1] :
( member(sK15(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK13(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_287])]) ).
fof(f1492,plain,
( spl21_174
<=> ! [X0,X1] :
( ~ ilf_type(sK15(sK13(power_set(X0)),X1),set_type)
| member(sK15(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK13(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_174])]) ).
fof(f1519,plain,
( ! [X0,X1] :
( member(sK15(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK13(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_174 ),
inference(resolution,[],[f1493,f233]) ).
fof(f1493,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(sK13(power_set(X0)),X1),set_type)
| member(sK15(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK13(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_174 ),
inference(avatar_component_clause,[],[f1492]) ).
fof(f2692,plain,
( spl21_286
| ~ spl21_98
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1084,f1065,f816,f2690]) ).
fof(f2690,plain,
( spl21_286
<=> ! [X0] :
( empty(sK13(power_set(X0)))
| ~ ilf_type(sK13(power_set(X0)),set_type)
| ~ ilf_type(sK19(sK13(power_set(X0))),set_type)
| member(sK19(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_286])]) ).
fof(f816,plain,
( spl21_98
<=> ! [X0,X1] :
( ~ member(X0,sK13(power_set(X1)))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK13(power_set(X1)),set_type)
| empty(power_set(X1))
| ~ ilf_type(power_set(X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_98])]) ).
fof(f1065,plain,
( spl21_131
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| member(sK19(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_131])]) ).
fof(f1084,plain,
( ! [X0] :
( empty(sK13(power_set(X0)))
| ~ ilf_type(sK13(power_set(X0)),set_type)
| ~ ilf_type(sK19(sK13(power_set(X0))),set_type)
| member(sK19(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type) )
| ~ spl21_98
| ~ spl21_131 ),
inference(duplicate_literal_removal,[],[f1075]) ).
fof(f1075,plain,
( ! [X0] :
( empty(sK13(power_set(X0)))
| ~ ilf_type(sK13(power_set(X0)),set_type)
| ~ ilf_type(sK19(sK13(power_set(X0))),set_type)
| member(sK19(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type) )
| ~ spl21_98
| ~ spl21_131 ),
inference(resolution,[],[f1066,f817]) ).
fof(f817,plain,
( ! [X0,X1] :
( ~ member(X0,sK13(power_set(X1)))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK13(power_set(X1)),set_type)
| empty(power_set(X1))
| ~ ilf_type(power_set(X1),set_type) )
| ~ spl21_98 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f1066,plain,
( ! [X0] :
( member(sK19(X0),X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_131 ),
inference(avatar_component_clause,[],[f1065]) ).
fof(f2688,plain,
( ~ spl21_9
| spl21_276 ),
inference(avatar_contradiction_clause,[],[f2687]) ).
fof(f2687,plain,
( $false
| ~ spl21_9
| spl21_276 ),
inference(resolution,[],[f2386,f233]) ).
fof(f2386,plain,
( ~ ilf_type(sK16(sK5,sK8,sK7),set_type)
| spl21_276 ),
inference(avatar_component_clause,[],[f2384]) ).
fof(f2384,plain,
( spl21_276
<=> ilf_type(sK16(sK5,sK8,sK7),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_276])]) ).
fof(f2427,plain,
( spl21_285
| ~ spl21_9
| ~ spl21_172 ),
inference(avatar_split_clause,[],[f1486,f1478,f232,f2425]) ).
fof(f2425,plain,
( spl21_285
<=> ! [X0,X1] :
( member(sK14(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK14(sK10(power_set(X0)),X1),X1)
| sP2(sK10(power_set(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_285])]) ).
fof(f1478,plain,
( spl21_172
<=> ! [X0,X1] :
( ~ ilf_type(sK14(sK10(power_set(X0)),X1),set_type)
| member(sK14(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK14(sK10(power_set(X0)),X1),X1)
| sP2(sK10(power_set(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_172])]) ).
fof(f1486,plain,
( ! [X0,X1] :
( member(sK14(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK14(sK10(power_set(X0)),X1),X1)
| sP2(sK10(power_set(X0)),X1) )
| ~ spl21_9
| ~ spl21_172 ),
inference(resolution,[],[f1479,f233]) ).
fof(f1479,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(sK10(power_set(X0)),X1),set_type)
| member(sK14(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK14(sK10(power_set(X0)),X1),X1)
| sP2(sK10(power_set(X0)),X1) )
| ~ spl21_172 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f2423,plain,
( spl21_284
| ~ spl21_9
| ~ spl21_171 ),
inference(avatar_split_clause,[],[f1485,f1474,f232,f2421]) ).
fof(f2421,plain,
( spl21_284
<=> ! [X0,X1] :
( member(sK14(X0,sK10(power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1))
| member(sK14(X0,sK10(power_set(X1))),X0)
| sP2(X0,sK10(power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_284])]) ).
fof(f1474,plain,
( spl21_171
<=> ! [X0,X1] :
( ~ ilf_type(sK14(X0,sK10(power_set(X1))),set_type)
| member(sK14(X0,sK10(power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1))
| member(sK14(X0,sK10(power_set(X1))),X0)
| sP2(X0,sK10(power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_171])]) ).
fof(f1485,plain,
( ! [X0,X1] :
( member(sK14(X0,sK10(power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1))
| member(sK14(X0,sK10(power_set(X1))),X0)
| sP2(X0,sK10(power_set(X1))) )
| ~ spl21_9
| ~ spl21_171 ),
inference(resolution,[],[f1475,f233]) ).
fof(f1475,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,sK10(power_set(X1))),set_type)
| member(sK14(X0,sK10(power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1))
| member(sK14(X0,sK10(power_set(X1))),X0)
| sP2(X0,sK10(power_set(X1))) )
| ~ spl21_171 ),
inference(avatar_component_clause,[],[f1474]) ).
fof(f2418,plain,
( spl21_283
| ~ spl21_50
| ~ spl21_150 ),
inference(avatar_split_clause,[],[f1298,f1282,f450,f2416]) ).
fof(f2416,plain,
( spl21_283
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| sK15(X0,X1) = ordered_pair(sK11(sK15(X0,X1)),sK12(sK15(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ sP0(X0)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_283])]) ).
fof(f450,plain,
( spl21_50
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_50])]) ).
fof(f1282,plain,
( spl21_150
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sK15(X1,X0) = ordered_pair(sK11(sK15(X1,X0)),sK12(sK15(X1,X0)))
| member(X1,power_set(X0))
| ~ sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_150])]) ).
fof(f1298,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| sK15(X0,X1) = ordered_pair(sK11(sK15(X0,X1)),sK12(sK15(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ sP0(X0)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) )
| ~ spl21_50
| ~ spl21_150 ),
inference(duplicate_literal_removal,[],[f1286]) ).
fof(f1286,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| sK15(X0,X1) = ordered_pair(sK11(sK15(X0,X1)),sK12(sK15(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ sP0(X0)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_50
| ~ spl21_150 ),
inference(resolution,[],[f1283,f451]) ).
fof(f451,plain,
( ! [X3,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_50 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f1283,plain,
( ! [X0,X1] :
( member(X1,power_set(X0))
| ~ ilf_type(X1,set_type)
| sK15(X1,X0) = ordered_pair(sK11(sK15(X1,X0)),sK12(sK15(X1,X0)))
| ~ ilf_type(X0,set_type)
| ~ sP0(X1) )
| ~ spl21_150 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f2414,plain,
( spl21_282
| ~ spl21_33
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1216,f1205,f342,f2412]) ).
fof(f2412,plain,
( spl21_282
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| member(sK14(image(X0,X1),X2),X2)
| sP2(image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_282])]) ).
fof(f342,plain,
( spl21_33
<=> ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| member(sK14(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_33])]) ).
fof(f1205,plain,
( spl21_144
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(X0,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_144])]) ).
fof(f1216,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| member(sK14(image(X0,X1),X2),X2)
| sP2(image(X0,X1),X2) )
| ~ spl21_33
| ~ spl21_144 ),
inference(resolution,[],[f1206,f343]) ).
fof(f343,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X1)
| member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_33 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f1206,plain,
( ! [X2,X0,X1] :
( ~ member(X1,image(X0,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_144 ),
inference(avatar_component_clause,[],[f1205]) ).
fof(f2410,plain,
( spl21_281
| ~ spl21_33
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1214,f1205,f342,f2408]) ).
fof(f2408,plain,
( spl21_281
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| member(sK14(X0,image(X1,X2)),X0)
| sP2(X0,image(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_281])]) ).
fof(f1214,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| member(sK14(X0,image(X1,X2)),X0)
| sP2(X0,image(X1,X2)) )
| ~ spl21_33
| ~ spl21_144 ),
inference(resolution,[],[f1206,f343]) ).
fof(f2406,plain,
( spl21_280
| ~ spl21_49
| ~ spl21_142 ),
inference(avatar_split_clause,[],[f1193,f1189,f441,f2404]) ).
fof(f2404,plain,
( spl21_280
<=> ! [X2,X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(X2,set_type)
| member(X2,power_set(cross_product(X0,X1)))
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_280])]) ).
fof(f441,plain,
( spl21_49
<=> ! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_49])]) ).
fof(f1189,plain,
( spl21_142
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_142])]) ).
fof(f1193,plain,
( ! [X2,X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(X2,set_type)
| member(X2,power_set(cross_product(X0,X1)))
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_49
| ~ spl21_142 ),
inference(resolution,[],[f1190,f442]) ).
fof(f442,plain,
( ! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_49 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f1190,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_142 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f2402,plain,
( spl21_279
| ~ spl21_50
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1153,f1131,f450,f2400]) ).
fof(f2400,plain,
( spl21_279
<=> ! [X2,X0,X1] :
( sP2(X0,power_set(X1))
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(X2,sK14(X0,power_set(X1)))
| ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_279])]) ).
fof(f1131,plain,
( spl21_138
<=> ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_138])]) ).
fof(f1153,plain,
( ! [X2,X0,X1] :
( sP2(X0,power_set(X1))
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(X2,sK14(X0,power_set(X1)))
| ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type) )
| ~ spl21_50
| ~ spl21_138 ),
inference(resolution,[],[f1132,f451]) ).
fof(f1132,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X1)
| sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_138 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f2398,plain,
( spl21_278
| ~ spl21_50
| ~ spl21_137 ),
inference(avatar_split_clause,[],[f1140,f1127,f450,f2396]) ).
fof(f2396,plain,
( spl21_278
<=> ! [X2,X0,X1] :
( sP2(power_set(X0),X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X2,sK14(power_set(X0),X1))
| ~ ilf_type(X2,set_type)
| member(X2,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_278])]) ).
fof(f1127,plain,
( spl21_137
<=> ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_137])]) ).
fof(f1140,plain,
( ! [X2,X0,X1] :
( sP2(power_set(X0),X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| ~ member(X2,sK14(power_set(X0),X1))
| ~ ilf_type(X2,set_type)
| member(X2,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type) )
| ~ spl21_50
| ~ spl21_137 ),
inference(resolution,[],[f1128,f451]) ).
fof(f1128,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X0)
| sP2(X0,X1)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_137 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f2393,plain,
( spl21_277
| ~ spl21_42
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1177,f1167,f389,f2391]) ).
fof(f2391,plain,
( spl21_277
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK15(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(image(X0,X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(image(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_277])]) ).
fof(f389,plain,
( spl21_42
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| member(sK15(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_42])]) ).
fof(f1167,plain,
( spl21_140
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(X0,X2))
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_140])]) ).
fof(f1177,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(image(X0,X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(image(X0,X1),set_type) )
| ~ spl21_42
| ~ spl21_140 ),
inference(resolution,[],[f1168,f390]) ).
fof(f390,plain,
( ! [X0,X1] :
( member(sK15(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_42 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f1168,plain,
( ! [X2,X0,X1] :
( ~ member(X1,image(X0,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X2) )
| ~ spl21_140 ),
inference(avatar_component_clause,[],[f1167]) ).
fof(f2387,plain,
( ~ spl21_125
| ~ spl21_223
| ~ spl21_275
| ~ spl21_276
| ~ spl21_124
| ~ spl21_232 ),
inference(avatar_split_clause,[],[f1902,f1867,f1016,f2384,f2380,f1795,f1027]) ).
fof(f1016,plain,
( spl21_124
<=> ! [X0] :
( ~ member(sK16(X0,sK8,sK7),sK5)
| ~ ilf_type(sK16(X0,sK8,sK7),set_type)
| ~ member(sK16(X0,sK8,sK7),sK6)
| ~ ilf_type(X0,set_type)
| ~ member(sK8,image(sK7,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_124])]) ).
fof(f1867,plain,
( spl21_232
<=> member(sK16(sK5,sK8,sK7),sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_232])]) ).
fof(f1902,plain,
( ~ ilf_type(sK16(sK5,sK8,sK7),set_type)
| ~ member(sK16(sK5,sK8,sK7),sK5)
| ~ ilf_type(sK5,set_type)
| ~ member(sK8,image(sK7,sK5))
| ~ spl21_124
| ~ spl21_232 ),
inference(resolution,[],[f1869,f1017]) ).
fof(f1017,plain,
( ! [X0] :
( ~ member(sK16(X0,sK8,sK7),sK6)
| ~ ilf_type(sK16(X0,sK8,sK7),set_type)
| ~ member(sK16(X0,sK8,sK7),sK5)
| ~ ilf_type(X0,set_type)
| ~ member(sK8,image(sK7,X0)) )
| ~ spl21_124 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1869,plain,
( member(sK16(sK5,sK8,sK7),sK6)
| ~ spl21_232 ),
inference(avatar_component_clause,[],[f1867]) ).
fof(f2377,plain,
( spl21_274
| ~ spl21_9
| ~ spl21_167 ),
inference(avatar_split_clause,[],[f1441,f1438,f232,f2375]) ).
fof(f2375,plain,
( spl21_274
<=> ! [X0,X1] :
( ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| relation_like(sK19(power_set(cross_product(X0,X1))))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_274])]) ).
fof(f1438,plain,
( spl21_167
<=> ! [X0,X1] :
( ~ ilf_type(sK19(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| relation_like(sK19(power_set(cross_product(X0,X1))))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_167])]) ).
fof(f1441,plain,
( ! [X0,X1] :
( ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| relation_like(sK19(power_set(cross_product(X0,X1))))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_167 ),
inference(resolution,[],[f1439,f233]) ).
fof(f1439,plain,
( ! [X0,X1] :
( ~ ilf_type(sK19(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| relation_like(sK19(power_set(cross_product(X0,X1))))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_167 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f2373,plain,
( spl21_273
| ~ spl21_137
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1215,f1205,f1127,f2371]) ).
fof(f2371,plain,
( spl21_273
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP2(image(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_273])]) ).
fof(f1215,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP2(image(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) )
| ~ spl21_137
| ~ spl21_144 ),
inference(resolution,[],[f1206,f1128]) ).
fof(f2369,plain,
( spl21_272
| ~ spl21_138
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1213,f1205,f1131,f2367]) ).
fof(f2367,plain,
( spl21_272
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| sP2(X0,image(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_272])]) ).
fof(f1213,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type)
| sP2(X0,image(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_138
| ~ spl21_144 ),
inference(resolution,[],[f1206,f1132]) ).
fof(f2272,plain,
( spl21_271
| ~ spl21_9
| ~ spl21_166 ),
inference(avatar_split_clause,[],[f1436,f1433,f232,f2270]) ).
fof(f2270,plain,
( spl21_271
<=> ! [X0,X1] :
( member(sK15(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK10(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_271])]) ).
fof(f1433,plain,
( spl21_166
<=> ! [X0,X1] :
( ~ ilf_type(sK15(sK10(power_set(X0)),X1),set_type)
| member(sK15(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK10(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_166])]) ).
fof(f1436,plain,
( ! [X0,X1] :
( member(sK15(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK10(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_166 ),
inference(resolution,[],[f1434,f233]) ).
fof(f1434,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(sK10(power_set(X0)),X1),set_type)
| member(sK15(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK10(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_166 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f2268,plain,
( spl21_270
| ~ spl21_9
| ~ spl21_165 ),
inference(avatar_split_clause,[],[f1431,f1427,f232,f2266]) ).
fof(f2266,plain,
( spl21_270
<=> ! [X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ilf_type(sK14(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_270])]) ).
fof(f1427,plain,
( spl21_165
<=> ! [X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| ilf_type(sK14(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_165])]) ).
fof(f1431,plain,
( ! [X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ilf_type(sK14(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1) )
| ~ spl21_9
| ~ spl21_165 ),
inference(resolution,[],[f1428,f233]) ).
fof(f1428,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(power_set(X0),X1),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ilf_type(sK14(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1) )
| ~ spl21_165 ),
inference(avatar_component_clause,[],[f1427]) ).
fof(f2264,plain,
( spl21_269
| ~ spl21_9
| ~ spl21_164 ),
inference(avatar_split_clause,[],[f1430,f1423,f232,f2262]) ).
fof(f2262,plain,
( spl21_269
<=> ! [X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ilf_type(sK14(X1,power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(X1,power_set(X0)),X1)
| sP2(X1,power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_269])]) ).
fof(f1423,plain,
( spl21_164
<=> ! [X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK14(X1,power_set(X0)),set_type)
| ilf_type(sK14(X1,power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(X1,power_set(X0)),X1)
| sP2(X1,power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_164])]) ).
fof(f1430,plain,
( ! [X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ilf_type(sK14(X1,power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(X1,power_set(X0)),X1)
| sP2(X1,power_set(X0)) )
| ~ spl21_9
| ~ spl21_164 ),
inference(resolution,[],[f1424,f233]) ).
fof(f1424,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X1,power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ilf_type(sK14(X1,power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(X1,power_set(X0)),X1)
| sP2(X1,power_set(X0)) )
| ~ spl21_164 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f2260,plain,
( spl21_268
| ~ spl21_33
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1176,f1167,f342,f2258]) ).
fof(f2258,plain,
( spl21_268
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(sK14(image(X0,X1),X2),X2)
| sP2(image(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_268])]) ).
fof(f1176,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| member(sK14(image(X0,X1),X2),X2)
| sP2(image(X0,X1),X2) )
| ~ spl21_33
| ~ spl21_140 ),
inference(resolution,[],[f1168,f343]) ).
fof(f2256,plain,
( spl21_267
| ~ spl21_33
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1174,f1167,f342,f2254]) ).
fof(f2254,plain,
( spl21_267
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| member(sK14(X0,image(X1,X2)),X0)
| sP2(X0,image(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_267])]) ).
fof(f1174,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| member(sK14(X0,image(X1,X2)),X0)
| sP2(X0,image(X1,X2)) )
| ~ spl21_33
| ~ spl21_140 ),
inference(resolution,[],[f1168,f343]) ).
fof(f2252,plain,
( spl21_266
| ~ spl21_95
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1085,f1065,f791,f2250]) ).
fof(f2250,plain,
( spl21_266
<=> ! [X0] :
( empty(sK10(power_set(X0)))
| ~ ilf_type(sK10(power_set(X0)),set_type)
| ~ ilf_type(sK19(sK10(power_set(X0))),set_type)
| member(sK19(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| sP0(power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_266])]) ).
fof(f791,plain,
( spl21_95
<=> ! [X0,X1] :
( ~ member(X0,sK10(power_set(X1)))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_95])]) ).
fof(f1085,plain,
( ! [X0] :
( empty(sK10(power_set(X0)))
| ~ ilf_type(sK10(power_set(X0)),set_type)
| ~ ilf_type(sK19(sK10(power_set(X0))),set_type)
| member(sK19(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| sP0(power_set(X0)) )
| ~ spl21_95
| ~ spl21_131 ),
inference(duplicate_literal_removal,[],[f1074]) ).
fof(f1074,plain,
( ! [X0] :
( empty(sK10(power_set(X0)))
| ~ ilf_type(sK10(power_set(X0)),set_type)
| ~ ilf_type(sK19(sK10(power_set(X0))),set_type)
| member(sK19(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0)) )
| ~ spl21_95
| ~ spl21_131 ),
inference(resolution,[],[f1066,f792]) ).
fof(f792,plain,
( ! [X0,X1] :
( ~ member(X0,sK10(power_set(X1)))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1)) )
| ~ spl21_95 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f2222,plain,
( spl21_265
| ~ spl21_131
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1219,f1205,f1065,f2220]) ).
fof(f2220,plain,
( spl21_265
<=> ! [X0,X1] :
( ~ ilf_type(sK19(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_265])]) ).
fof(f1219,plain,
( ! [X0,X1] :
( ~ ilf_type(sK19(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) )
| ~ spl21_131
| ~ spl21_144 ),
inference(resolution,[],[f1206,f1066]) ).
fof(f2218,plain,
( ~ spl21_9
| spl21_251 ),
inference(avatar_contradiction_clause,[],[f2217]) ).
fof(f2217,plain,
( $false
| ~ spl21_9
| spl21_251 ),
inference(resolution,[],[f2074,f233]) ).
fof(f2074,plain,
( ~ ilf_type(sK12(sK13(sK7)),set_type)
| spl21_251 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f2072,plain,
( spl21_251
<=> ilf_type(sK12(sK13(sK7)),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_251])]) ).
fof(f2216,plain,
( spl21_264
| ~ spl21_24
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1212,f1205,f300,f2214]) ).
fof(f2214,plain,
( spl21_264
<=> ! [X0,X1] :
( ~ ilf_type(sK13(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_264])]) ).
fof(f300,plain,
( spl21_24
<=> ! [X0] :
( empty(X0)
| member(sK13(X0),X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_24])]) ).
fof(f1212,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) )
| ~ spl21_24
| ~ spl21_144 ),
inference(resolution,[],[f1206,f301]) ).
fof(f301,plain,
( ! [X0] :
( member(sK13(X0),X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f2212,plain,
( spl21_263
| ~ spl21_43
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1111,f1100,f393,f2210]) ).
fof(f2210,plain,
( spl21_263
<=> ! [X0,X1] :
( ~ ilf_type(sK15(X0,power_set(X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(sK15(X0,power_set(X1)))
| member(X0,power_set(power_set(X1)))
| ~ ilf_type(power_set(X1),set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_263])]) ).
fof(f393,plain,
( spl21_43
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK15(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_43])]) ).
fof(f1100,plain,
( spl21_134
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X1,power_set(X0))
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_134])]) ).
fof(f1111,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(X0,power_set(X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(sK15(X0,power_set(X1)))
| member(X0,power_set(power_set(X1)))
| ~ ilf_type(power_set(X1),set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_43
| ~ spl21_134 ),
inference(resolution,[],[f1101,f394]) ).
fof(f394,plain,
( ! [X0,X1] :
( ~ member(sK15(X0,X1),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_43 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f1101,plain,
( ! [X0,X1] :
( member(X1,power_set(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ empty(X1) )
| ~ spl21_134 ),
inference(avatar_component_clause,[],[f1100]) ).
fof(f2208,plain,
( spl21_262
| ~ spl21_50
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1073,f1065,f450,f2206]) ).
fof(f2206,plain,
( spl21_262
<=> ! [X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X1,sK19(power_set(X0)))
| ~ ilf_type(X1,set_type)
| member(X1,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK19(power_set(X0)),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_262])]) ).
fof(f1073,plain,
( ! [X0,X1] :
( empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X1,sK19(power_set(X0)))
| ~ ilf_type(X1,set_type)
| member(X1,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK19(power_set(X0)),set_type) )
| ~ spl21_50
| ~ spl21_131 ),
inference(resolution,[],[f1066,f451]) ).
fof(f2146,plain,
( spl21_261
| ~ spl21_9
| ~ spl21_161 ),
inference(avatar_split_clause,[],[f1385,f1358,f232,f2144]) ).
fof(f2144,plain,
( spl21_261
<=> ! [X0] :
( member(sK13(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| empty(sK13(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_261])]) ).
fof(f1358,plain,
( spl21_161
<=> ! [X0] :
( ~ ilf_type(sK13(sK13(power_set(X0))),set_type)
| member(sK13(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| empty(sK13(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_161])]) ).
fof(f1385,plain,
( ! [X0] :
( member(sK13(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| empty(sK13(power_set(X0))) )
| ~ spl21_9
| ~ spl21_161 ),
inference(resolution,[],[f1359,f233]) ).
fof(f1359,plain,
( ! [X0] :
( ~ ilf_type(sK13(sK13(power_set(X0))),set_type)
| member(sK13(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| empty(sK13(power_set(X0))) )
| ~ spl21_161 ),
inference(avatar_component_clause,[],[f1358]) ).
fof(f2142,plain,
( spl21_260
| ~ spl21_9
| ~ spl21_160 ),
inference(avatar_split_clause,[],[f1384,f1354,f232,f2140]) ).
fof(f2140,plain,
( spl21_260
<=> ! [X0] :
( member(sK10(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| sP0(sK13(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_260])]) ).
fof(f1354,plain,
( spl21_160
<=> ! [X0] :
( ~ ilf_type(sK10(sK13(power_set(X0))),set_type)
| member(sK10(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| sP0(sK13(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_160])]) ).
fof(f1384,plain,
( ! [X0] :
( member(sK10(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| sP0(sK13(power_set(X0))) )
| ~ spl21_9
| ~ spl21_160 ),
inference(resolution,[],[f1355,f233]) ).
fof(f1355,plain,
( ! [X0] :
( ~ ilf_type(sK10(sK13(power_set(X0))),set_type)
| member(sK10(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| sP0(sK13(power_set(X0))) )
| ~ spl21_160 ),
inference(avatar_component_clause,[],[f1354]) ).
fof(f2138,plain,
( spl21_259
| ~ spl21_137
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1175,f1167,f1127,f2136]) ).
fof(f2136,plain,
( spl21_259
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP2(image(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_259])]) ).
fof(f1175,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(image(X0,X1),X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP2(image(X0,X1),X2)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) )
| ~ spl21_137
| ~ spl21_140 ),
inference(resolution,[],[f1168,f1128]) ).
fof(f2134,plain,
( ~ spl21_9
| spl21_250 ),
inference(avatar_contradiction_clause,[],[f2133]) ).
fof(f2133,plain,
( $false
| ~ spl21_9
| spl21_250 ),
inference(resolution,[],[f2070,f233]) ).
fof(f2070,plain,
( ~ ilf_type(sK11(sK13(sK7)),set_type)
| spl21_250 ),
inference(avatar_component_clause,[],[f2068]) ).
fof(f2068,plain,
( spl21_250
<=> ilf_type(sK11(sK13(sK7)),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_250])]) ).
fof(f2132,plain,
( spl21_258
| ~ spl21_138
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1173,f1167,f1131,f2130]) ).
fof(f2130,plain,
( spl21_258
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| sP2(X0,image(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_258])]) ).
fof(f1173,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,image(X1,X2)),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ empty(X2)
| sP2(X0,image(X1,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_138
| ~ spl21_140 ),
inference(resolution,[],[f1168,f1132]) ).
fof(f2112,plain,
( spl21_257
| ~ spl21_9
| ~ spl21_156 ),
inference(avatar_split_clause,[],[f1340,f1337,f232,f2110]) ).
fof(f2110,plain,
( spl21_257
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| image4(X0,X1,sK18(cross_product(X0,X1)),X2) = image(sK18(cross_product(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_257])]) ).
fof(f1337,plain,
( spl21_156
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(X1,X0),set_type)
| ~ ilf_type(X2,set_type)
| image4(X1,X0,sK18(cross_product(X1,X0)),X2) = image(sK18(cross_product(X1,X0)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_156])]) ).
fof(f1340,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| image4(X0,X1,sK18(cross_product(X0,X1)),X2) = image(sK18(cross_product(X0,X1)),X2) )
| ~ spl21_9
| ~ spl21_156 ),
inference(resolution,[],[f1338,f233]) ).
fof(f1338,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(cross_product(X1,X0),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| image4(X1,X0,sK18(cross_product(X1,X0)),X2) = image(sK18(cross_product(X1,X0)),X2) )
| ~ spl21_156 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f2108,plain,
( spl21_256
| ~ spl21_34
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1110,f1100,f346,f2106]) ).
fof(f2106,plain,
( spl21_256
<=> ! [X0,X1] :
( ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(sK14(X0,power_set(X1)))
| ~ member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_256])]) ).
fof(f346,plain,
( spl21_34
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ member(sK14(X0,X1),X0)
| ~ member(sK14(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_34])]) ).
fof(f1110,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(sK14(X0,power_set(X1)))
| ~ member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1)) )
| ~ spl21_34
| ~ spl21_134 ),
inference(resolution,[],[f1101,f347]) ).
fof(f347,plain,
( ! [X0,X1] :
( ~ member(sK14(X0,X1),X1)
| ~ member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_34 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f2090,plain,
( spl21_255
| ~ spl21_34
| ~ spl21_148 ),
inference(avatar_split_clause,[],[f1272,f1238,f346,f2088]) ).
fof(f2088,plain,
( spl21_255
<=> ! [X0,X1] :
( ~ sP0(X0)
| sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| sP2(X0,X1)
| ~ member(sK14(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_255])]) ).
fof(f1238,plain,
( spl21_148
<=> ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ sP0(X0)
| member(sK14(X0,X1),X1)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_148])]) ).
fof(f1272,plain,
( ! [X0,X1] :
( ~ sP0(X0)
| sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| sP2(X0,X1)
| ~ member(sK14(X0,X1),X0) )
| ~ spl21_34
| ~ spl21_148 ),
inference(duplicate_literal_removal,[],[f1257]) ).
fof(f1257,plain,
( ! [X0,X1] :
( ~ sP0(X0)
| sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| sP2(X0,X1)
| ~ member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_34
| ~ spl21_148 ),
inference(resolution,[],[f1239,f347]) ).
fof(f1239,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X1)
| ~ sP0(X0)
| sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| sP2(X0,X1) )
| ~ spl21_148 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f2086,plain,
( spl21_254
| ~ spl21_131
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1179,f1167,f1065,f2084]) ).
fof(f2084,plain,
( spl21_254
<=> ! [X0,X1] :
( ~ ilf_type(sK19(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_254])]) ).
fof(f1179,plain,
( ! [X0,X1] :
( ~ ilf_type(sK19(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) )
| ~ spl21_131
| ~ spl21_140 ),
inference(resolution,[],[f1168,f1066]) ).
fof(f2082,plain,
( spl21_253
| ~ spl21_24
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1172,f1167,f300,f2080]) ).
fof(f2080,plain,
( spl21_253
<=> ! [X0,X1] :
( ~ ilf_type(sK13(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_253])]) ).
fof(f1172,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| empty(image(X0,X1))
| ~ ilf_type(image(X0,X1),set_type) )
| ~ spl21_24
| ~ spl21_140 ),
inference(resolution,[],[f1168,f301]) ).
fof(f2078,plain,
( ~ spl21_250
| ~ spl21_251
| spl21_252
| ~ spl21_39
| ~ spl21_240 ),
inference(avatar_split_clause,[],[f1981,f1949,f374,f2076,f2072,f2068]) ).
fof(f2076,plain,
( spl21_252
<=> ! [X0] :
( sK10(X0) != sK13(sK7)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_252])]) ).
fof(f374,plain,
( spl21_39
<=> ! [X2,X0,X3] :
( sP0(X0)
| ordered_pair(X2,X3) != sK10(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_39])]) ).
fof(f1949,plain,
( spl21_240
<=> sK13(sK7) = ordered_pair(sK11(sK13(sK7)),sK12(sK13(sK7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_240])]) ).
fof(f1981,plain,
( ! [X0] :
( sK10(X0) != sK13(sK7)
| sP0(X0)
| ~ ilf_type(sK12(sK13(sK7)),set_type)
| ~ ilf_type(sK11(sK13(sK7)),set_type) )
| ~ spl21_39
| ~ spl21_240 ),
inference(superposition,[],[f375,f1951]) ).
fof(f1951,plain,
( sK13(sK7) = ordered_pair(sK11(sK13(sK7)),sK12(sK13(sK7)))
| ~ spl21_240 ),
inference(avatar_component_clause,[],[f1949]) ).
fof(f375,plain,
( ! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK10(X0)
| sP0(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_39 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f2008,plain,
( spl21_249
| ~ spl21_9
| ~ spl21_152 ),
inference(avatar_split_clause,[],[f1310,f1305,f232,f2006]) ).
fof(f2006,plain,
( spl21_249
<=> ! [X0] :
( member(sK13(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| empty(sK10(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_249])]) ).
fof(f1305,plain,
( spl21_152
<=> ! [X0] :
( ~ ilf_type(sK13(sK10(power_set(X0))),set_type)
| member(sK13(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| empty(sK10(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_152])]) ).
fof(f1310,plain,
( ! [X0] :
( member(sK13(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| empty(sK10(power_set(X0))) )
| ~ spl21_9
| ~ spl21_152 ),
inference(resolution,[],[f1306,f233]) ).
fof(f1306,plain,
( ! [X0] :
( ~ ilf_type(sK13(sK10(power_set(X0))),set_type)
| member(sK13(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| empty(sK10(power_set(X0))) )
| ~ spl21_152 ),
inference(avatar_component_clause,[],[f1305]) ).
fof(f2004,plain,
( spl21_248
| ~ spl21_9
| ~ spl21_151 ),
inference(avatar_split_clause,[],[f1309,f1301,f232,f2002]) ).
fof(f2002,plain,
( spl21_248
<=> ! [X0] :
( member(sK10(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| sP0(sK10(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_248])]) ).
fof(f1301,plain,
( spl21_151
<=> ! [X0] :
( ~ ilf_type(sK10(sK10(power_set(X0))),set_type)
| member(sK10(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| sP0(sK10(power_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_151])]) ).
fof(f1309,plain,
( ! [X0] :
( member(sK10(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| sP0(sK10(power_set(X0))) )
| ~ spl21_9
| ~ spl21_151 ),
inference(resolution,[],[f1302,f233]) ).
fof(f1302,plain,
( ! [X0] :
( ~ ilf_type(sK10(sK10(power_set(X0))),set_type)
| member(sK10(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| sP0(sK10(power_set(X0))) )
| ~ spl21_151 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f2000,plain,
( spl21_247
| ~ spl21_17
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1211,f1205,f267,f1998]) ).
fof(f1998,plain,
( spl21_247
<=> ! [X0,X1] :
( ~ ilf_type(sK10(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_247])]) ).
fof(f267,plain,
( spl21_17
<=> ! [X0] :
( sP0(X0)
| member(sK10(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).
fof(f1211,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(image(X0,X1)) )
| ~ spl21_17
| ~ spl21_144 ),
inference(resolution,[],[f1206,f268]) ).
fof(f268,plain,
( ! [X0] :
( member(sK10(X0),X0)
| sP0(X0) )
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f1996,plain,
( spl21_246
| ~ spl21_41
| ~ spl21_131 ),
inference(avatar_split_clause,[],[f1069,f1065,f383,f1994]) ).
fof(f1994,plain,
( spl21_246
<=> ! [X0] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| sK19(X0) = ordered_pair(sK11(sK19(X0)),sK12(sK19(X0)))
| ~ ilf_type(sK19(X0),set_type)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_246])]) ).
fof(f1069,plain,
( ! [X0] :
( empty(X0)
| ~ ilf_type(X0,set_type)
| sK19(X0) = ordered_pair(sK11(sK19(X0)),sK12(sK19(X0)))
| ~ ilf_type(sK19(X0),set_type)
| ~ sP0(X0) )
| ~ spl21_41
| ~ spl21_131 ),
inference(resolution,[],[f1066,f384]) ).
fof(f1991,plain,
( spl21_245
| ~ spl21_94
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1117,f1100,f770,f1989]) ).
fof(f1989,plain,
( spl21_245
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ilf_type(X0,subset_type(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_245])]) ).
fof(f770,plain,
( spl21_94
<=> ! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_94])]) ).
fof(f1117,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ilf_type(X0,subset_type(X1)) )
| ~ spl21_94
| ~ spl21_134 ),
inference(duplicate_literal_removal,[],[f1103]) ).
fof(f1103,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_94
| ~ spl21_134 ),
inference(resolution,[],[f1101,f771]) ).
fof(f771,plain,
( ! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_94 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f1979,plain,
( spl21_244
| ~ spl21_17
| ~ spl21_140 ),
inference(avatar_split_clause,[],[f1171,f1167,f267,f1977]) ).
fof(f1977,plain,
( spl21_244
<=> ! [X0,X1] :
( ~ ilf_type(sK10(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP0(image(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_244])]) ).
fof(f1171,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(image(X0,X1)),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type)
| ~ empty(X1)
| sP0(image(X0,X1)) )
| ~ spl21_17
| ~ spl21_140 ),
inference(resolution,[],[f1168,f268]) ).
fof(f1975,plain,
( spl21_242
| spl21_243
| ~ spl21_41
| ~ spl21_134 ),
inference(avatar_split_clause,[],[f1115,f1100,f383,f1973,f1970]) ).
fof(f1970,plain,
( spl21_242
<=> ! [X1] :
( ~ ilf_type(X1,set_type)
| ~ sP0(power_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_242])]) ).
fof(f1973,plain,
( spl21_243
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_243])]) ).
fof(f1115,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ sP0(power_set(X1)) )
| ~ spl21_41
| ~ spl21_134 ),
inference(duplicate_literal_removal,[],[f1105]) ).
fof(f1105,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ ilf_type(X0,set_type)
| ~ sP0(power_set(X1)) )
| ~ spl21_41
| ~ spl21_134 ),
inference(resolution,[],[f1101,f384]) ).
fof(f1967,plain,
( spl21_241
| ~ spl21_9
| ~ spl21_143 ),
inference(avatar_split_clause,[],[f1208,f1201,f232,f1965]) ).
fof(f1965,plain,
( spl21_241
<=> ! [X2,X0,X1] :
( image4(X0,X1,sK17(X1,X0),X2) = image(sK17(X1,X0),X2)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_241])]) ).
fof(f1201,plain,
( spl21_143
<=> ! [X2,X0,X1] :
( image4(X0,X1,sK17(X1,X0),X2) = image(sK17(X1,X0),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_143])]) ).
fof(f1208,plain,
( ! [X2,X0,X1] :
( image4(X0,X1,sK17(X1,X0),X2) = image(sK17(X1,X0),X2)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_143 ),
inference(resolution,[],[f1202,f233]) ).
fof(f1202,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,set_type)
| image4(X0,X1,sK17(X1,X0),X2) = image(sK17(X1,X0),X2)
| ~ ilf_type(X0,set_type) )
| ~ spl21_143 ),
inference(avatar_component_clause,[],[f1201]) ).
fof(f1955,plain,
( ~ spl21_126
| ~ spl21_127
| ~ spl21_75
| ~ spl21_223
| ~ spl21_37
| ~ spl21_125
| ~ spl21_144 ),
inference(avatar_split_clause,[],[f1888,f1205,f1027,f358,f1795,f659,f1038,f1034]) ).
fof(f1034,plain,
( spl21_126
<=> ilf_type(sK7,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_126])]) ).
fof(f1038,plain,
( spl21_127
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_127])]) ).
fof(f1888,plain,
( ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK5,set_type)
| ~ ilf_type(sK7,binary_relation_type)
| ~ empty(sK7)
| ~ ilf_type(sK7,set_type)
| ~ spl21_125
| ~ spl21_144 ),
inference(resolution,[],[f1028,f1206]) ).
fof(f1028,plain,
( member(sK8,image(sK7,sK5))
| ~ spl21_125 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1952,plain,
( spl21_240
| spl21_127
| ~ spl21_122
| ~ spl21_238 ),
inference(avatar_split_clause,[],[f1940,f1937,f1006,f1038,f1949]) ).
fof(f1937,plain,
( spl21_238
<=> ! [X0] :
( ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_238])]) ).
fof(f1940,plain,
( empty(sK7)
| sK13(sK7) = ordered_pair(sK11(sK13(sK7)),sK12(sK13(sK7)))
| ~ spl21_122
| ~ spl21_238 ),
inference(resolution,[],[f1938,f1008]) ).
fof(f1008,plain,
( sP0(sK7)
| ~ spl21_122 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1938,plain,
( ! [X0] :
( ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) )
| ~ spl21_238 ),
inference(avatar_component_clause,[],[f1937]) ).
fof(f1947,plain,
( spl21_239
| ~ spl21_22
| ~ spl21_142 ),
inference(avatar_split_clause,[],[f1198,f1189,f288,f1945]) ).
fof(f1945,plain,
( spl21_239
<=> ! [X0] :
( empty(power_set(X0))
| ~ ilf_type(sK18(X0),set_type)
| member(sK18(X0),power_set(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_239])]) ).
fof(f288,plain,
( spl21_22
<=> ! [X0] :
( ilf_type(sK18(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_22])]) ).
fof(f1198,plain,
( ! [X0] :
( empty(power_set(X0))
| ~ ilf_type(sK18(X0),set_type)
| member(sK18(X0),power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_22
| ~ spl21_142 ),
inference(duplicate_literal_removal,[],[f1195]) ).
fof(f1195,plain,
( ! [X0] :
( empty(power_set(X0))
| ~ ilf_type(sK18(X0),set_type)
| member(sK18(X0),power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_22
| ~ spl21_142 ),
inference(resolution,[],[f1190,f289]) ).
fof(f289,plain,
( ! [X0] :
( ilf_type(sK18(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f1939,plain,
( spl21_238
| ~ spl21_9
| ~ spl21_141 ),
inference(avatar_split_clause,[],[f1192,f1181,f232,f1937]) ).
fof(f1181,plain,
( spl21_141
<=> ! [X0] :
( sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0)))
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_141])]) ).
fof(f1192,plain,
( ! [X0] :
( ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) )
| ~ spl21_9
| ~ spl21_141 ),
inference(resolution,[],[f1182,f233]) ).
fof(f1182,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ~ sP0(X0)
| empty(X0)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0))) )
| ~ spl21_141 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f1922,plain,
( spl21_237
| ~ spl21_34
| ~ spl21_138 ),
inference(avatar_split_clause,[],[f1160,f1131,f346,f1920]) ).
fof(f1920,plain,
( spl21_237
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(sK14(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_237])]) ).
fof(f1160,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(sK14(X0,X1),X0) )
| ~ spl21_34
| ~ spl21_138 ),
inference(duplicate_literal_removal,[],[f1148]) ).
fof(f1148,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| ~ member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_34
| ~ spl21_138 ),
inference(resolution,[],[f1132,f347]) ).
fof(f1917,plain,
( spl21_236
| ~ spl21_120
| ~ spl21_133 ),
inference(avatar_split_clause,[],[f1098,f1095,f995,f1915]) ).
fof(f1915,plain,
( spl21_236
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sP0(sK18(cross_product(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_236])]) ).
fof(f995,plain,
( spl21_120
<=> ! [X0] :
( ~ relation_like(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_120])]) ).
fof(f1095,plain,
( spl21_133
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK18(cross_product(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_133])]) ).
fof(f1098,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sP0(sK18(cross_product(X0,X1))) )
| ~ spl21_120
| ~ spl21_133 ),
inference(resolution,[],[f1096,f996]) ).
fof(f996,plain,
( ! [X0] :
( ~ relation_like(X0)
| sP0(X0) )
| ~ spl21_120 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f1096,plain,
( ! [X0,X1] :
( relation_like(sK18(cross_product(X1,X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_133 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1901,plain,
( spl21_235
| ~ spl21_9
| ~ spl21_139 ),
inference(avatar_split_clause,[],[f1165,f1162,f232,f1899]) ).
fof(f1899,plain,
( spl21_235
<=> ! [X0] :
( empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_235])]) ).
fof(f1162,plain,
( spl21_139
<=> ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_139])]) ).
fof(f1165,plain,
( ! [X0] :
( empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0)) )
| ~ spl21_9
| ~ spl21_139 ),
inference(resolution,[],[f1163,f233]) ).
fof(f1163,plain,
( ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0)) )
| ~ spl21_139 ),
inference(avatar_component_clause,[],[f1162]) ).
fof(f1897,plain,
( spl21_234
| ~ spl21_9
| ~ spl21_136 ),
inference(avatar_split_clause,[],[f1134,f1123,f232,f1895]) ).
fof(f1895,plain,
( spl21_234
<=> ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_234])]) ).
fof(f1123,plain,
( spl21_136
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_136])]) ).
fof(f1134,plain,
( ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1))
| ~ spl21_9
| ~ spl21_136 ),
inference(resolution,[],[f1124,f233]) ).
fof(f1124,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)) )
| ~ spl21_136 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f1881,plain,
( ~ spl21_37
| ~ spl21_75
| ~ spl21_62
| spl21_233
| ~ spl21_12
| ~ spl21_55 ),
inference(avatar_split_clause,[],[f1023,f490,f245,f1879,f584,f659,f358]) ).
fof(f584,plain,
( spl21_62
<=> ilf_type(sK9,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_62])]) ).
fof(f490,plain,
( spl21_55
<=> ! [X0,X3,X2,X1] :
( member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_55])]) ).
fof(f1023,plain,
( ! [X0] :
( ~ member(sK9,X0)
| member(sK8,image(sK7,X0))
| ~ ilf_type(sK9,set_type)
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_12
| ~ spl21_55 ),
inference(resolution,[],[f247,f491]) ).
fof(f491,plain,
( ! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X3,X1),X2)
| ~ member(X3,X0)
| member(X1,image(X2,X0))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_55 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f1870,plain,
( ~ spl21_58
| ~ spl21_63
| spl21_232
| ~ spl21_5
| ~ spl21_228 ),
inference(avatar_split_clause,[],[f1826,f1823,f213,f1867,f588,f502]) ).
fof(f502,plain,
( spl21_58
<=> ilf_type(sK4,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_58])]) ).
fof(f588,plain,
( spl21_63
<=> ilf_type(sK6,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_63])]) ).
fof(f213,plain,
( spl21_5
<=> ilf_type(sK7,relation_type(sK6,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).
fof(f1823,plain,
( spl21_228
<=> ! [X0,X1] :
( member(sK16(sK5,sK8,sK7),X0)
| ~ ilf_type(sK7,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_228])]) ).
fof(f1826,plain,
( member(sK16(sK5,sK8,sK7),sK6)
| ~ ilf_type(sK6,set_type)
| ~ ilf_type(sK4,set_type)
| ~ spl21_5
| ~ spl21_228 ),
inference(resolution,[],[f1824,f215]) ).
fof(f215,plain,
( ilf_type(sK7,relation_type(sK6,sK4))
| ~ spl21_5 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f1824,plain,
( ! [X0,X1] :
( ~ ilf_type(sK7,relation_type(X0,X1))
| member(sK16(sK5,sK8,sK7),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_228 ),
inference(avatar_component_clause,[],[f1823]) ).
fof(f1865,plain,
( spl21_231
| ~ spl21_120
| ~ spl21_132 ),
inference(avatar_split_clause,[],[f1093,f1090,f995,f1863]) ).
fof(f1863,plain,
( spl21_231
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sP0(sK17(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_231])]) ).
fof(f1090,plain,
( spl21_132
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK17(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_132])]) ).
fof(f1093,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sP0(sK17(X1,X0)) )
| ~ spl21_120
| ~ spl21_132 ),
inference(resolution,[],[f1091,f996]) ).
fof(f1091,plain,
( ! [X0,X1] :
( relation_like(sK17(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_132 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f1843,plain,
( ~ spl21_62
| ~ spl21_37
| spl21_230
| ~ spl21_12
| ~ spl21_56 ),
inference(avatar_split_clause,[],[f1022,f494,f245,f1841,f358,f584]) ).
fof(f1841,plain,
( spl21_230
<=> ! [X0,X1] :
( member(sK9,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK7,relation_type(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_230])]) ).
fof(f494,plain,
( spl21_56
<=> ! [X4,X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_56])]) ).
fof(f1022,plain,
( ! [X0,X1] :
( member(sK9,X0)
| ~ ilf_type(sK7,relation_type(X0,X1))
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK9,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_12
| ~ spl21_56 ),
inference(resolution,[],[f247,f495]) ).
fof(f495,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_56 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f1839,plain,
( ~ spl21_7
| ~ spl21_8
| ~ spl21_11
| ~ spl21_12 ),
inference(avatar_split_clause,[],[f1833,f245,f241,f227,f222]) ).
fof(f227,plain,
( spl21_8
<=> ilf_type(sK9,member_type(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_8])]) ).
fof(f241,plain,
( spl21_11
<=> ! [X5] :
( ~ member(X5,sK5)
| ~ ilf_type(X5,member_type(sK6))
| ~ member(ordered_pair(X5,sK8),sK7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).
fof(f1833,plain,
( ~ ilf_type(sK9,member_type(sK6))
| ~ member(sK9,sK5)
| ~ spl21_11
| ~ spl21_12 ),
inference(resolution,[],[f247,f242]) ).
fof(f242,plain,
( ! [X5] :
( ~ member(ordered_pair(X5,sK8),sK7)
| ~ ilf_type(X5,member_type(sK6))
| ~ member(X5,sK5) )
| ~ spl21_11 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f1831,plain,
( ~ spl21_122
| ~ spl21_75
| spl21_229
| ~ spl21_223
| ~ spl21_37
| ~ spl21_125
| ~ spl21_179 ),
inference(avatar_split_clause,[],[f1531,f1512,f1027,f358,f1795,f1828,f659,f1006]) ).
fof(f1828,plain,
( spl21_229
<=> ordered_pair(sK16(sK5,sK8,sK7),sK8) = ordered_pair(sK11(ordered_pair(sK16(sK5,sK8,sK7),sK8)),sK12(ordered_pair(sK16(sK5,sK8,sK7),sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_229])]) ).
fof(f1512,plain,
( spl21_179
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(sK16(X2,X1,X0),X1) = ordered_pair(sK11(ordered_pair(sK16(X2,X1,X0),X1)),sK12(ordered_pair(sK16(X2,X1,X0),X1)))
| ~ member(X1,image(X0,X2))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_179])]) ).
fof(f1531,plain,
( ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK5,set_type)
| ordered_pair(sK16(sK5,sK8,sK7),sK8) = ordered_pair(sK11(ordered_pair(sK16(sK5,sK8,sK7),sK8)),sK12(ordered_pair(sK16(sK5,sK8,sK7),sK8)))
| ~ ilf_type(sK7,binary_relation_type)
| ~ sP0(sK7)
| ~ spl21_125
| ~ spl21_179 ),
inference(resolution,[],[f1513,f1028]) ).
fof(f1513,plain,
( ! [X2,X0,X1] :
( ~ member(X1,image(X0,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(sK16(X2,X1,X0),X1) = ordered_pair(sK11(ordered_pair(sK16(X2,X1,X0),X1)),sK12(ordered_pair(sK16(X2,X1,X0),X1)))
| ~ ilf_type(X0,binary_relation_type)
| ~ sP0(X0) )
| ~ spl21_179 ),
inference(avatar_component_clause,[],[f1512]) ).
fof(f1825,plain,
( ~ spl21_223
| ~ spl21_75
| spl21_228
| ~ spl21_37
| ~ spl21_125
| ~ spl21_162 ),
inference(avatar_split_clause,[],[f1388,f1362,f1027,f358,f1823,f659,f1795]) ).
fof(f1362,plain,
( spl21_162
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| member(sK16(X4,X3,X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X3,image(X0,X4))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_162])]) ).
fof(f1388,plain,
( ! [X0,X1] :
( ~ ilf_type(sK8,set_type)
| member(sK16(sK5,sK8,sK7),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK7,relation_type(X0,X1))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK5,set_type) )
| ~ spl21_125
| ~ spl21_162 ),
inference(resolution,[],[f1363,f1028]) ).
fof(f1363,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X3,image(X0,X4))
| ~ ilf_type(X3,set_type)
| member(sK16(X4,X3,X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_162 ),
inference(avatar_component_clause,[],[f1362]) ).
fof(f1821,plain,
( ~ spl21_9
| spl21_227 ),
inference(avatar_contradiction_clause,[],[f1820]) ).
fof(f1820,plain,
( $false
| ~ spl21_9
| spl21_227 ),
inference(resolution,[],[f1818,f233]) ).
fof(f1818,plain,
( ~ ilf_type(sK16(sK6,sK8,sK7),set_type)
| spl21_227 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f1816,plain,
( spl21_227
<=> ilf_type(sK16(sK6,sK8,sK7),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_227])]) ).
fof(f1819,plain,
( ~ spl21_37
| ~ spl21_75
| ~ spl21_225
| ~ spl21_63
| ~ spl21_226
| ~ spl21_227
| ~ spl21_51
| ~ spl21_124 ),
inference(avatar_split_clause,[],[f1063,f1016,f459,f1816,f1812,f588,f1808,f659,f358]) ).
fof(f1808,plain,
( spl21_225
<=> member(sK8,image(sK7,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_225])]) ).
fof(f1812,plain,
( spl21_226
<=> member(sK16(sK6,sK8,sK7),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_226])]) ).
fof(f1063,plain,
( ~ ilf_type(sK16(sK6,sK8,sK7),set_type)
| ~ member(sK16(sK6,sK8,sK7),sK5)
| ~ ilf_type(sK6,set_type)
| ~ member(sK8,image(sK7,sK6))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ spl21_51
| ~ spl21_124 ),
inference(duplicate_literal_removal,[],[f1062]) ).
fof(f1062,plain,
( ~ ilf_type(sK16(sK6,sK8,sK7),set_type)
| ~ member(sK16(sK6,sK8,sK7),sK5)
| ~ ilf_type(sK6,set_type)
| ~ member(sK8,image(sK7,sK6))
| ~ member(sK8,image(sK7,sK6))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK6,set_type)
| ~ spl21_51
| ~ spl21_124 ),
inference(resolution,[],[f1017,f460]) ).
fof(f1805,plain,
( spl21_224
| ~ spl21_25
| ~ spl21_118 ),
inference(avatar_split_clause,[],[f989,f985,f304,f1803]) ).
fof(f1803,plain,
( spl21_224
<=> ! [X0,X1] :
( ~ sP2(X0,X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_224])]) ).
fof(f304,plain,
( spl21_25
<=> ! [X0,X1] :
( X0 = X1
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_25])]) ).
fof(f985,plain,
( spl21_118
<=> ! [X0,X1] : sP3(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_118])]) ).
fof(f989,plain,
( ! [X0,X1] :
( ~ sP2(X0,X1)
| X0 = X1 )
| ~ spl21_25
| ~ spl21_118 ),
inference(resolution,[],[f986,f305]) ).
fof(f305,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| ~ sP2(X1,X0)
| X0 = X1 )
| ~ spl21_25 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f986,plain,
( ! [X0,X1] : sP3(X0,X1)
| ~ spl21_118 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f1800,plain,
( ~ spl21_9
| spl21_223 ),
inference(avatar_contradiction_clause,[],[f1799]) ).
fof(f1799,plain,
( $false
| ~ spl21_9
| spl21_223 ),
inference(resolution,[],[f1797,f233]) ).
fof(f1797,plain,
( ~ ilf_type(sK5,set_type)
| spl21_223 ),
inference(avatar_component_clause,[],[f1795]) ).
fof(f1798,plain,
( ~ spl21_223
| ~ spl21_75
| spl21_129
| ~ spl21_37
| ~ spl21_125
| ~ spl21_155 ),
inference(avatar_split_clause,[],[f1324,f1320,f1027,f358,f1051,f659,f1795]) ).
fof(f1051,plain,
( spl21_129
<=> ! [X0,X1] :
( member(sK8,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK7,relation_type(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_129])]) ).
fof(f1320,plain,
( spl21_155
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| member(X3,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X3,image(X0,X4))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_155])]) ).
fof(f1324,plain,
( ! [X0,X1] :
( ~ ilf_type(sK8,set_type)
| member(sK8,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK7,relation_type(X1,X0))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK5,set_type) )
| ~ spl21_125
| ~ spl21_155 ),
inference(resolution,[],[f1321,f1028]) ).
fof(f1321,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(X3,image(X0,X4))
| ~ ilf_type(X3,set_type)
| member(X3,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_155 ),
inference(avatar_component_clause,[],[f1320]) ).
fof(f1773,plain,
( spl21_222
| ~ spl21_52
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f963,f960,f469,f1771]) ).
fof(f1771,plain,
( spl21_222
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(ordered_pair(sK16(X3,X4,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X4),set_type)
| member(ordered_pair(sK16(X3,X4,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| ~ member(X4,image(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3))
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),binary_relation_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_222])]) ).
fof(f469,plain,
( spl21_52
<=> ! [X2,X0,X1] :
( member(ordered_pair(sK16(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_52])]) ).
fof(f960,plain,
( spl21_115
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(power_set(X1),X2))
| ~ ilf_type(power_set(X1),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,ordered_pair(sK16(X2,X0,power_set(X1)),X0))
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X0,power_set(X1)),X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_115])]) ).
fof(f963,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(ordered_pair(sK16(X3,X4,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X4),set_type)
| member(ordered_pair(sK16(X3,X4,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| ~ member(X4,image(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3))
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),binary_relation_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_52
| ~ spl21_115 ),
inference(resolution,[],[f961,f470]) ).
fof(f470,plain,
( ! [X2,X0,X1] :
( member(ordered_pair(sK16(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f961,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,ordered_pair(sK16(X2,X0,power_set(X1)),X0))
| ~ ilf_type(power_set(X1),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X0,image(power_set(X1),X2))
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X0,power_set(X1)),X0),set_type) )
| ~ spl21_115 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f1768,plain,
( spl21_221
| ~ spl21_52
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f948,f945,f469,f1766]) ).
fof(f1766,plain,
( spl21_221
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(ordered_pair(sK16(X3,X4,sK16(power_set(X2),X1,X0)),X4),set_type)
| member(ordered_pair(sK16(X3,X4,sK16(power_set(X2),X1,X0)),X4),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| ~ member(X4,image(sK16(power_set(X2),X1,X0),X3))
| ~ ilf_type(sK16(power_set(X2),X1,X0),binary_relation_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_221])]) ).
fof(f945,plain,
( spl21_114
<=> ! [X0,X3,X2,X1] :
( ~ member(X0,image(X1,power_set(X2)))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X3,sK16(power_set(X2),X0,X1))
| ~ ilf_type(X3,set_type)
| member(X3,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_114])]) ).
fof(f948,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(ordered_pair(sK16(X3,X4,sK16(power_set(X2),X1,X0)),X4),set_type)
| member(ordered_pair(sK16(X3,X4,sK16(power_set(X2),X1,X0)),X4),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| ~ member(X4,image(sK16(power_set(X2),X1,X0),X3))
| ~ ilf_type(sK16(power_set(X2),X1,X0),binary_relation_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_52
| ~ spl21_114 ),
inference(resolution,[],[f946,f470]) ).
fof(f946,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X3,sK16(power_set(X2),X0,X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X0,image(X1,power_set(X2)))
| ~ ilf_type(X3,set_type)
| member(X3,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X0,X1),set_type) )
| ~ spl21_114 ),
inference(avatar_component_clause,[],[f945]) ).
fof(f1762,plain,
( spl21_220
| ~ spl21_33
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f967,f960,f342,f1760]) ).
fof(f1760,plain,
( spl21_220
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK14(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),set_type)
| member(sK14(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| member(sK14(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),X3)
| sP2(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_220])]) ).
fof(f967,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK14(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),set_type)
| member(sK14(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| member(sK14(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),X3)
| sP2(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3) )
| ~ spl21_33
| ~ spl21_115 ),
inference(resolution,[],[f961,f343]) ).
fof(f1758,plain,
( spl21_219
| ~ spl21_33
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f966,f960,f342,f1756]) ).
fof(f1756,plain,
( spl21_219
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK14(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),set_type)
| member(sK14(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| member(sK14(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X3)
| sP2(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_219])]) ).
fof(f966,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK14(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),set_type)
| member(sK14(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| member(sK14(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X3)
| sP2(X3,ordered_pair(sK16(X2,X1,power_set(X0)),X1)) )
| ~ spl21_33
| ~ spl21_115 ),
inference(resolution,[],[f961,f343]) ).
fof(f1753,plain,
( spl21_218
| ~ spl21_51
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f971,f960,f459,f1751]) ).
fof(f1751,plain,
( spl21_218
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK16(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3,X4),set_type)
| member(sK16(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3,X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| ~ member(X3,image(X4,ordered_pair(sK16(X2,X1,power_set(X0)),X1)))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_218])]) ).
fof(f971,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK16(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3,X4),set_type)
| member(sK16(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3,X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| ~ member(X3,image(X4,ordered_pair(sK16(X2,X1,power_set(X0)),X1)))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_51
| ~ spl21_115 ),
inference(duplicate_literal_removal,[],[f970]) ).
fof(f970,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK16(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3,X4),set_type)
| member(sK16(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3,X4),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| ~ member(X3,image(X4,ordered_pair(sK16(X2,X1,power_set(X0)),X1)))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type) )
| ~ spl21_51
| ~ spl21_115 ),
inference(resolution,[],[f961,f460]) ).
fof(f1749,plain,
( ~ spl21_58
| spl21_217
| ~ spl21_50
| ~ spl21_191 ),
inference(avatar_split_clause,[],[f1719,f1599,f450,f1747,f502]) ).
fof(f1747,plain,
( spl21_217
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| member(X1,sK4)
| ~ ilf_type(X1,set_type)
| ~ member(X1,image(sK7,X0))
| ~ ilf_type(image(sK7,X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_217])]) ).
fof(f1599,plain,
( spl21_191
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| member(image(sK7,X0),power_set(sK4))
| ~ ilf_type(image(sK7,X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_191])]) ).
fof(f1719,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(image(sK7,X0),set_type)
| ~ member(X1,image(sK7,X0))
| ~ ilf_type(X1,set_type)
| member(X1,sK4)
| ~ ilf_type(sK4,set_type) )
| ~ spl21_50
| ~ spl21_191 ),
inference(duplicate_literal_removal,[],[f1714]) ).
fof(f1714,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(image(sK7,X0),set_type)
| ~ member(X1,image(sK7,X0))
| ~ ilf_type(X1,set_type)
| member(X1,sK4)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(image(sK7,X0),set_type) )
| ~ spl21_50
| ~ spl21_191 ),
inference(resolution,[],[f1600,f451]) ).
fof(f1600,plain,
( ! [X0] :
( member(image(sK7,X0),power_set(sK4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(image(sK7,X0),set_type) )
| ~ spl21_191 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f1743,plain,
( spl21_216
| ~ spl21_42
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f972,f960,f389,f1741]) ).
fof(f1741,plain,
( spl21_216
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK15(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),set_type)
| member(sK15(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| member(ordered_pair(sK16(X2,X1,power_set(X0)),X1),power_set(X3))
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_216])]) ).
fof(f972,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK15(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),set_type)
| member(sK15(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| member(ordered_pair(sK16(X2,X1,power_set(X0)),X1),power_set(X3))
| ~ ilf_type(X3,set_type) )
| ~ spl21_42
| ~ spl21_115 ),
inference(duplicate_literal_removal,[],[f969]) ).
fof(f969,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK15(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),set_type)
| member(sK15(ordered_pair(sK16(X2,X1,power_set(X0)),X1),X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| member(ordered_pair(sK16(X2,X1,power_set(X0)),X1),power_set(X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type) )
| ~ spl21_42
| ~ spl21_115 ),
inference(resolution,[],[f961,f390]) ).
fof(f1739,plain,
( spl21_215
| ~ spl21_52
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f897,f894,f469,f1737]) ).
fof(f1737,plain,
( spl21_215
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK15(power_set(X2),X3)),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK15(power_set(X2),X3)),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK15(power_set(X2),X3),set_type)
| member(power_set(X2),power_set(X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(sK15(power_set(X2),X3),X0))
| ~ ilf_type(sK15(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_215])]) ).
fof(f894,plain,
( spl21_107
<=> ! [X2,X0,X1] :
( ~ member(X0,sK15(power_set(X1),X2))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK15(power_set(X1),X2),set_type)
| member(power_set(X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(power_set(X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_107])]) ).
fof(f897,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK15(power_set(X2),X3)),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK15(power_set(X2),X3)),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK15(power_set(X2),X3),set_type)
| member(power_set(X2),power_set(X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(sK15(power_set(X2),X3),X0))
| ~ ilf_type(sK15(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_107 ),
inference(resolution,[],[f895,f470]) ).
fof(f895,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK15(power_set(X1),X2))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK15(power_set(X1),X2),set_type)
| member(power_set(X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(power_set(X1),set_type) )
| ~ spl21_107 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f1732,plain,
( spl21_214
| ~ spl21_51
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f956,f945,f459,f1730]) ).
fof(f1730,plain,
( spl21_214
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK16(sK16(power_set(X2),X1,X0),X3,X4),set_type)
| member(sK16(sK16(power_set(X2),X1,X0),X3,X4),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| ~ member(X3,image(X4,sK16(power_set(X2),X1,X0)))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_214])]) ).
fof(f956,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK16(sK16(power_set(X2),X1,X0),X3,X4),set_type)
| member(sK16(sK16(power_set(X2),X1,X0),X3,X4),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| ~ member(X3,image(X4,sK16(power_set(X2),X1,X0)))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_51
| ~ spl21_114 ),
inference(duplicate_literal_removal,[],[f955]) ).
fof(f955,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK16(sK16(power_set(X2),X1,X0),X3,X4),set_type)
| member(sK16(sK16(power_set(X2),X1,X0),X3,X4),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| ~ member(X3,image(X4,sK16(power_set(X2),X1,X0)))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type) )
| ~ spl21_51
| ~ spl21_114 ),
inference(resolution,[],[f946,f460]) ).
fof(f1728,plain,
( spl21_213
| ~ spl21_52
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f878,f859,f469,f1726]) ).
fof(f1726,plain,
( spl21_213
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK14(power_set(X2),X3)),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK14(power_set(X2),X3)),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(power_set(X2),X3),set_type)
| member(sK14(power_set(X2),X3),X3)
| sP2(power_set(X2),X3)
| ~ member(X1,image(sK14(power_set(X2),X3),X0))
| ~ ilf_type(sK14(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_213])]) ).
fof(f859,plain,
( spl21_104
<=> ! [X2,X0,X1] :
( ~ member(X0,sK14(power_set(X1),X2))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(power_set(X1),X2),set_type)
| member(sK14(power_set(X1),X2),X2)
| sP2(power_set(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_104])]) ).
fof(f878,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK14(power_set(X2),X3)),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK14(power_set(X2),X3)),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(power_set(X2),X3),set_type)
| member(sK14(power_set(X2),X3),X3)
| sP2(power_set(X2),X3)
| ~ member(X1,image(sK14(power_set(X2),X3),X0))
| ~ ilf_type(sK14(power_set(X2),X3),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_104 ),
inference(resolution,[],[f860,f470]) ).
fof(f860,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK14(power_set(X1),X2))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(power_set(X1),X2),set_type)
| member(sK14(power_set(X1),X2),X2)
| sP2(power_set(X1),X2) )
| ~ spl21_104 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f1724,plain,
( spl21_212
| ~ spl21_52
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f862,f855,f469,f1722]) ).
fof(f1722,plain,
( spl21_212
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK14(X2,power_set(X3))),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK14(X2,power_set(X3))),X1),X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(sK14(X2,power_set(X3)),set_type)
| member(sK14(X2,power_set(X3)),X2)
| sP2(X2,power_set(X3))
| ~ member(X1,image(sK14(X2,power_set(X3)),X0))
| ~ ilf_type(sK14(X2,power_set(X3)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_212])]) ).
fof(f855,plain,
( spl21_103
<=> ! [X2,X0,X1] :
( ~ member(X0,sK14(X1,power_set(X2)))
| ~ ilf_type(X0,set_type)
| member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(X1,power_set(X2)),set_type)
| member(sK14(X1,power_set(X2)),X1)
| sP2(X1,power_set(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_103])]) ).
fof(f862,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK14(X2,power_set(X3))),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK14(X2,power_set(X3))),X1),X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(sK14(X2,power_set(X3)),set_type)
| member(sK14(X2,power_set(X3)),X2)
| sP2(X2,power_set(X3))
| ~ member(X1,image(sK14(X2,power_set(X3)),X0))
| ~ ilf_type(sK14(X2,power_set(X3)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_103 ),
inference(resolution,[],[f856,f470]) ).
fof(f856,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK14(X1,power_set(X2)))
| ~ ilf_type(X0,set_type)
| member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(X1,power_set(X2)),set_type)
| member(sK14(X1,power_set(X2)),X1)
| sP2(X1,power_set(X2)) )
| ~ spl21_103 ),
inference(avatar_component_clause,[],[f855]) ).
fof(f1710,plain,
( spl21_211
| ~ spl21_33
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f952,f945,f342,f1708]) ).
fof(f1708,plain,
( spl21_211
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK14(sK16(power_set(X2),X1,X0),X3),set_type)
| member(sK14(sK16(power_set(X2),X1,X0),X3),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| member(sK14(sK16(power_set(X2),X1,X0),X3),X3)
| sP2(sK16(power_set(X2),X1,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_211])]) ).
fof(f952,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK14(sK16(power_set(X2),X1,X0),X3),set_type)
| member(sK14(sK16(power_set(X2),X1,X0),X3),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| member(sK14(sK16(power_set(X2),X1,X0),X3),X3)
| sP2(sK16(power_set(X2),X1,X0),X3) )
| ~ spl21_33
| ~ spl21_114 ),
inference(resolution,[],[f946,f343]) ).
fof(f1706,plain,
( spl21_210
| ~ spl21_33
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f951,f945,f342,f1704]) ).
fof(f1704,plain,
( spl21_210
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK14(X3,sK16(power_set(X2),X1,X0)),set_type)
| member(sK14(X3,sK16(power_set(X2),X1,X0)),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| member(sK14(X3,sK16(power_set(X2),X1,X0)),X3)
| sP2(X3,sK16(power_set(X2),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_210])]) ).
fof(f951,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK14(X3,sK16(power_set(X2),X1,X0)),set_type)
| member(sK14(X3,sK16(power_set(X2),X1,X0)),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| member(sK14(X3,sK16(power_set(X2),X1,X0)),X3)
| sP2(X3,sK16(power_set(X2),X1,X0)) )
| ~ spl21_33
| ~ spl21_114 ),
inference(resolution,[],[f946,f343]) ).
fof(f1700,plain,
( spl21_209
| ~ spl21_24
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f973,f960,f300,f1698]) ).
fof(f1698,plain,
( spl21_209
<=> ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK13(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),set_type)
| member(sK13(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| empty(ordered_pair(sK16(X2,X1,power_set(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_209])]) ).
fof(f973,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK13(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),set_type)
| member(sK13(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| empty(ordered_pair(sK16(X2,X1,power_set(X0)),X1)) )
| ~ spl21_24
| ~ spl21_115 ),
inference(duplicate_literal_removal,[],[f965]) ).
fof(f965,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK13(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),set_type)
| member(sK13(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| empty(ordered_pair(sK16(X2,X1,power_set(X0)),X1))
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type) )
| ~ spl21_24
| ~ spl21_115 ),
inference(resolution,[],[f961,f301]) ).
fof(f1696,plain,
( spl21_208
| ~ spl21_17
| ~ spl21_115 ),
inference(avatar_split_clause,[],[f964,f960,f267,f1694]) ).
fof(f1694,plain,
( spl21_208
<=> ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK10(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),set_type)
| member(sK10(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| sP0(ordered_pair(sK16(X2,X1,power_set(X0)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_208])]) ).
fof(f964,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(power_set(X0),X2))
| ~ ilf_type(sK10(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),set_type)
| member(sK10(ordered_pair(sK16(X2,X1,power_set(X0)),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X1,power_set(X0)),X1),set_type)
| sP0(ordered_pair(sK16(X2,X1,power_set(X0)),X1)) )
| ~ spl21_17
| ~ spl21_115 ),
inference(resolution,[],[f961,f268]) ).
fof(f1691,plain,
( spl21_207
| ~ spl21_42
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f957,f945,f389,f1689]) ).
fof(f1689,plain,
( spl21_207
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK15(sK16(power_set(X2),X1,X0),X3),set_type)
| member(sK15(sK16(power_set(X2),X1,X0),X3),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| member(sK16(power_set(X2),X1,X0),power_set(X3))
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_207])]) ).
fof(f957,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK15(sK16(power_set(X2),X1,X0),X3),set_type)
| member(sK15(sK16(power_set(X2),X1,X0),X3),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| member(sK16(power_set(X2),X1,X0),power_set(X3))
| ~ ilf_type(X3,set_type) )
| ~ spl21_42
| ~ spl21_114 ),
inference(duplicate_literal_removal,[],[f954]) ).
fof(f954,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK15(sK16(power_set(X2),X1,X0),X3),set_type)
| member(sK15(sK16(power_set(X2),X1,X0),X3),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| member(sK16(power_set(X2),X1,X0),power_set(X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type) )
| ~ spl21_42
| ~ spl21_114 ),
inference(resolution,[],[f946,f390]) ).
fof(f1685,plain,
( spl21_206
| ~ spl21_51
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f905,f894,f459,f1683]) ).
fof(f1683,plain,
( spl21_206
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(sK16(sK15(power_set(X0),X1),X2,X3),set_type)
| member(sK16(sK15(power_set(X0),X1),X2,X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X2,image(X3,sK15(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_206])]) ).
fof(f905,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(sK15(power_set(X0),X1),X2,X3),set_type)
| member(sK16(sK15(power_set(X0),X1),X2,X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X2,image(X3,sK15(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_51
| ~ spl21_107 ),
inference(duplicate_literal_removal,[],[f904]) ).
fof(f904,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(sK15(power_set(X0),X1),X2,X3),set_type)
| member(sK16(sK15(power_set(X0),X1),X2,X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X2,image(X3,sK15(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type) )
| ~ spl21_51
| ~ spl21_107 ),
inference(resolution,[],[f895,f460]) ).
fof(f1681,plain,
( spl21_205
| ~ spl21_52
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f819,f816,f469,f1679]) ).
fof(f1679,plain,
( spl21_205
<=> ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK13(power_set(X2))),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK13(power_set(X2))),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK13(power_set(X2)),set_type)
| empty(power_set(X2))
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(sK13(power_set(X2)),X0))
| ~ ilf_type(sK13(power_set(X2)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_205])]) ).
fof(f819,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK13(power_set(X2))),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK13(power_set(X2))),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK13(power_set(X2)),set_type)
| empty(power_set(X2))
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(sK13(power_set(X2)),X0))
| ~ ilf_type(sK13(power_set(X2)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_98 ),
inference(resolution,[],[f817,f470]) ).
fof(f1673,plain,
( spl21_204
| ~ spl21_33
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f901,f894,f342,f1671]) ).
fof(f1671,plain,
( spl21_204
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(sK15(power_set(X0),X1),X2),set_type)
| member(sK14(sK15(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| member(sK14(sK15(power_set(X0),X1),X2),X2)
| sP2(sK15(power_set(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_204])]) ).
fof(f901,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(sK15(power_set(X0),X1),X2),set_type)
| member(sK14(sK15(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| member(sK14(sK15(power_set(X0),X1),X2),X2)
| sP2(sK15(power_set(X0),X1),X2) )
| ~ spl21_33
| ~ spl21_107 ),
inference(resolution,[],[f895,f343]) ).
fof(f1669,plain,
( spl21_203
| ~ spl21_33
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f900,f894,f342,f1667]) ).
fof(f1667,plain,
( spl21_203
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,sK15(power_set(X1),X2)),set_type)
| member(sK14(X0,sK15(power_set(X1),X2)),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK15(power_set(X1),X2),set_type)
| member(power_set(X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(power_set(X1),set_type)
| member(sK14(X0,sK15(power_set(X1),X2)),X0)
| sP2(X0,sK15(power_set(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_203])]) ).
fof(f900,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,sK15(power_set(X1),X2)),set_type)
| member(sK14(X0,sK15(power_set(X1),X2)),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK15(power_set(X1),X2),set_type)
| member(power_set(X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(power_set(X1),set_type)
| member(sK14(X0,sK15(power_set(X1),X2)),X0)
| sP2(X0,sK15(power_set(X1),X2)) )
| ~ spl21_33
| ~ spl21_107 ),
inference(resolution,[],[f895,f343]) ).
fof(f1665,plain,
( ~ spl21_58
| ~ spl21_14
| ~ spl21_190 ),
inference(avatar_split_clause,[],[f1637,f1595,f255,f502]) ).
fof(f255,plain,
( spl21_14
<=> ! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).
fof(f1595,plain,
( spl21_190
<=> empty(power_set(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_190])]) ).
fof(f1637,plain,
( ~ ilf_type(sK4,set_type)
| ~ spl21_14
| ~ spl21_190 ),
inference(resolution,[],[f1597,f256]) ).
fof(f256,plain,
( ! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_14 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f1597,plain,
( empty(power_set(sK4))
| ~ spl21_190 ),
inference(avatar_component_clause,[],[f1595]) ).
fof(f1664,plain,
( spl21_202
| ~ spl21_51
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f886,f859,f459,f1662]) ).
fof(f1662,plain,
( spl21_202
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(sK16(sK14(power_set(X0),X1),X2,X3),set_type)
| member(sK16(sK14(power_set(X0),X1),X2,X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| ~ member(X2,image(X3,sK14(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_202])]) ).
fof(f886,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(sK14(power_set(X0),X1),X2,X3),set_type)
| member(sK16(sK14(power_set(X0),X1),X2,X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| ~ member(X2,image(X3,sK14(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_51
| ~ spl21_104 ),
inference(duplicate_literal_removal,[],[f885]) ).
fof(f885,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(sK14(power_set(X0),X1),X2,X3),set_type)
| member(sK16(sK14(power_set(X0),X1),X2,X3),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| ~ member(X2,image(X3,sK14(power_set(X0),X1)))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type) )
| ~ spl21_51
| ~ spl21_104 ),
inference(resolution,[],[f860,f460]) ).
fof(f1660,plain,
( spl21_201
| ~ spl21_51
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f870,f855,f459,f1658]) ).
fof(f1658,plain,
( spl21_201
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(sK16(sK14(X0,power_set(X1)),X2,X3),set_type)
| member(sK16(sK14(X0,power_set(X1)),X2,X3),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| ~ member(X2,image(X3,sK14(X0,power_set(X1))))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_201])]) ).
fof(f870,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(sK14(X0,power_set(X1)),X2,X3),set_type)
| member(sK16(sK14(X0,power_set(X1)),X2,X3),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| ~ member(X2,image(X3,sK14(X0,power_set(X1))))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_51
| ~ spl21_103 ),
inference(duplicate_literal_removal,[],[f869]) ).
fof(f869,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(sK16(sK14(X0,power_set(X1)),X2,X3),set_type)
| member(sK16(sK14(X0,power_set(X1)),X2,X3),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| ~ member(X2,image(X3,sK14(X0,power_set(X1))))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type) )
| ~ spl21_51
| ~ spl21_103 ),
inference(resolution,[],[f856,f460]) ).
fof(f1651,plain,
( spl21_200
| ~ spl21_33
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f882,f859,f342,f1649]) ).
fof(f1649,plain,
( spl21_200
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(sK14(power_set(X0),X1),X2),set_type)
| member(sK14(sK14(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| member(sK14(sK14(power_set(X0),X1),X2),X2)
| sP2(sK14(power_set(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_200])]) ).
fof(f882,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(sK14(power_set(X0),X1),X2),set_type)
| member(sK14(sK14(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| member(sK14(sK14(power_set(X0),X1),X2),X2)
| sP2(sK14(power_set(X0),X1),X2) )
| ~ spl21_33
| ~ spl21_104 ),
inference(resolution,[],[f860,f343]) ).
fof(f1647,plain,
( spl21_199
| ~ spl21_33
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f881,f859,f342,f1645]) ).
fof(f1645,plain,
( spl21_199
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,sK14(power_set(X1),X2)),set_type)
| member(sK14(X0,sK14(power_set(X1),X2)),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(power_set(X1),X2),set_type)
| member(sK14(power_set(X1),X2),X2)
| sP2(power_set(X1),X2)
| member(sK14(X0,sK14(power_set(X1),X2)),X0)
| sP2(X0,sK14(power_set(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_199])]) ).
fof(f881,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,sK14(power_set(X1),X2)),set_type)
| member(sK14(X0,sK14(power_set(X1),X2)),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(power_set(X1),X2),set_type)
| member(sK14(power_set(X1),X2),X2)
| sP2(power_set(X1),X2)
| member(sK14(X0,sK14(power_set(X1),X2)),X0)
| sP2(X0,sK14(power_set(X1),X2)) )
| ~ spl21_33
| ~ spl21_104 ),
inference(resolution,[],[f860,f343]) ).
fof(f1643,plain,
( spl21_198
| ~ spl21_33
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f866,f855,f342,f1641]) ).
fof(f1641,plain,
( spl21_198
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(sK14(X0,power_set(X1)),X2),set_type)
| member(sK14(sK14(X0,power_set(X1)),X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| member(sK14(sK14(X0,power_set(X1)),X2),X2)
| sP2(sK14(X0,power_set(X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_198])]) ).
fof(f866,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(sK14(X0,power_set(X1)),X2),set_type)
| member(sK14(sK14(X0,power_set(X1)),X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| member(sK14(sK14(X0,power_set(X1)),X2),X2)
| sP2(sK14(X0,power_set(X1)),X2) )
| ~ spl21_33
| ~ spl21_103 ),
inference(resolution,[],[f856,f343]) ).
fof(f1636,plain,
( spl21_197
| ~ spl21_33
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f865,f855,f342,f1634]) ).
fof(f1634,plain,
( spl21_197
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,sK14(X1,power_set(X2))),set_type)
| member(sK14(X0,sK14(X1,power_set(X2))),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(X1,power_set(X2)),set_type)
| member(sK14(X1,power_set(X2)),X1)
| sP2(X1,power_set(X2))
| member(sK14(X0,sK14(X1,power_set(X2))),X0)
| sP2(X0,sK14(X1,power_set(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_197])]) ).
fof(f865,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK14(X0,sK14(X1,power_set(X2))),set_type)
| member(sK14(X0,sK14(X1,power_set(X2))),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(X1,power_set(X2)),set_type)
| member(sK14(X1,power_set(X2)),X1)
| sP2(X1,power_set(X2))
| member(sK14(X0,sK14(X1,power_set(X2))),X0)
| sP2(X0,sK14(X1,power_set(X2))) )
| ~ spl21_33
| ~ spl21_103 ),
inference(resolution,[],[f856,f343]) ).
fof(f1632,plain,
( spl21_196
| ~ spl21_52
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f802,f791,f469,f1630]) ).
fof(f1630,plain,
( spl21_196
<=> ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK10(power_set(X2))),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK10(power_set(X2))),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK10(power_set(X2)),set_type)
| sP0(power_set(X2))
| ~ member(X1,image(sK10(power_set(X2)),X0))
| ~ ilf_type(sK10(power_set(X2)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_196])]) ).
fof(f802,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X0,X1,sK10(power_set(X2))),X1),set_type)
| member(ordered_pair(sK16(X0,X1,sK10(power_set(X2))),X1),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK10(power_set(X2)),set_type)
| sP0(power_set(X2))
| ~ member(X1,image(sK10(power_set(X2)),X0))
| ~ ilf_type(sK10(power_set(X2)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_95 ),
inference(resolution,[],[f792,f470]) ).
fof(f1618,plain,
( spl21_195
| ~ spl21_24
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f958,f945,f300,f1616]) ).
fof(f1616,plain,
( spl21_195
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK13(sK16(power_set(X2),X1,X0)),set_type)
| member(sK13(sK16(power_set(X2),X1,X0)),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| empty(sK16(power_set(X2),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_195])]) ).
fof(f958,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK13(sK16(power_set(X2),X1,X0)),set_type)
| member(sK13(sK16(power_set(X2),X1,X0)),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| empty(sK16(power_set(X2),X1,X0)) )
| ~ spl21_24
| ~ spl21_114 ),
inference(duplicate_literal_removal,[],[f950]) ).
fof(f950,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK13(sK16(power_set(X2),X1,X0)),set_type)
| member(sK13(sK16(power_set(X2),X1,X0)),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| empty(sK16(power_set(X2),X1,X0))
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type) )
| ~ spl21_24
| ~ spl21_114 ),
inference(resolution,[],[f946,f301]) ).
fof(f1614,plain,
( spl21_194
| ~ spl21_17
| ~ spl21_114 ),
inference(avatar_split_clause,[],[f949,f945,f267,f1612]) ).
fof(f1612,plain,
( spl21_194
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK10(sK16(power_set(X2),X1,X0)),set_type)
| member(sK10(sK16(power_set(X2),X1,X0)),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| sP0(sK16(power_set(X2),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_194])]) ).
fof(f949,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X1,image(X0,power_set(X2)))
| ~ ilf_type(sK10(sK16(power_set(X2),X1,X0)),set_type)
| member(sK10(sK16(power_set(X2),X1,X0)),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X1,X0),set_type)
| sP0(sK16(power_set(X2),X1,X0)) )
| ~ spl21_17
| ~ spl21_114 ),
inference(resolution,[],[f946,f268]) ).
fof(f1610,plain,
( spl21_193
| ~ spl21_54
| ~ spl21_110 ),
inference(avatar_split_clause,[],[f932,f922,f483,f1608]) ).
fof(f1608,plain,
( spl21_193
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,relation_type(X1,cross_product(X2,X3)))
| ~ ilf_type(cross_product(X2,X3),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type)
| image4(X2,X3,image4(X1,cross_product(X2,X3),X0,X4),X5) = image(image4(X1,cross_product(X2,X3),X0,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_193])]) ).
fof(f483,plain,
( spl21_54
<=> ! [X0,X3,X2,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_54])]) ).
fof(f922,plain,
( spl21_110
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,cross_product(X3,X4)))
| ~ ilf_type(cross_product(X3,X4),set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(image4(X2,cross_product(X3,X4),X1,X0),relation_type(X3,X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_110])]) ).
fof(f932,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ ilf_type(X0,relation_type(X1,cross_product(X2,X3)))
| ~ ilf_type(cross_product(X2,X3),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type)
| image4(X2,X3,image4(X1,cross_product(X2,X3),X0,X4),X5) = image(image4(X1,cross_product(X2,X3),X0,X4),X5) )
| ~ spl21_54
| ~ spl21_110 ),
inference(duplicate_literal_removal,[],[f931]) ).
fof(f931,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ ilf_type(X0,relation_type(X1,cross_product(X2,X3)))
| ~ ilf_type(cross_product(X2,X3),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type)
| image4(X2,X3,image4(X1,cross_product(X2,X3),X0,X4),X5) = image(image4(X1,cross_product(X2,X3),X0,X4),X5)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_54
| ~ spl21_110 ),
inference(resolution,[],[f923,f484]) ).
fof(f484,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_54 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f923,plain,
( ! [X2,X3,X0,X1,X4] :
( ilf_type(image4(X2,cross_product(X3,X4),X1,X0),relation_type(X3,X4))
| ~ ilf_type(X1,relation_type(X2,cross_product(X3,X4)))
| ~ ilf_type(cross_product(X3,X4),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_110 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f1605,plain,
( spl21_192
| ~ spl21_42
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f906,f894,f389,f1603]) ).
fof(f1603,plain,
( spl21_192
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK15(power_set(X0),X1),X2),set_type)
| member(sK15(sK15(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| member(sK15(power_set(X0),X1),power_set(X2))
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_192])]) ).
fof(f906,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK15(power_set(X0),X1),X2),set_type)
| member(sK15(sK15(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| member(sK15(power_set(X0),X1),power_set(X2))
| ~ ilf_type(X2,set_type) )
| ~ spl21_42
| ~ spl21_107 ),
inference(duplicate_literal_removal,[],[f903]) ).
fof(f903,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK15(power_set(X0),X1),X2),set_type)
| member(sK15(sK15(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| member(sK15(power_set(X0),X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type) )
| ~ spl21_42
| ~ spl21_107 ),
inference(resolution,[],[f895,f390]) ).
fof(f1601,plain,
( ~ spl21_58
| spl21_190
| spl21_191
| ~ spl21_142
| ~ spl21_180 ),
inference(avatar_split_clause,[],[f1568,f1524,f1189,f1599,f1595,f502]) ).
fof(f1524,plain,
( spl21_180
<=> ! [X0] :
( ilf_type(image(sK7,X0),subset_type(sK4))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_180])]) ).
fof(f1568,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| empty(power_set(sK4))
| ~ ilf_type(image(sK7,X0),set_type)
| member(image(sK7,X0),power_set(sK4))
| ~ ilf_type(sK4,set_type) )
| ~ spl21_142
| ~ spl21_180 ),
inference(resolution,[],[f1525,f1190]) ).
fof(f1525,plain,
( ! [X0] :
( ilf_type(image(sK7,X0),subset_type(sK4))
| ~ ilf_type(X0,set_type) )
| ~ spl21_180 ),
inference(avatar_component_clause,[],[f1524]) ).
fof(f1587,plain,
( spl21_189
| ~ spl21_42
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f887,f859,f389,f1585]) ).
fof(f1585,plain,
( spl21_189
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK14(power_set(X0),X1),X2),set_type)
| member(sK15(sK14(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| member(sK14(power_set(X0),X1),power_set(X2))
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_189])]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK14(power_set(X0),X1),X2),set_type)
| member(sK15(sK14(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| member(sK14(power_set(X0),X1),power_set(X2))
| ~ ilf_type(X2,set_type) )
| ~ spl21_42
| ~ spl21_104 ),
inference(duplicate_literal_removal,[],[f884]) ).
fof(f884,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK14(power_set(X0),X1),X2),set_type)
| member(sK15(sK14(power_set(X0),X1),X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| member(sK14(power_set(X0),X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type) )
| ~ spl21_42
| ~ spl21_104 ),
inference(resolution,[],[f860,f390]) ).
fof(f1583,plain,
( spl21_188
| ~ spl21_42
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f871,f855,f389,f1581]) ).
fof(f1581,plain,
( spl21_188
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK14(X0,power_set(X1)),X2),set_type)
| member(sK15(sK14(X0,power_set(X1)),X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| member(sK14(X0,power_set(X1)),power_set(X2))
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_188])]) ).
fof(f871,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK14(X0,power_set(X1)),X2),set_type)
| member(sK15(sK14(X0,power_set(X1)),X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| member(sK14(X0,power_set(X1)),power_set(X2))
| ~ ilf_type(X2,set_type) )
| ~ spl21_42
| ~ spl21_103 ),
inference(duplicate_literal_removal,[],[f868]) ).
fof(f868,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK15(sK14(X0,power_set(X1)),X2),set_type)
| member(sK15(sK14(X0,power_set(X1)),X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| member(sK14(X0,power_set(X1)),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type) )
| ~ spl21_42
| ~ spl21_103 ),
inference(resolution,[],[f856,f390]) ).
fof(f1579,plain,
( spl21_187
| ~ spl21_52
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f778,f770,f469,f1577]) ).
fof(f1577,plain,
( spl21_187
<=> ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(ordered_pair(sK16(X1,X2,power_set(X0)),X2),set_type)
| ilf_type(ordered_pair(sK16(X1,X2,power_set(X0)),X2),subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ member(X2,image(power_set(X0),X1))
| ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_187])]) ).
fof(f778,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(ordered_pair(sK16(X1,X2,power_set(X0)),X2),set_type)
| ilf_type(ordered_pair(sK16(X1,X2,power_set(X0)),X2),subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ member(X2,image(power_set(X0),X1))
| ~ ilf_type(power_set(X0),binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_52
| ~ spl21_94 ),
inference(resolution,[],[f771,f470]) ).
fof(f1574,plain,
( spl21_186
| ~ spl21_51
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f827,f816,f459,f1572]) ).
fof(f1572,plain,
( spl21_186
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK16(sK13(power_set(X0)),X1,X2),set_type)
| member(sK16(sK13(power_set(X0)),X1,X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X1,image(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_186])]) ).
fof(f827,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK16(sK13(power_set(X0)),X1,X2),set_type)
| member(sK16(sK13(power_set(X0)),X1,X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X1,image(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_98 ),
inference(duplicate_literal_removal,[],[f826]) ).
fof(f826,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK16(sK13(power_set(X0)),X1,X2),set_type)
| member(sK16(sK13(power_set(X0)),X1,X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| ~ member(X1,image(X2,sK13(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type) )
| ~ spl21_51
| ~ spl21_98 ),
inference(resolution,[],[f817,f460]) ).
fof(f1567,plain,
( spl21_185
| ~ spl21_33
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f823,f816,f342,f1565]) ).
fof(f1565,plain,
( spl21_185
<=> ! [X0,X1] :
( ~ ilf_type(sK14(sK13(power_set(X0)),X1),set_type)
| member(sK14(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK14(sK13(power_set(X0)),X1),X1)
| sP2(sK13(power_set(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_185])]) ).
fof(f823,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(sK13(power_set(X0)),X1),set_type)
| member(sK14(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK14(sK13(power_set(X0)),X1),X1)
| sP2(sK13(power_set(X0)),X1) )
| ~ spl21_33
| ~ spl21_98 ),
inference(resolution,[],[f817,f343]) ).
fof(f1563,plain,
( spl21_184
| ~ spl21_33
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f822,f816,f342,f1561]) ).
fof(f1561,plain,
( spl21_184
<=> ! [X0,X1] :
( ~ ilf_type(sK14(X0,sK13(power_set(X1))),set_type)
| member(sK14(X0,sK13(power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK13(power_set(X1)),set_type)
| empty(power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| member(sK14(X0,sK13(power_set(X1))),X0)
| sP2(X0,sK13(power_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_184])]) ).
fof(f822,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,sK13(power_set(X1))),set_type)
| member(sK14(X0,sK13(power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK13(power_set(X1)),set_type)
| empty(power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| member(sK14(X0,sK13(power_set(X1))),X0)
| sP2(X0,sK13(power_set(X1))) )
| ~ spl21_33
| ~ spl21_98 ),
inference(resolution,[],[f817,f343]) ).
fof(f1556,plain,
( spl21_183
| ~ spl21_24
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f907,f894,f300,f1554]) ).
fof(f1554,plain,
( spl21_183
<=> ! [X0,X1] :
( ~ ilf_type(sK13(sK15(power_set(X0),X1)),set_type)
| member(sK13(sK15(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(sK15(power_set(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_183])]) ).
fof(f907,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK15(power_set(X0),X1)),set_type)
| member(sK13(sK15(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(sK15(power_set(X0),X1)) )
| ~ spl21_24
| ~ spl21_107 ),
inference(duplicate_literal_removal,[],[f899]) ).
fof(f899,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK15(power_set(X0),X1)),set_type)
| member(sK13(sK15(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(sK15(power_set(X0),X1))
| ~ ilf_type(sK15(power_set(X0),X1),set_type) )
| ~ spl21_24
| ~ spl21_107 ),
inference(resolution,[],[f895,f301]) ).
fof(f1552,plain,
( spl21_182
| ~ spl21_17
| ~ spl21_107 ),
inference(avatar_split_clause,[],[f898,f894,f267,f1550]) ).
fof(f1550,plain,
( spl21_182
<=> ! [X0,X1] :
( ~ ilf_type(sK10(sK15(power_set(X0),X1)),set_type)
| member(sK10(sK15(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| sP0(sK15(power_set(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_182])]) ).
fof(f898,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(sK15(power_set(X0),X1)),set_type)
| member(sK10(sK15(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type)
| sP0(sK15(power_set(X0),X1)) )
| ~ spl21_17
| ~ spl21_107 ),
inference(resolution,[],[f895,f268]) ).
fof(f1548,plain,
( spl21_181
| ~ spl21_51
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f810,f791,f459,f1546]) ).
fof(f1546,plain,
( spl21_181
<=> ! [X2,X0,X1] :
( ~ ilf_type(sK16(sK10(power_set(X0)),X1,X2),set_type)
| member(sK16(sK10(power_set(X0)),X1,X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| ~ member(X1,image(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_181])]) ).
fof(f810,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK16(sK10(power_set(X0)),X1,X2),set_type)
| member(sK16(sK10(power_set(X0)),X1,X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| ~ member(X1,image(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_95 ),
inference(duplicate_literal_removal,[],[f809]) ).
fof(f809,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK16(sK10(power_set(X0)),X1,X2),set_type)
| member(sK16(sK10(power_set(X0)),X1,X2),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| ~ member(X1,image(X2,sK10(power_set(X0))))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type) )
| ~ spl21_51
| ~ spl21_95 ),
inference(resolution,[],[f792,f460]) ).
fof(f1526,plain,
( ~ spl21_63
| ~ spl21_58
| ~ spl21_5
| spl21_180
| ~ spl21_53
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f837,f645,f473,f1524,f213,f502,f588]) ).
fof(f473,plain,
( spl21_53
<=> ! [X0,X3,X2,X1] :
( ilf_type(image4(X0,X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_53])]) ).
fof(f645,plain,
( spl21_72
<=> ! [X0] : image(sK7,X0) = image4(sK6,sK4,sK7,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_72])]) ).
fof(f837,plain,
( ! [X0] :
( ilf_type(image(sK7,X0),subset_type(sK4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK7,relation_type(sK6,sK4))
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK6,set_type) )
| ~ spl21_53
| ~ spl21_72 ),
inference(superposition,[],[f474,f646]) ).
fof(f646,plain,
( ! [X0] : image(sK7,X0) = image4(sK6,sK4,sK7,X0)
| ~ spl21_72 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f474,plain,
( ! [X2,X3,X0,X1] :
( ilf_type(image4(X0,X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_53 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f1514,plain,
( spl21_179
| ~ spl21_9
| ~ spl21_116 ),
inference(avatar_split_clause,[],[f978,f975,f232,f1512]) ).
fof(f975,plain,
( spl21_116
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(sK16(X2,X0,X1),X0) = ordered_pair(sK11(ordered_pair(sK16(X2,X0,X1),X0)),sK12(ordered_pair(sK16(X2,X0,X1),X0)))
| ~ ilf_type(ordered_pair(sK16(X2,X0,X1),X0),set_type)
| ~ sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_116])]) ).
fof(f978,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(sK16(X2,X1,X0),X1) = ordered_pair(sK11(ordered_pair(sK16(X2,X1,X0),X1)),sK12(ordered_pair(sK16(X2,X1,X0),X1)))
| ~ member(X1,image(X0,X2))
| ~ sP0(X0) )
| ~ spl21_9
| ~ spl21_116 ),
inference(resolution,[],[f976,f233]) ).
fof(f976,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X2,X0,X1),X0),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(sK16(X2,X0,X1),X0) = ordered_pair(sK11(ordered_pair(sK16(X2,X0,X1),X0)),sK12(ordered_pair(sK16(X2,X0,X1),X0)))
| ~ member(X0,image(X1,X2))
| ~ sP0(X1) )
| ~ spl21_116 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f1510,plain,
( spl21_178
| ~ spl21_24
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f888,f859,f300,f1508]) ).
fof(f888,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK14(power_set(X0),X1)),set_type)
| member(sK13(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| empty(sK14(power_set(X0),X1)) )
| ~ spl21_24
| ~ spl21_104 ),
inference(duplicate_literal_removal,[],[f880]) ).
fof(f880,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK14(power_set(X0),X1)),set_type)
| member(sK13(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| empty(sK14(power_set(X0),X1))
| ~ ilf_type(sK14(power_set(X0),X1),set_type) )
| ~ spl21_24
| ~ spl21_104 ),
inference(resolution,[],[f860,f301]) ).
fof(f1506,plain,
( spl21_177
| ~ spl21_17
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f879,f859,f267,f1504]) ).
fof(f879,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(sK14(power_set(X0),X1)),set_type)
| member(sK10(sK14(power_set(X0),X1)),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1)
| sP0(sK14(power_set(X0),X1)) )
| ~ spl21_17
| ~ spl21_104 ),
inference(resolution,[],[f860,f268]) ).
fof(f1502,plain,
( spl21_176
| ~ spl21_24
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f872,f855,f300,f1500]) ).
fof(f872,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK14(X0,power_set(X1))),set_type)
| member(sK13(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| empty(sK14(X0,power_set(X1))) )
| ~ spl21_24
| ~ spl21_103 ),
inference(duplicate_literal_removal,[],[f864]) ).
fof(f864,plain,
( ! [X0,X1] :
( ~ ilf_type(sK13(sK14(X0,power_set(X1))),set_type)
| member(sK13(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| empty(sK14(X0,power_set(X1)))
| ~ ilf_type(sK14(X0,power_set(X1)),set_type) )
| ~ spl21_24
| ~ spl21_103 ),
inference(resolution,[],[f856,f301]) ).
fof(f1498,plain,
( spl21_175
| ~ spl21_17
| ~ spl21_103 ),
inference(avatar_split_clause,[],[f863,f855,f267,f1496]) ).
fof(f863,plain,
( ! [X0,X1] :
( ~ ilf_type(sK10(sK14(X0,power_set(X1))),set_type)
| member(sK10(sK14(X0,power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(X0,power_set(X1)),set_type)
| member(sK14(X0,power_set(X1)),X0)
| sP2(X0,power_set(X1))
| sP0(sK14(X0,power_set(X1))) )
| ~ spl21_17
| ~ spl21_103 ),
inference(resolution,[],[f856,f268]) ).
fof(f1494,plain,
( spl21_174
| ~ spl21_42
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f828,f816,f389,f1492]) ).
fof(f828,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(sK13(power_set(X0)),X1),set_type)
| member(sK15(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK13(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_42
| ~ spl21_98 ),
inference(duplicate_literal_removal,[],[f825]) ).
fof(f825,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(sK13(power_set(X0)),X1),set_type)
| member(sK15(sK13(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| member(sK13(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type) )
| ~ spl21_42
| ~ spl21_98 ),
inference(resolution,[],[f817,f390]) ).
fof(f1490,plain,
( spl21_173
| ~ spl21_48
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f774,f762,f437,f1488]) ).
fof(f1488,plain,
( spl21_173
<=> ! [X0,X1] :
( ~ ilf_type(sK19(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| ilf_type(sK19(power_set(cross_product(X0,X1))),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_173])]) ).
fof(f437,plain,
( spl21_48
<=> ! [X0,X1,X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_48])]) ).
fof(f762,plain,
( spl21_92
<=> ! [X0] :
( ilf_type(sK19(power_set(X0)),subset_type(X0))
| ~ ilf_type(sK19(power_set(X0)),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_92])]) ).
fof(f774,plain,
( ! [X0,X1] :
( ~ ilf_type(sK19(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| ilf_type(sK19(power_set(cross_product(X0,X1))),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_48
| ~ spl21_92 ),
inference(resolution,[],[f763,f438]) ).
fof(f438,plain,
( ! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_48 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f763,plain,
( ! [X0] :
( ilf_type(sK19(power_set(X0)),subset_type(X0))
| ~ ilf_type(sK19(power_set(X0)),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0)) )
| ~ spl21_92 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f1480,plain,
( spl21_172
| ~ spl21_33
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f806,f791,f342,f1478]) ).
fof(f806,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(sK10(power_set(X0)),X1),set_type)
| member(sK14(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK14(sK10(power_set(X0)),X1),X1)
| sP2(sK10(power_set(X0)),X1) )
| ~ spl21_33
| ~ spl21_95 ),
inference(resolution,[],[f792,f343]) ).
fof(f1476,plain,
( spl21_171
| ~ spl21_33
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f805,f791,f342,f1474]) ).
fof(f805,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,sK10(power_set(X1))),set_type)
| member(sK14(X0,sK10(power_set(X1))),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1))
| member(sK14(X0,sK10(power_set(X1))),X0)
| sP2(X0,sK10(power_set(X1))) )
| ~ spl21_33
| ~ spl21_95 ),
inference(resolution,[],[f792,f343]) ).
fof(f1472,plain,
( spl21_170
| ~ spl21_51
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f786,f770,f459,f1470]) ).
fof(f1470,plain,
( spl21_170
<=> ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK16(power_set(X0),X1,X2),set_type)
| ilf_type(sK16(power_set(X0),X1,X2),subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ member(X1,image(X2,power_set(X0)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_170])]) ).
fof(f786,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK16(power_set(X0),X1,X2),set_type)
| ilf_type(sK16(power_set(X0),X1,X2),subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ member(X1,image(X2,power_set(X0)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_51
| ~ spl21_94 ),
inference(duplicate_literal_removal,[],[f785]) ).
fof(f785,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK16(power_set(X0),X1,X2),set_type)
| ilf_type(sK16(power_set(X0),X1,X2),subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ member(X1,image(X2,power_set(X0)))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type) )
| ~ spl21_51
| ~ spl21_94 ),
inference(resolution,[],[f771,f460]) ).
fof(f1449,plain,
( spl21_169
| ~ spl21_77
| ~ spl21_108 ),
inference(avatar_split_clause,[],[f918,f909,f668,f1447]) ).
fof(f1447,plain,
( spl21_169
<=> ! [X2,X0,X1] :
( member(X0,image(X1,power_set(sK16(X2,X0,X1))))
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(sK16(X2,X0,X1)),set_type)
| ~ member(X0,image(X1,X2))
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_169])]) ).
fof(f668,plain,
( spl21_77
<=> ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_77])]) ).
fof(f909,plain,
( spl21_108
<=> ! [X0,X3,X2,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,image(X2,X3))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_108])]) ).
fof(f918,plain,
( ! [X2,X0,X1] :
( member(X0,image(X1,power_set(sK16(X2,X0,X1))))
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(sK16(X2,X0,X1)),set_type)
| ~ member(X0,image(X1,X2))
| ~ ilf_type(X2,set_type) )
| ~ spl21_77
| ~ spl21_108 ),
inference(duplicate_literal_removal,[],[f917]) ).
fof(f917,plain,
( ! [X2,X0,X1] :
( member(X0,image(X1,power_set(sK16(X2,X0,X1))))
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(sK16(X2,X0,X1)),set_type)
| ~ member(X0,image(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(X2,X0,X1),set_type) )
| ~ spl21_77
| ~ spl21_108 ),
inference(resolution,[],[f910,f669]) ).
fof(f669,plain,
( ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_77 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f910,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,image(X2,X3))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_108 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f1445,plain,
( spl21_168
| ~ spl21_9
| ~ spl21_123 ),
inference(avatar_split_clause,[],[f1014,f1011,f232,f1443]) ).
fof(f1443,plain,
( spl21_168
<=> ! [X0] :
( ~ empty(X0)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_168])]) ).
fof(f1011,plain,
( spl21_123
<=> ! [X0] :
( ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_123])]) ).
fof(f1014,plain,
( ! [X0] :
( ~ empty(X0)
| sP0(X0) )
| ~ spl21_9
| ~ spl21_123 ),
inference(resolution,[],[f1012,f233]) ).
fof(f1012,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| sP0(X0) )
| ~ spl21_123 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f1440,plain,
( spl21_167
| ~ spl21_40
| ~ spl21_92 ),
inference(avatar_split_clause,[],[f775,f762,f378,f1438]) ).
fof(f378,plain,
( spl21_40
<=> ! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_40])]) ).
fof(f775,plain,
( ! [X0,X1] :
( ~ ilf_type(sK19(power_set(cross_product(X0,X1))),set_type)
| ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| relation_like(sK19(power_set(cross_product(X0,X1))))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_40
| ~ spl21_92 ),
inference(resolution,[],[f763,f379]) ).
fof(f379,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_40 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f1435,plain,
( spl21_166
| ~ spl21_42
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f811,f791,f389,f1433]) ).
fof(f811,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(sK10(power_set(X0)),X1),set_type)
| member(sK15(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK10(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_42
| ~ spl21_95 ),
inference(duplicate_literal_removal,[],[f808]) ).
fof(f808,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(sK10(power_set(X0)),X1),set_type)
| member(sK15(sK10(power_set(X0)),X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| member(sK10(power_set(X0)),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type) )
| ~ spl21_42
| ~ spl21_95 ),
inference(resolution,[],[f792,f390]) ).
fof(f1429,plain,
( spl21_165
| ~ spl21_33
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f782,f770,f342,f1427]) ).
fof(f782,plain,
( ! [X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK14(power_set(X0),X1),set_type)
| ilf_type(sK14(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(power_set(X0),X1),X1)
| sP2(power_set(X0),X1) )
| ~ spl21_33
| ~ spl21_94 ),
inference(resolution,[],[f771,f343]) ).
fof(f1425,plain,
( spl21_164
| ~ spl21_33
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f781,f770,f342,f1423]) ).
fof(f781,plain,
( ! [X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK14(X1,power_set(X0)),set_type)
| ilf_type(sK14(X1,power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(sK14(X1,power_set(X0)),X1)
| sP2(X1,power_set(X0)) )
| ~ spl21_33
| ~ spl21_94 ),
inference(resolution,[],[f771,f343]) ).
fof(f1406,plain,
( spl21_163
| ~ spl21_9
| ~ spl21_113 ),
inference(avatar_split_clause,[],[f943,f940,f232,f1404]) ).
fof(f1404,plain,
( spl21_163
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| sK16(X2,X1,X0) = ordered_pair(sK11(sK16(X2,X1,X0)),sK12(sK16(X2,X1,X0)))
| ~ member(X1,image(X0,X2))
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_163])]) ).
fof(f940,plain,
( spl21_113
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| sK16(X2,X0,X1) = ordered_pair(sK11(sK16(X2,X0,X1)),sK12(sK16(X2,X0,X1)))
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ sP0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_113])]) ).
fof(f943,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| sK16(X2,X1,X0) = ordered_pair(sK11(sK16(X2,X1,X0)),sK12(sK16(X2,X1,X0)))
| ~ member(X1,image(X0,X2))
| ~ sP0(X2) )
| ~ spl21_9
| ~ spl21_113 ),
inference(resolution,[],[f941,f233]) ).
fof(f941,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| sK16(X2,X0,X1) = ordered_pair(sK11(sK16(X2,X0,X1)),sK12(sK16(X2,X0,X1)))
| ~ member(X0,image(X1,X2))
| ~ sP0(X2) )
| ~ spl21_113 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f1364,plain,
( spl21_162
| ~ spl21_9
| ~ spl21_112 ),
inference(avatar_split_clause,[],[f938,f935,f232,f1362]) ).
fof(f935,plain,
( spl21_112
<=> ! [X4,X0,X3,X2,X1] :
( member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_112])]) ).
fof(f938,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| member(sK16(X4,X3,X0),X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X3,image(X0,X4))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_9
| ~ spl21_112 ),
inference(resolution,[],[f936,f233]) ).
fof(f936,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_112 ),
inference(avatar_component_clause,[],[f935]) ).
fof(f1360,plain,
( spl21_161
| ~ spl21_24
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f829,f816,f300,f1358]) ).
fof(f829,plain,
( ! [X0] :
( ~ ilf_type(sK13(sK13(power_set(X0))),set_type)
| member(sK13(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| empty(sK13(power_set(X0))) )
| ~ spl21_24
| ~ spl21_98 ),
inference(duplicate_literal_removal,[],[f821]) ).
fof(f821,plain,
( ! [X0] :
( ~ ilf_type(sK13(sK13(power_set(X0))),set_type)
| member(sK13(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| empty(sK13(power_set(X0)))
| ~ ilf_type(sK13(power_set(X0)),set_type) )
| ~ spl21_24
| ~ spl21_98 ),
inference(resolution,[],[f817,f301]) ).
fof(f1356,plain,
( spl21_160
| ~ spl21_17
| ~ spl21_98 ),
inference(avatar_split_clause,[],[f820,f816,f267,f1354]) ).
fof(f820,plain,
( ! [X0] :
( ~ ilf_type(sK10(sK13(power_set(X0))),set_type)
| member(sK10(sK13(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13(power_set(X0)),set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type)
| sP0(sK13(power_set(X0))) )
| ~ spl21_17
| ~ spl21_98 ),
inference(resolution,[],[f817,f268]) ).
fof(f1352,plain,
( spl21_159
| ~ spl21_42
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f787,f770,f389,f1350]) ).
fof(f1350,plain,
( spl21_159
<=> ! [X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| ilf_type(sK15(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_159])]) ).
fof(f787,plain,
( ! [X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| ilf_type(sK15(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_42
| ~ spl21_94 ),
inference(duplicate_literal_removal,[],[f784]) ).
fof(f784,plain,
( ! [X0,X1] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK15(power_set(X0),X1),set_type)
| ilf_type(sK15(power_set(X0),X1),subset_type(X0))
| ~ ilf_type(X0,set_type)
| member(power_set(X0),power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(power_set(X0),set_type) )
| ~ spl21_42
| ~ spl21_94 ),
inference(resolution,[],[f771,f390]) ).
fof(f1348,plain,
( spl21_158
| ~ spl21_55
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f676,f668,f490,f1346]) ).
fof(f1346,plain,
( spl21_158
<=> ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ member(X0,X2)
| member(X1,image(power_set(ordered_pair(X0,X1)),X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_158])]) ).
fof(f676,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| ~ member(X0,X2)
| member(X1,image(power_set(ordered_pair(X0,X1)),X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_55
| ~ spl21_77 ),
inference(resolution,[],[f669,f491]) ).
fof(f1344,plain,
( spl21_157
| ~ spl21_18
| ~ spl21_118 ),
inference(avatar_split_clause,[],[f988,f985,f271,f1342]) ).
fof(f1342,plain,
( spl21_157
<=> ! [X0] : sP2(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_157])]) ).
fof(f271,plain,
( spl21_18
<=> ! [X1] :
( sP2(X1,X1)
| ~ sP3(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).
fof(f988,plain,
( ! [X0] : sP2(X0,X0)
| ~ spl21_18
| ~ spl21_118 ),
inference(resolution,[],[f986,f272]) ).
fof(f272,plain,
( ! [X1] :
( ~ sP3(X1,X1)
| sP2(X1,X1) )
| ~ spl21_18 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f1339,plain,
( spl21_156
| ~ spl21_54
| ~ spl21_90 ),
inference(avatar_split_clause,[],[f755,f747,f483,f1337]) ).
fof(f747,plain,
( spl21_90
<=> ! [X0,X1] :
( ilf_type(sK18(cross_product(X0,X1)),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_90])]) ).
fof(f755,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(X1,X0),set_type)
| ~ ilf_type(X2,set_type)
| image4(X1,X0,sK18(cross_product(X1,X0)),X2) = image(sK18(cross_product(X1,X0)),X2) )
| ~ spl21_54
| ~ spl21_90 ),
inference(duplicate_literal_removal,[],[f754]) ).
fof(f754,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(X1,X0),set_type)
| ~ ilf_type(X2,set_type)
| image4(X1,X0,sK18(cross_product(X1,X0)),X2) = image(sK18(cross_product(X1,X0)),X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_54
| ~ spl21_90 ),
inference(resolution,[],[f748,f484]) ).
fof(f748,plain,
( ! [X0,X1] :
( ilf_type(sK18(cross_product(X0,X1)),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) )
| ~ spl21_90 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f1322,plain,
( spl21_155
| ~ spl21_9
| ~ spl21_109 ),
inference(avatar_split_clause,[],[f920,f913,f232,f1320]) ).
fof(f913,plain,
( spl21_109
<=> ! [X4,X0,X3,X2,X1] :
( member(X0,X1)
| ~ ilf_type(X2,relation_type(X3,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X0,image(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_109])]) ).
fof(f920,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X3,set_type)
| member(X3,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X3,image(X0,X4))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_9
| ~ spl21_109 ),
inference(resolution,[],[f914,f233]) ).
fof(f914,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X2,relation_type(X3,X1))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X0,image(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_109 ),
inference(avatar_component_clause,[],[f913]) ).
fof(f1318,plain,
( spl21_154
| ~ spl21_56
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f675,f668,f494,f1316]) ).
fof(f1316,plain,
( spl21_154
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| member(X0,X2)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_154])]) ).
fof(f675,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| member(X0,X2)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),relation_type(X2,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_56
| ~ spl21_77 ),
inference(resolution,[],[f669,f495]) ).
fof(f1314,plain,
( spl21_153
| ~ spl21_57
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f674,f668,f498,f1312]) ).
fof(f1312,plain,
( spl21_153
<=> ! [X0,X3,X2,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| member(X1,X2)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),relation_type(X3,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_153])]) ).
fof(f498,plain,
( spl21_57
<=> ! [X4,X0,X3,X2,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_57])]) ).
fof(f674,plain,
( ! [X2,X3,X0,X1] :
( ~ ilf_type(ordered_pair(X0,X1),set_type)
| member(X1,X2)
| ~ ilf_type(power_set(ordered_pair(X0,X1)),relation_type(X3,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_57
| ~ spl21_77 ),
inference(resolution,[],[f669,f499]) ).
fof(f499,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_57 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f1307,plain,
( spl21_152
| ~ spl21_24
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f812,f791,f300,f1305]) ).
fof(f812,plain,
( ! [X0] :
( ~ ilf_type(sK13(sK10(power_set(X0))),set_type)
| member(sK13(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| empty(sK10(power_set(X0))) )
| ~ spl21_24
| ~ spl21_95 ),
inference(duplicate_literal_removal,[],[f804]) ).
fof(f804,plain,
( ! [X0] :
( ~ ilf_type(sK13(sK10(power_set(X0))),set_type)
| member(sK13(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| empty(sK10(power_set(X0)))
| ~ ilf_type(sK10(power_set(X0)),set_type) )
| ~ spl21_24
| ~ spl21_95 ),
inference(resolution,[],[f792,f301]) ).
fof(f1303,plain,
( spl21_151
| ~ spl21_17
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f803,f791,f267,f1301]) ).
fof(f803,plain,
( ! [X0] :
( ~ ilf_type(sK10(sK10(power_set(X0))),set_type)
| member(sK10(sK10(power_set(X0))),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK10(power_set(X0)),set_type)
| sP0(power_set(X0))
| sP0(sK10(power_set(X0))) )
| ~ spl21_17
| ~ spl21_95 ),
inference(resolution,[],[f792,f268]) ).
fof(f1284,plain,
( spl21_150
| ~ spl21_9
| ~ spl21_102 ),
inference(avatar_split_clause,[],[f853,f850,f232,f1282]) ).
fof(f850,plain,
( spl21_102
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| sK15(X0,X1) = ordered_pair(sK11(sK15(X0,X1)),sK12(sK15(X0,X1)))
| ~ ilf_type(sK15(X0,X1),set_type)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_102])]) ).
fof(f853,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| sK15(X1,X0) = ordered_pair(sK11(sK15(X1,X0)),sK12(sK15(X1,X0)))
| member(X1,power_set(X0))
| ~ sP0(X1) )
| ~ spl21_9
| ~ spl21_102 ),
inference(resolution,[],[f851,f233]) ).
fof(f851,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| sK15(X0,X1) = ordered_pair(sK11(sK15(X0,X1)),sK12(sK15(X0,X1)))
| member(X0,power_set(X1))
| ~ sP0(X0) )
| ~ spl21_102 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f1276,plain,
( spl21_149
| ~ spl21_17
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f779,f770,f267,f1274]) ).
fof(f1274,plain,
( spl21_149
<=> ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK10(power_set(X0)),set_type)
| ilf_type(sK10(power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| sP0(power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_149])]) ).
fof(f779,plain,
( ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK10(power_set(X0)),set_type)
| ilf_type(sK10(power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| sP0(power_set(X0)) )
| ~ spl21_17
| ~ spl21_94 ),
inference(resolution,[],[f771,f268]) ).
fof(f1240,plain,
( spl21_148
| ~ spl21_9
| ~ spl21_101 ),
inference(avatar_split_clause,[],[f848,f844,f232,f1238]) ).
fof(f844,plain,
( spl21_101
<=> ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ sP0(X0)
| member(sK14(X0,X1),X1)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_101])]) ).
fof(f848,plain,
( ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ sP0(X0)
| member(sK14(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_9
| ~ spl21_101 ),
inference(resolution,[],[f845,f233]) ).
fof(f845,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,X1),set_type)
| sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ sP0(X0)
| member(sK14(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_101 ),
inference(avatar_component_clause,[],[f844]) ).
fof(f1236,plain,
( spl21_147
| ~ spl21_9
| ~ spl21_100 ),
inference(avatar_split_clause,[],[f847,f840,f232,f1234]) ).
fof(f1234,plain,
( spl21_147
<=> ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ sP0(X1)
| member(sK14(X0,X1),X0)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_147])]) ).
fof(f840,plain,
( spl21_100
<=> ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ sP0(X1)
| member(sK14(X0,X1),X0)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_100])]) ).
fof(f847,plain,
( ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ sP0(X1)
| member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_9
| ~ spl21_100 ),
inference(resolution,[],[f841,f233]) ).
fof(f841,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,X1),set_type)
| sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ sP0(X1)
| member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_100 ),
inference(avatar_component_clause,[],[f840]) ).
fof(f1232,plain,
( spl21_146
| ~ spl21_71
| ~ spl21_120 ),
inference(avatar_split_clause,[],[f998,f995,f638,f1229]) ).
fof(f1229,plain,
( spl21_146
<=> sP0(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_146])]) ).
fof(f638,plain,
( spl21_71
<=> relation_like(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_71])]) ).
fof(f998,plain,
( sP0(sK20)
| ~ spl21_71
| ~ spl21_120 ),
inference(resolution,[],[f996,f640]) ).
fof(f640,plain,
( relation_like(sK20)
| ~ spl21_71 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f1223,plain,
( spl21_145
| ~ spl21_24
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f788,f770,f300,f1221]) ).
fof(f1221,plain,
( spl21_145
<=> ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK13(power_set(X0)),set_type)
| ilf_type(sK13(power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_145])]) ).
fof(f788,plain,
( ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK13(power_set(X0)),set_type)
| ilf_type(sK13(power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_24
| ~ spl21_94 ),
inference(duplicate_literal_removal,[],[f780]) ).
fof(f780,plain,
( ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(sK13(power_set(X0)),set_type)
| ilf_type(sK13(power_set(X0)),subset_type(X0))
| ~ ilf_type(X0,set_type)
| empty(power_set(X0))
| ~ ilf_type(power_set(X0),set_type) )
| ~ spl21_24
| ~ spl21_94 ),
inference(resolution,[],[f771,f301]) ).
fof(f1207,plain,
( spl21_144
| ~ spl21_9
| ~ spl21_99 ),
inference(avatar_split_clause,[],[f838,f831,f232,f1205]) ).
fof(f831,plain,
( spl21_99
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X0,X1),X0),set_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_99])]) ).
fof(f838,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(X0,X2))
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_99 ),
inference(resolution,[],[f832,f233]) ).
fof(f832,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(ordered_pair(sK16(X2,X0,X1),X0),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X0,image(X1,X2))
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_99 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f1203,plain,
( spl21_143
| ~ spl21_9
| ~ spl21_97 ),
inference(avatar_split_clause,[],[f814,f799,f232,f1201]) ).
fof(f799,plain,
( spl21_97
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| image4(X1,X2,sK17(X2,X1),X0) = image(sK17(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_97])]) ).
fof(f814,plain,
( ! [X2,X0,X1] :
( image4(X0,X1,sK17(X1,X0),X2) = image(sK17(X1,X0),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_97 ),
inference(resolution,[],[f800,f233]) ).
fof(f800,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X2,set_type)
| image4(X1,X2,sK17(X2,X1),X0) = image(sK17(X2,X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_97 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f1191,plain,
( spl21_142
| ~ spl21_9
| ~ spl21_93 ),
inference(avatar_split_clause,[],[f776,f766,f232,f1189]) ).
fof(f766,plain,
( spl21_93
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_93])]) ).
fof(f776,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_93 ),
inference(resolution,[],[f767,f233]) ).
fof(f767,plain,
( ! [X0,X1] :
( ~ ilf_type(power_set(X1),set_type)
| member(X0,power_set(X1))
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_93 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f1184,plain,
( spl21_125
| ~ spl21_6
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f836,f645,f218,f1027]) ).
fof(f218,plain,
( spl21_6
<=> member(sK8,image4(sK6,sK4,sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).
fof(f836,plain,
( member(sK8,image(sK7,sK5))
| ~ spl21_6
| ~ spl21_72 ),
inference(superposition,[],[f220,f646]) ).
fof(f220,plain,
( member(sK8,image4(sK6,sK4,sK7,sK5))
| ~ spl21_6 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f1183,plain,
( spl21_141
| ~ spl21_9
| ~ spl21_91 ),
inference(avatar_split_clause,[],[f773,f758,f232,f1181]) ).
fof(f758,plain,
( spl21_91
<=> ! [X0] :
( sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0)))
| ~ ilf_type(sK13(X0),set_type)
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_91])]) ).
fof(f773,plain,
( ! [X0] :
( sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0)))
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_91 ),
inference(resolution,[],[f759,f233]) ).
fof(f759,plain,
( ! [X0] :
( ~ ilf_type(sK13(X0),set_type)
| sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0)))
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_91 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f1169,plain,
( spl21_140
| ~ spl21_9
| ~ spl21_96 ),
inference(avatar_split_clause,[],[f813,f795,f232,f1167]) ).
fof(f795,plain,
( spl21_96
<=> ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ empty(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_96])]) ).
fof(f813,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,image(X0,X2))
| ~ empty(X2) )
| ~ spl21_9
| ~ spl21_96 ),
inference(resolution,[],[f796,f233]) ).
fof(f796,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X0,image(X1,X2))
| ~ empty(X2) )
| ~ spl21_96 ),
inference(avatar_component_clause,[],[f795]) ).
fof(f1164,plain,
( spl21_139
| ~ spl21_77
| ~ spl21_94 ),
inference(avatar_split_clause,[],[f789,f770,f668,f1162]) ).
fof(f789,plain,
( ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0)) )
| ~ spl21_77
| ~ spl21_94 ),
inference(duplicate_literal_removal,[],[f777]) ).
fof(f777,plain,
( ! [X0] :
( ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_77
| ~ spl21_94 ),
inference(resolution,[],[f771,f669]) ).
fof(f1133,plain,
( spl21_138
| ~ spl21_9
| ~ spl21_89 ),
inference(avatar_split_clause,[],[f745,f741,f232,f1131]) ).
fof(f741,plain,
( spl21_89
<=> ! [X0,X1] :
( member(sK14(X0,X1),X1)
| sP2(X0,X1)
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_89])]) ).
fof(f745,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_89 ),
inference(resolution,[],[f742,f233]) ).
fof(f742,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,X1),set_type)
| sP2(X0,X1)
| member(sK14(X0,X1),X1)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_89 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f1129,plain,
( spl21_137
| ~ spl21_9
| ~ spl21_88 ),
inference(avatar_split_clause,[],[f744,f737,f232,f1127]) ).
fof(f737,plain,
( spl21_88
<=> ! [X0,X1] :
( member(sK14(X0,X1),X0)
| sP2(X0,X1)
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_88])]) ).
fof(f744,plain,
( ! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_88 ),
inference(resolution,[],[f738,f233]) ).
fof(f738,plain,
( ! [X0,X1] :
( ~ ilf_type(sK14(X0,X1),set_type)
| sP2(X0,X1)
| member(sK14(X0,X1),X0)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_88 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f1125,plain,
( spl21_136
| ~ spl21_9
| ~ spl21_86 ),
inference(avatar_split_clause,[],[f730,f727,f232,f1123]) ).
fof(f727,plain,
( spl21_86
<=> ! [X0,X1] :
( ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_86])]) ).
fof(f730,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)) )
| ~ spl21_9
| ~ spl21_86 ),
inference(resolution,[],[f728,f233]) ).
fof(f728,plain,
( ! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)) )
| ~ spl21_86 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f1121,plain,
( spl21_135
| ~ spl21_41
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f678,f668,f383,f1119]) ).
fof(f1119,plain,
( spl21_135
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ sP0(power_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_135])]) ).
fof(f678,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ sP0(power_set(X0)) )
| ~ spl21_41
| ~ spl21_77 ),
inference(duplicate_literal_removal,[],[f672]) ).
fof(f672,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ordered_pair(sK11(X0),sK12(X0)) = X0
| ~ ilf_type(X0,set_type)
| ~ sP0(power_set(X0)) )
| ~ spl21_41
| ~ spl21_77 ),
inference(resolution,[],[f669,f384]) ).
fof(f1102,plain,
( spl21_134
| ~ spl21_9
| ~ spl21_87 ),
inference(avatar_split_clause,[],[f735,f732,f232,f1100]) ).
fof(f732,plain,
( spl21_87
<=> ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(X0,X1),set_type)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_87])]) ).
fof(f735,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X1,power_set(X0))
| ~ empty(X1) )
| ~ spl21_9
| ~ spl21_87 ),
inference(resolution,[],[f733,f233]) ).
fof(f733,plain,
( ! [X0,X1] :
( ~ ilf_type(sK15(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1))
| ~ empty(X0) )
| ~ spl21_87 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f1097,plain,
( spl21_133
| ~ spl21_9
| ~ spl21_84 ),
inference(avatar_split_clause,[],[f725,f717,f232,f1095]) ).
fof(f717,plain,
( spl21_84
<=> ! [X0,X1] :
( relation_like(sK18(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_84])]) ).
fof(f725,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK18(cross_product(X1,X0))) )
| ~ spl21_9
| ~ spl21_84 ),
inference(resolution,[],[f718,f233]) ).
fof(f718,plain,
( ! [X0,X1] :
( ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| relation_like(sK18(cross_product(X0,X1))) )
| ~ spl21_84 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f1092,plain,
( spl21_132
| ~ spl21_38
| ~ spl21_83 ),
inference(avatar_split_clause,[],[f715,f709,f363,f1090]) ).
fof(f363,plain,
( spl21_38
<=> ! [X0,X1] :
( ilf_type(sK17(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_38])]) ).
fof(f709,plain,
( spl21_83
<=> ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_83])]) ).
fof(f715,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK17(X0,X1)) )
| ~ spl21_38
| ~ spl21_83 ),
inference(duplicate_literal_removal,[],[f714]) ).
fof(f714,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(sK17(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_38
| ~ spl21_83 ),
inference(resolution,[],[f710,f364]) ).
fof(f364,plain,
( ! [X0,X1] :
( ilf_type(sK17(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_38 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f710,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0) )
| ~ spl21_83 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f1067,plain,
( spl21_131
| ~ spl21_9
| ~ spl21_82 ),
inference(avatar_split_clause,[],[f712,f705,f232,f1065]) ).
fof(f705,plain,
( spl21_82
<=> ! [X0] :
( member(sK19(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(sK19(X0),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_82])]) ).
fof(f712,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| empty(X0)
| member(sK19(X0),X0) )
| ~ spl21_9
| ~ spl21_82 ),
inference(resolution,[],[f706,f233]) ).
fof(f706,plain,
( ! [X0] :
( ~ ilf_type(sK19(X0),set_type)
| ~ ilf_type(X0,set_type)
| empty(X0)
| member(sK19(X0),X0) )
| ~ spl21_82 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f1061,plain,
( ~ spl21_130
| ~ spl21_62
| spl21_66
| ~ spl21_41
| ~ spl21_64 ),
inference(avatar_split_clause,[],[f1031,f592,f383,f615,f584,f1058]) ).
fof(f1058,plain,
( spl21_130
<=> sP0(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_130])]) ).
fof(f615,plain,
( spl21_66
<=> sK9 = ordered_pair(sK11(sK9),sK12(sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_66])]) ).
fof(f592,plain,
( spl21_64
<=> member(sK9,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_64])]) ).
fof(f1031,plain,
( sK9 = ordered_pair(sK11(sK9),sK12(sK9))
| ~ ilf_type(sK9,set_type)
| ~ sP0(sK6)
| ~ spl21_41
| ~ spl21_64 ),
inference(resolution,[],[f594,f384]) ).
fof(f594,plain,
( member(sK9,sK6)
| ~ spl21_64 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f1053,plain,
( ~ spl21_62
| ~ spl21_37
| spl21_129
| ~ spl21_12
| ~ spl21_57 ),
inference(avatar_split_clause,[],[f1021,f498,f245,f1051,f358,f584]) ).
fof(f1021,plain,
( ! [X0,X1] :
( member(sK8,X0)
| ~ ilf_type(sK7,relation_type(X1,X0))
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(sK9,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_12
| ~ spl21_57 ),
inference(resolution,[],[f247,f499]) ).
fof(f1049,plain,
( ~ spl21_9
| spl21_128 ),
inference(avatar_contradiction_clause,[],[f1048]) ).
fof(f1048,plain,
( $false
| ~ spl21_9
| spl21_128 ),
inference(resolution,[],[f1044,f233]) ).
fof(f1044,plain,
( ~ ilf_type(ordered_pair(sK9,sK8),set_type)
| spl21_128 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f1047,plain,
( ~ spl21_9
| spl21_126 ),
inference(avatar_contradiction_clause,[],[f1046]) ).
fof(f1046,plain,
( $false
| ~ spl21_9
| spl21_126 ),
inference(resolution,[],[f1036,f233]) ).
fof(f1036,plain,
( ~ ilf_type(sK7,set_type)
| spl21_126 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f1045,plain,
( ~ spl21_126
| ~ spl21_127
| ~ spl21_128
| ~ spl21_12
| ~ spl21_29 ),
inference(avatar_split_clause,[],[f1025,f321,f245,f1042,f1038,f1034]) ).
fof(f321,plain,
( spl21_29
<=> ! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_29])]) ).
fof(f1025,plain,
( ~ ilf_type(ordered_pair(sK9,sK8),set_type)
| ~ empty(sK7)
| ~ ilf_type(sK7,set_type)
| ~ spl21_12
| ~ spl21_29 ),
inference(resolution,[],[f247,f322]) ).
fof(f322,plain,
( ! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_29 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f1030,plain,
( ~ spl21_125
| spl21_6
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f1019,f645,f218,f1027]) ).
fof(f1019,plain,
( ~ member(sK8,image(sK7,sK5))
| spl21_6
| ~ spl21_72 ),
inference(forward_demodulation,[],[f219,f646]) ).
fof(f219,plain,
( ~ member(sK8,image4(sK6,sK4,sK7,sK5))
| spl21_6 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f1018,plain,
( spl21_3
| ~ spl21_63
| spl21_124
| ~ spl21_47
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f752,f663,f409,f1016,f588,f203]) ).
fof(f203,plain,
( spl21_3
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).
fof(f409,plain,
( spl21_47
<=> ! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_47])]) ).
fof(f663,plain,
( spl21_76
<=> ! [X0] :
( ~ member(sK8,image(sK7,X0))
| ~ member(sK16(X0,sK8,sK7),sK5)
| ~ ilf_type(sK16(X0,sK8,sK7),member_type(sK6))
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_76])]) ).
fof(f752,plain,
( ! [X0] :
( ~ member(sK16(X0,sK8,sK7),sK5)
| ~ member(sK8,image(sK7,X0))
| ~ ilf_type(X0,set_type)
| ~ member(sK16(X0,sK8,sK7),sK6)
| ~ ilf_type(sK6,set_type)
| empty(sK6)
| ~ ilf_type(sK16(X0,sK8,sK7),set_type) )
| ~ spl21_47
| ~ spl21_76 ),
inference(resolution,[],[f664,f410]) ).
fof(f410,plain,
( ! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) )
| ~ spl21_47 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f664,plain,
( ! [X0] :
( ~ ilf_type(sK16(X0,sK8,sK7),member_type(sK6))
| ~ member(sK16(X0,sK8,sK7),sK5)
| ~ member(sK8,image(sK7,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_76 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f1013,plain,
( spl21_123
| ~ spl21_9
| ~ spl21_81 ),
inference(avatar_split_clause,[],[f703,f700,f232,f1011]) ).
fof(f700,plain,
( spl21_81
<=> ! [X0] :
( ~ ilf_type(sK10(X0),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_81])]) ).
fof(f703,plain,
( ! [X0] :
( ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) )
| ~ spl21_9
| ~ spl21_81 ),
inference(resolution,[],[f701,f233]) ).
fof(f701,plain,
( ! [X0] :
( ~ ilf_type(sK10(X0),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) )
| ~ spl21_81 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f1009,plain,
( spl21_122
| ~ spl21_79
| ~ spl21_120 ),
inference(avatar_split_clause,[],[f999,f995,f690,f1006]) ).
fof(f690,plain,
( spl21_79
<=> relation_like(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_79])]) ).
fof(f999,plain,
( sP0(sK7)
| ~ spl21_79
| ~ spl21_120 ),
inference(resolution,[],[f996,f691]) ).
fof(f691,plain,
( relation_like(sK7)
| ~ spl21_79 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f1004,plain,
( spl21_121
| ~ spl21_9
| ~ spl21_80 ),
inference(avatar_split_clause,[],[f698,f695,f232,f1002]) ).
fof(f1002,plain,
( spl21_121
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_121])]) ).
fof(f695,plain,
( spl21_80
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_80])]) ).
fof(f698,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl21_9
| ~ spl21_80 ),
inference(resolution,[],[f696,f233]) ).
fof(f696,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| unordered_pair(X0,X1) = unordered_pair(X1,X0) )
| ~ spl21_80 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f997,plain,
( spl21_120
| ~ spl21_15
| ~ spl21_19 ),
inference(avatar_split_clause,[],[f296,f275,f259,f995]) ).
fof(f259,plain,
( spl21_15
<=> ! [X0] :
( sP0(X0)
| ~ relation_like(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).
fof(f275,plain,
( spl21_19
<=> ! [X0] : sP1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).
fof(f296,plain,
( ! [X0] :
( ~ relation_like(X0)
| sP0(X0) )
| ~ spl21_15
| ~ spl21_19 ),
inference(resolution,[],[f276,f260]) ).
fof(f260,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ relation_like(X0)
| sP0(X0) )
| ~ spl21_15 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f276,plain,
( ! [X0] : sP1(X0)
| ~ spl21_19 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f993,plain,
( spl21_119
| ~ spl21_16
| ~ spl21_19 ),
inference(avatar_split_clause,[],[f295,f275,f263,f991]) ).
fof(f991,plain,
( spl21_119
<=> ! [X0] :
( ~ sP0(X0)
| relation_like(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_119])]) ).
fof(f263,plain,
( spl21_16
<=> ! [X0] :
( relation_like(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).
fof(f295,plain,
( ! [X0] :
( ~ sP0(X0)
| relation_like(X0) )
| ~ spl21_16
| ~ spl21_19 ),
inference(resolution,[],[f276,f264]) ).
fof(f264,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| relation_like(X0) )
| ~ spl21_16 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f987,plain,
( spl21_118
| ~ spl21_9
| ~ spl21_74 ),
inference(avatar_split_clause,[],[f657,f654,f232,f985]) ).
fof(f654,plain,
( spl21_74
<=> ! [X0,X1] :
( sP3(X0,X1)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_74])]) ).
fof(f657,plain,
( ! [X0,X1] : sP3(X0,X1)
| ~ spl21_9
| ~ spl21_74 ),
inference(resolution,[],[f655,f233]) ).
fof(f655,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| sP3(X0,X1) )
| ~ spl21_74 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f983,plain,
( ~ spl21_117
| ~ spl21_37
| spl21_68
| ~ spl21_41
| ~ spl21_59 ),
inference(avatar_split_clause,[],[f547,f506,f383,f624,f358,f980]) ).
fof(f980,plain,
( spl21_117
<=> sP0(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_117])]) ).
fof(f624,plain,
( spl21_68
<=> sK8 = ordered_pair(sK11(sK8),sK12(sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_68])]) ).
fof(f506,plain,
( spl21_59
<=> member(sK8,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_59])]) ).
fof(f547,plain,
( sK8 = ordered_pair(sK11(sK8),sK12(sK8))
| ~ ilf_type(sK8,set_type)
| ~ sP0(sK4)
| ~ spl21_41
| ~ spl21_59 ),
inference(resolution,[],[f508,f384]) ).
fof(f508,plain,
( member(sK8,sK4)
| ~ spl21_59 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f977,plain,
( spl21_116
| ~ spl21_41
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f477,f469,f383,f975]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ordered_pair(sK16(X2,X0,X1),X0) = ordered_pair(sK11(ordered_pair(sK16(X2,X0,X1),X0)),sK12(ordered_pair(sK16(X2,X0,X1),X0)))
| ~ ilf_type(ordered_pair(sK16(X2,X0,X1),X0),set_type)
| ~ sP0(X1) )
| ~ spl21_41
| ~ spl21_52 ),
inference(resolution,[],[f470,f384]) ).
fof(f962,plain,
( spl21_115
| ~ spl21_50
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f479,f469,f450,f960]) ).
fof(f479,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(power_set(X1),X2))
| ~ ilf_type(power_set(X1),binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,ordered_pair(sK16(X2,X0,power_set(X1)),X0))
| ~ ilf_type(X3,set_type)
| member(X3,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X0,power_set(X1)),X0),set_type) )
| ~ spl21_50
| ~ spl21_52 ),
inference(resolution,[],[f470,f451]) ).
fof(f947,plain,
( spl21_114
| ~ spl21_50
| ~ spl21_51 ),
inference(avatar_split_clause,[],[f466,f459,f450,f945]) ).
fof(f466,plain,
( ! [X2,X3,X0,X1] :
( ~ member(X0,image(X1,power_set(X2)))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X2),set_type)
| ~ member(X3,sK16(power_set(X2),X0,X1))
| ~ ilf_type(X3,set_type)
| member(X3,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(power_set(X2),X0,X1),set_type) )
| ~ spl21_50
| ~ spl21_51 ),
inference(resolution,[],[f460,f451]) ).
fof(f942,plain,
( spl21_113
| ~ spl21_41
| ~ spl21_51 ),
inference(avatar_split_clause,[],[f464,f459,f383,f940]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| sK16(X2,X0,X1) = ordered_pair(sK11(sK16(X2,X0,X1)),sK12(sK16(X2,X0,X1)))
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ sP0(X2) )
| ~ spl21_41
| ~ spl21_51 ),
inference(resolution,[],[f460,f384]) ).
fof(f937,plain,
( spl21_112
| ~ spl21_52
| ~ spl21_56 ),
inference(avatar_split_clause,[],[f513,f494,f469,f935]) ).
fof(f513,plain,
( ! [X2,X3,X0,X1,X4] :
( member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_56 ),
inference(duplicate_literal_removal,[],[f512]) ).
fof(f512,plain,
( ! [X2,X3,X0,X1,X4] :
( member(sK16(X0,X1,X2),X3)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_56 ),
inference(resolution,[],[f495,f470]) ).
fof(f929,plain,
( ~ spl21_111
| spl21_36
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f835,f645,f354,f926]) ).
fof(f926,plain,
( spl21_111
<=> empty(image(sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_111])]) ).
fof(f354,plain,
( spl21_36
<=> empty(image4(sK6,sK4,sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_36])]) ).
fof(f835,plain,
( ~ empty(image(sK7,sK5))
| spl21_36
| ~ spl21_72 ),
inference(superposition,[],[f356,f646]) ).
fof(f356,plain,
( ~ empty(image4(sK6,sK4,sK7,sK5))
| spl21_36 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f924,plain,
( spl21_110
| ~ spl21_48
| ~ spl21_53 ),
inference(avatar_split_clause,[],[f480,f473,f437,f922]) ).
fof(f480,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,cross_product(X3,X4)))
| ~ ilf_type(cross_product(X3,X4),set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(image4(X2,cross_product(X3,X4),X1,X0),relation_type(X3,X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_48
| ~ spl21_53 ),
inference(resolution,[],[f474,f438]) ).
fof(f915,plain,
( spl21_109
| ~ spl21_52
| ~ spl21_57 ),
inference(avatar_split_clause,[],[f515,f498,f469,f913]) ).
fof(f515,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,X1)
| ~ ilf_type(X2,relation_type(X3,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X0,image(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_52
| ~ spl21_57 ),
inference(duplicate_literal_removal,[],[f514]) ).
fof(f514,plain,
( ! [X2,X3,X0,X1,X4] :
( member(X0,X1)
| ~ ilf_type(X2,relation_type(X3,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16(X4,X0,X2),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X0,image(X2,X4))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X4,set_type) )
| ~ spl21_52
| ~ spl21_57 ),
inference(resolution,[],[f499,f470]) ).
fof(f911,plain,
( spl21_108
| ~ spl21_52
| ~ spl21_55 ),
inference(avatar_split_clause,[],[f511,f490,f469,f909]) ).
fof(f511,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,image(X2,X3))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_55 ),
inference(duplicate_literal_removal,[],[f510]) ).
fof(f510,plain,
( ! [X2,X3,X0,X1] :
( ~ member(sK16(X0,X1,X2),X3)
| member(X1,image(X2,X3))
| ~ ilf_type(sK16(X0,X1,X2),set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_52
| ~ spl21_55 ),
inference(resolution,[],[f491,f470]) ).
fof(f896,plain,
( spl21_107
| ~ spl21_42
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f457,f450,f389,f894]) ).
fof(f457,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK15(power_set(X1),X2))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK15(power_set(X1),X2),set_type)
| member(power_set(X1),power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(power_set(X1),set_type) )
| ~ spl21_42
| ~ spl21_50 ),
inference(resolution,[],[f451,f390]) ).
fof(f892,plain,
( spl21_106
| ~ spl21_40
| ~ spl21_53 ),
inference(avatar_split_clause,[],[f481,f473,f378,f890]) ).
fof(f890,plain,
( spl21_106
<=> ! [X4,X0,X3,X2,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,cross_product(X3,X4)))
| ~ ilf_type(cross_product(X3,X4),set_type)
| ~ ilf_type(X2,set_type)
| relation_like(image4(X2,cross_product(X3,X4),X1,X0))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_106])]) ).
fof(f481,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,relation_type(X2,cross_product(X3,X4)))
| ~ ilf_type(cross_product(X3,X4),set_type)
| ~ ilf_type(X2,set_type)
| relation_like(image4(X2,cross_product(X3,X4),X1,X0))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
| ~ spl21_40
| ~ spl21_53 ),
inference(resolution,[],[f474,f379]) ).
fof(f877,plain,
( ~ spl21_105
| spl21_67
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f834,f645,f620,f874]) ).
fof(f874,plain,
( spl21_105
<=> sP0(image(sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_105])]) ).
fof(f620,plain,
( spl21_67
<=> sP0(image4(sK6,sK4,sK7,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_67])]) ).
fof(f834,plain,
( ~ sP0(image(sK7,sK5))
| spl21_67
| ~ spl21_72 ),
inference(superposition,[],[f622,f646]) ).
fof(f622,plain,
( ~ sP0(image4(sK6,sK4,sK7,sK5))
| spl21_67 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f861,plain,
( spl21_104
| ~ spl21_33
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f456,f450,f342,f859]) ).
fof(f456,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK14(power_set(X1),X2))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK14(power_set(X1),X2),set_type)
| member(sK14(power_set(X1),X2),X2)
| sP2(power_set(X1),X2) )
| ~ spl21_33
| ~ spl21_50 ),
inference(resolution,[],[f451,f343]) ).
fof(f857,plain,
( spl21_103
| ~ spl21_33
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f455,f450,f342,f855]) ).
fof(f455,plain,
( ! [X2,X0,X1] :
( ~ member(X0,sK14(X1,power_set(X2)))
| ~ ilf_type(X0,set_type)
| member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK14(X1,power_set(X2)),set_type)
| member(sK14(X1,power_set(X2)),X1)
| sP2(X1,power_set(X2)) )
| ~ spl21_33
| ~ spl21_50 ),
inference(resolution,[],[f451,f343]) ).
fof(f852,plain,
( spl21_102
| ~ spl21_41
| ~ spl21_42 ),
inference(avatar_split_clause,[],[f418,f389,f383,f850]) ).
fof(f418,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| sK15(X0,X1) = ordered_pair(sK11(sK15(X0,X1)),sK12(sK15(X0,X1)))
| ~ ilf_type(sK15(X0,X1),set_type)
| ~ sP0(X0) )
| ~ spl21_41
| ~ spl21_42 ),
inference(resolution,[],[f390,f384]) ).
fof(f846,plain,
( spl21_101
| ~ spl21_33
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f417,f383,f342,f844]) ).
fof(f417,plain,
( ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ sP0(X0)
| member(sK14(X0,X1),X1)
| sP2(X0,X1) )
| ~ spl21_33
| ~ spl21_41 ),
inference(resolution,[],[f384,f343]) ).
fof(f842,plain,
( spl21_100
| ~ spl21_33
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f416,f383,f342,f840]) ).
fof(f416,plain,
( ! [X0,X1] :
( sK14(X0,X1) = ordered_pair(sK11(sK14(X0,X1)),sK12(sK14(X0,X1)))
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ sP0(X1)
| member(sK14(X0,X1),X0)
| sP2(X0,X1) )
| ~ spl21_33
| ~ spl21_41 ),
inference(resolution,[],[f384,f343]) ).
fof(f833,plain,
( spl21_99
| ~ spl21_29
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f478,f469,f321,f831]) ).
fof(f478,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(ordered_pair(sK16(X2,X0,X1),X0),set_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_29
| ~ spl21_52 ),
inference(resolution,[],[f470,f322]) ).
fof(f818,plain,
( spl21_98
| ~ spl21_24
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f454,f450,f300,f816]) ).
fof(f454,plain,
( ! [X0,X1] :
( ~ member(X0,sK13(power_set(X1)))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK13(power_set(X1)),set_type)
| empty(power_set(X1))
| ~ ilf_type(power_set(X1),set_type) )
| ~ spl21_24
| ~ spl21_50 ),
inference(resolution,[],[f451,f301]) ).
fof(f801,plain,
( spl21_97
| ~ spl21_38
| ~ spl21_54 ),
inference(avatar_split_clause,[],[f488,f483,f363,f799]) ).
fof(f488,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| image4(X1,X2,sK17(X2,X1),X0) = image(sK17(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_38
| ~ spl21_54 ),
inference(duplicate_literal_removal,[],[f487]) ).
fof(f487,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| image4(X1,X2,sK17(X2,X1),X0) = image(sK17(X2,X1),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) )
| ~ spl21_38
| ~ spl21_54 ),
inference(resolution,[],[f484,f364]) ).
fof(f797,plain,
( spl21_96
| ~ spl21_29
| ~ spl21_51 ),
inference(avatar_split_clause,[],[f467,f459,f321,f795]) ).
fof(f467,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ empty(X2) )
| ~ spl21_29
| ~ spl21_51 ),
inference(duplicate_literal_removal,[],[f465]) ).
fof(f465,plain,
( ! [X2,X0,X1] :
( ~ member(X0,image(X1,X2))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(sK16(X2,X0,X1),set_type)
| ~ empty(X2)
| ~ ilf_type(X2,set_type) )
| ~ spl21_29
| ~ spl21_51 ),
inference(resolution,[],[f460,f322]) ).
fof(f793,plain,
( spl21_95
| ~ spl21_17
| ~ spl21_50 ),
inference(avatar_split_clause,[],[f453,f450,f267,f791]) ).
fof(f453,plain,
( ! [X0,X1] :
( ~ member(X0,sK10(power_set(X1)))
| ~ ilf_type(X0,set_type)
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(sK10(power_set(X1)),set_type)
| sP0(power_set(X1)) )
| ~ spl21_17
| ~ spl21_50 ),
inference(resolution,[],[f451,f268]) ).
fof(f772,plain,
( spl21_94
| ~ spl21_45
| ~ spl21_47 ),
inference(avatar_split_clause,[],[f435,f409,f401,f770]) ).
fof(f401,plain,
( spl21_45
<=> ! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_45])]) ).
fof(f435,plain,
( ! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_45
| ~ spl21_47 ),
inference(duplicate_literal_removal,[],[f432]) ).
fof(f432,plain,
( ! [X0,X1] :
( ~ member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_45
| ~ spl21_47 ),
inference(resolution,[],[f410,f402]) ).
fof(f402,plain,
( ! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_45 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f768,plain,
( spl21_93
| ~ spl21_44
| ~ spl21_46 ),
inference(avatar_split_clause,[],[f431,f405,f397,f766]) ).
fof(f397,plain,
( spl21_44
<=> ! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_44])]) ).
fof(f405,plain,
( spl21_46
<=> ! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_46])]) ).
fof(f431,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type) )
| ~ spl21_44
| ~ spl21_46 ),
inference(duplicate_literal_removal,[],[f426]) ).
fof(f426,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(power_set(X1),set_type)
| empty(power_set(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_44
| ~ spl21_46 ),
inference(resolution,[],[f406,f398]) ).
fof(f398,plain,
( ! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_44 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f406,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) )
| ~ spl21_46 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f764,plain,
( spl21_92
| ~ spl21_27
| ~ spl21_45 ),
inference(avatar_split_clause,[],[f424,f401,f313,f762]) ).
fof(f313,plain,
( spl21_27
<=> ! [X0] :
( ilf_type(sK19(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_27])]) ).
fof(f424,plain,
( ! [X0] :
( ilf_type(sK19(power_set(X0)),subset_type(X0))
| ~ ilf_type(sK19(power_set(X0)),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(power_set(X0),set_type)
| empty(power_set(X0)) )
| ~ spl21_27
| ~ spl21_45 ),
inference(resolution,[],[f402,f314]) ).
fof(f314,plain,
( ! [X0] :
( ilf_type(sK19(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) )
| ~ spl21_27 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f760,plain,
( spl21_91
| ~ spl21_24
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f415,f383,f300,f758]) ).
fof(f415,plain,
( ! [X0] :
( sK13(X0) = ordered_pair(sK11(sK13(X0)),sK12(sK13(X0)))
| ~ ilf_type(sK13(X0),set_type)
| ~ sP0(X0)
| empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_24
| ~ spl21_41 ),
inference(resolution,[],[f384,f301]) ).
fof(f750,plain,
( spl21_79
| ~ spl21_63
| ~ spl21_58
| ~ spl21_5
| ~ spl21_83 ),
inference(avatar_split_clause,[],[f713,f709,f213,f502,f588,f690]) ).
fof(f713,plain,
( ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK6,set_type)
| relation_like(sK7)
| ~ spl21_5
| ~ spl21_83 ),
inference(resolution,[],[f710,f215]) ).
fof(f749,plain,
( spl21_90
| ~ spl21_22
| ~ spl21_48 ),
inference(avatar_split_clause,[],[f444,f437,f288,f747]) ).
fof(f444,plain,
( ! [X0,X1] :
( ilf_type(sK18(cross_product(X0,X1)),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) )
| ~ spl21_22
| ~ spl21_48 ),
inference(resolution,[],[f438,f289]) ).
fof(f743,plain,
( spl21_89
| ~ spl21_29
| ~ spl21_33 ),
inference(avatar_split_clause,[],[f368,f342,f321,f741]) ).
fof(f368,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X1)
| sP2(X0,X1)
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_29
| ~ spl21_33 ),
inference(resolution,[],[f343,f322]) ).
fof(f739,plain,
( spl21_88
| ~ spl21_29
| ~ spl21_33 ),
inference(avatar_split_clause,[],[f367,f342,f321,f737]) ).
fof(f367,plain,
( ! [X0,X1] :
( member(sK14(X0,X1),X0)
| sP2(X0,X1)
| ~ ilf_type(sK14(X0,X1),set_type)
| ~ empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ spl21_29
| ~ spl21_33 ),
inference(resolution,[],[f343,f322]) ).
fof(f734,plain,
( spl21_87
| ~ spl21_29
| ~ spl21_42 ),
inference(avatar_split_clause,[],[f420,f389,f321,f732]) ).
fof(f420,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(X0,X1),set_type)
| ~ empty(X0) )
| ~ spl21_29
| ~ spl21_42 ),
inference(duplicate_literal_removal,[],[f419]) ).
fof(f419,plain,
( ! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK15(X0,X1),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_29
| ~ spl21_42 ),
inference(resolution,[],[f390,f322]) ).
fof(f729,plain,
( spl21_86
| ~ spl21_9
| ~ spl21_80
| ~ spl21_85 ),
inference(avatar_split_clause,[],[f724,f721,f695,f232,f727]) ).
fof(f721,plain,
( spl21_85
<=> ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_85])]) ).
fof(f724,plain,
( ! [X0,X1] :
( ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_9
| ~ spl21_80
| ~ spl21_85 ),
inference(forward_demodulation,[],[f722,f698]) ).
fof(f722,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) )
| ~ spl21_85 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f723,plain,
( spl21_85
| ~ spl21_9
| ~ spl21_61 ),
inference(avatar_split_clause,[],[f576,f520,f232,f721]) ).
fof(f520,plain,
( spl21_61
<=> ! [X2,X3] :
( ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(ordered_pair(X2,X3),set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_61])]) ).
fof(f576,plain,
( ! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)) )
| ~ spl21_9
| ~ spl21_61 ),
inference(resolution,[],[f521,f233]) ).
fof(f521,plain,
( ! [X2,X3] :
( ~ ilf_type(ordered_pair(X2,X3),set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2)) )
| ~ spl21_61 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f719,plain,
( spl21_84
| ~ spl21_22
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f381,f378,f288,f717]) ).
fof(f381,plain,
( ! [X0,X1] :
( relation_like(sK18(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) )
| ~ spl21_22
| ~ spl21_40 ),
inference(resolution,[],[f379,f289]) ).
fof(f711,plain,
( spl21_83
| ~ spl21_40
| ~ spl21_49 ),
inference(avatar_split_clause,[],[f447,f441,f378,f709]) ).
fof(f447,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0) )
| ~ spl21_40
| ~ spl21_49 ),
inference(duplicate_literal_removal,[],[f446]) ).
fof(f446,plain,
( ! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) )
| ~ spl21_40
| ~ spl21_49 ),
inference(resolution,[],[f442,f379]) ).
fof(f707,plain,
( spl21_82
| ~ spl21_27
| ~ spl21_46 ),
inference(avatar_split_clause,[],[f430,f405,f313,f705]) ).
fof(f430,plain,
( ! [X0] :
( member(sK19(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(sK19(X0),set_type) )
| ~ spl21_27
| ~ spl21_46 ),
inference(duplicate_literal_removal,[],[f429]) ).
fof(f429,plain,
( ! [X0] :
( member(sK19(X0),X0)
| ~ ilf_type(X0,set_type)
| empty(X0)
| ~ ilf_type(sK19(X0),set_type)
| ~ ilf_type(X0,set_type)
| empty(X0) )
| ~ spl21_27
| ~ spl21_46 ),
inference(resolution,[],[f406,f314]) ).
fof(f702,plain,
( spl21_81
| ~ spl21_17
| ~ spl21_29 ),
inference(avatar_split_clause,[],[f326,f321,f267,f700]) ).
fof(f326,plain,
( ! [X0] :
( ~ ilf_type(sK10(X0),set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type)
| sP0(X0) )
| ~ spl21_17
| ~ spl21_29 ),
inference(resolution,[],[f322,f268]) ).
fof(f697,plain,
( spl21_80
| ~ spl21_9
| ~ spl21_32 ),
inference(avatar_split_clause,[],[f366,f338,f232,f695]) ).
fof(f338,plain,
( spl21_32
<=> ! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_32])]) ).
fof(f366,plain,
( ! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_32 ),
inference(resolution,[],[f339,f233]) ).
fof(f339,plain,
( ! [X0,X1] :
( ~ ilf_type(X1,set_type)
| unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_32 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f693,plain,
( ~ spl21_79
| ~ spl21_73
| spl21_75 ),
inference(avatar_split_clause,[],[f666,f659,f649,f690]) ).
fof(f649,plain,
( spl21_73
<=> ! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_73])]) ).
fof(f666,plain,
( ~ relation_like(sK7)
| ~ spl21_73
| spl21_75 ),
inference(resolution,[],[f661,f650]) ).
fof(f650,plain,
( ! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) )
| ~ spl21_73 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f661,plain,
( ~ ilf_type(sK7,binary_relation_type)
| spl21_75 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f683,plain,
( spl21_78
| ~ spl21_33 ),
inference(avatar_split_clause,[],[f369,f342,f681]) ).
fof(f681,plain,
( spl21_78
<=> ! [X0] :
( member(sK14(X0,X0),X0)
| sP2(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_78])]) ).
fof(f369,plain,
( ! [X0] :
( member(sK14(X0,X0),X0)
| sP2(X0,X0) )
| ~ spl21_33 ),
inference(factoring,[],[f343]) ).
fof(f670,plain,
( spl21_77
| ~ spl21_42
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f422,f393,f389,f668]) ).
fof(f422,plain,
( ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type) )
| ~ spl21_42
| ~ spl21_43 ),
inference(duplicate_literal_removal,[],[f421]) ).
fof(f421,plain,
( ! [X0] :
( member(X0,power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) )
| ~ spl21_42
| ~ spl21_43 ),
inference(resolution,[],[f394,f390]) ).
fof(f665,plain,
( ~ spl21_37
| ~ spl21_75
| spl21_76
| ~ spl21_11
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f476,f469,f241,f663,f659,f358]) ).
fof(f476,plain,
( ! [X0] :
( ~ member(sK8,image(sK7,X0))
| ~ ilf_type(sK7,binary_relation_type)
| ~ ilf_type(sK8,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK16(X0,sK8,sK7),member_type(sK6))
| ~ member(sK16(X0,sK8,sK7),sK5) )
| ~ spl21_11
| ~ spl21_52 ),
inference(resolution,[],[f470,f242]) ).
fof(f656,plain,
( spl21_74
| ~ spl21_9
| ~ spl21_26 ),
inference(avatar_split_clause,[],[f311,f308,f232,f654]) ).
fof(f308,plain,
( spl21_26
<=> ! [X0,X1] :
( sP3(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_26])]) ).
fof(f311,plain,
( ! [X0,X1] :
( sP3(X0,X1)
| ~ ilf_type(X0,set_type) )
| ~ spl21_9
| ~ spl21_26 ),
inference(resolution,[],[f309,f233]) ).
fof(f309,plain,
( ! [X0,X1] :
( ~ ilf_type(X1,set_type)
| sP3(X0,X1)
| ~ ilf_type(X0,set_type) )
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f651,plain,
( spl21_73
| ~ spl21_9
| ~ spl21_23 ),
inference(avatar_split_clause,[],[f298,f292,f232,f649]) ).
fof(f292,plain,
( spl21_23
<=> ! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_23])]) ).
fof(f298,plain,
( ! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) )
| ~ spl21_9
| ~ spl21_23 ),
inference(resolution,[],[f293,f233]) ).
fof(f293,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) )
| ~ spl21_23 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f647,plain,
( spl21_72
| ~ spl21_9
| ~ spl21_69 ),
inference(avatar_split_clause,[],[f632,f629,f232,f645]) ).
fof(f629,plain,
( spl21_69
<=> ! [X0] :
( ~ ilf_type(X0,set_type)
| image(sK7,X0) = image4(sK6,sK4,sK7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_69])]) ).
fof(f632,plain,
( ! [X0] : image(sK7,X0) = image4(sK6,sK4,sK7,X0)
| ~ spl21_9
| ~ spl21_69 ),
inference(resolution,[],[f630,f233]) ).
fof(f630,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| image(sK7,X0) = image4(sK6,sK4,sK7,X0) )
| ~ spl21_69 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f643,plain,
( ~ spl21_9
| spl21_70 ),
inference(avatar_contradiction_clause,[],[f642]) ).
fof(f642,plain,
( $false
| ~ spl21_9
| spl21_70 ),
inference(resolution,[],[f636,f233]) ).
fof(f636,plain,
( ~ ilf_type(sK20,set_type)
| spl21_70 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f634,plain,
( spl21_70
<=> ilf_type(sK20,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_70])]) ).
fof(f641,plain,
( ~ spl21_70
| spl21_71
| ~ spl21_10
| ~ spl21_21 ),
inference(avatar_split_clause,[],[f297,f284,f236,f638,f634]) ).
fof(f236,plain,
( spl21_10
<=> ilf_type(sK20,binary_relation_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).
fof(f284,plain,
( spl21_21
<=> ! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_21])]) ).
fof(f297,plain,
( relation_like(sK20)
| ~ ilf_type(sK20,set_type)
| ~ spl21_10
| ~ spl21_21 ),
inference(resolution,[],[f285,f238]) ).
fof(f238,plain,
( ilf_type(sK20,binary_relation_type)
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f285,plain,
( ! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0)
| ~ ilf_type(X0,set_type) )
| ~ spl21_21 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f631,plain,
( ~ spl21_63
| ~ spl21_58
| spl21_69
| ~ spl21_5
| ~ spl21_54 ),
inference(avatar_split_clause,[],[f596,f483,f213,f629,f502,f588]) ).
fof(f596,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| image(sK7,X0) = image4(sK6,sK4,sK7,X0)
| ~ ilf_type(sK4,set_type)
| ~ ilf_type(sK6,set_type) )
| ~ spl21_5
| ~ spl21_54 ),
inference(resolution,[],[f484,f215]) ).
fof(f627,plain,
( ~ spl21_67
| ~ spl21_37
| spl21_68
| ~ spl21_6
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f412,f383,f218,f624,f358,f620]) ).
fof(f412,plain,
( sK8 = ordered_pair(sK11(sK8),sK12(sK8))
| ~ ilf_type(sK8,set_type)
| ~ sP0(image4(sK6,sK4,sK7,sK5))
| ~ spl21_6
| ~ spl21_41 ),
inference(resolution,[],[f384,f220]) ).
fof(f618,plain,
( ~ spl21_65
| ~ spl21_62
| spl21_66
| ~ spl21_7
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f413,f383,f222,f615,f584,f611]) ).
fof(f611,plain,
( spl21_65
<=> sP0(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_65])]) ).
fof(f413,plain,
( sK9 = ordered_pair(sK11(sK9),sK12(sK9))
| ~ ilf_type(sK9,set_type)
| ~ sP0(sK5)
| ~ spl21_7
| ~ spl21_41 ),
inference(resolution,[],[f384,f224]) ).
fof(f224,plain,
( member(sK9,sK5)
| ~ spl21_7 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f608,plain,
( ~ spl21_9
| spl21_63 ),
inference(avatar_contradiction_clause,[],[f607]) ).
fof(f607,plain,
( $false
| ~ spl21_9
| spl21_63 ),
inference(resolution,[],[f590,f233]) ).
fof(f590,plain,
( ~ ilf_type(sK6,set_type)
| spl21_63 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f606,plain,
( ~ spl21_9
| spl21_62 ),
inference(avatar_contradiction_clause,[],[f605]) ).
fof(f605,plain,
( $false
| ~ spl21_9
| spl21_62 ),
inference(resolution,[],[f586,f233]) ).
fof(f586,plain,
( ~ ilf_type(sK9,set_type)
| spl21_62 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f595,plain,
( ~ spl21_62
| spl21_3
| ~ spl21_63
| spl21_64
| ~ spl21_8
| ~ spl21_46 ),
inference(avatar_split_clause,[],[f428,f405,f227,f592,f588,f203,f584]) ).
fof(f428,plain,
( member(sK9,sK6)
| ~ ilf_type(sK6,set_type)
| empty(sK6)
| ~ ilf_type(sK9,set_type)
| ~ spl21_8
| ~ spl21_46 ),
inference(resolution,[],[f406,f229]) ).
fof(f229,plain,
( ilf_type(sK9,member_type(sK6))
| ~ spl21_8 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f527,plain,
( ~ spl21_9
| spl21_58 ),
inference(avatar_contradiction_clause,[],[f526]) ).
fof(f526,plain,
( $false
| ~ spl21_9
| spl21_58 ),
inference(resolution,[],[f504,f233]) ).
fof(f504,plain,
( ~ ilf_type(sK4,set_type)
| spl21_58 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f524,plain,
( ~ spl21_9
| ~ spl21_60 ),
inference(avatar_contradiction_clause,[],[f523]) ).
fof(f523,plain,
( $false
| ~ spl21_9
| ~ spl21_60 ),
inference(resolution,[],[f518,f233]) ).
fof(f518,plain,
( ! [X0] : ~ ilf_type(X0,set_type)
| ~ spl21_60 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f517,plain,
( spl21_60
<=> ! [X0] : ~ ilf_type(X0,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_60])]) ).
fof(f522,plain,
( spl21_60
| spl21_60
| spl21_61 ),
inference(avatar_split_clause,[],[f190,f520,f517,f517]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) = unordered_pair(unordered_pair(X2,X3),singleton(X2))
| ~ ilf_type(ordered_pair(X2,X3),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(equality_resolution,[],[f174]) ).
fof(f174,plain,
! [X2,X3,X0,X1,X4] :
( unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4
| ordered_pair(X2,X3) != X4
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ( ordered_pair(X2,X3) = X4
| unordered_pair(unordered_pair(X2,X3),singleton(X2)) != X4 )
& ( unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4
| ordered_pair(X2,X3) != X4 ) )
| ~ ilf_type(X4,set_type) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( ordered_pair(X2,X3) = X4
<=> unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4 )
| ~ ilf_type(X4,set_type) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ordered_pair(X2,X3) = X4
<=> unordered_pair(unordered_pair(X2,X3),singleton(X2)) = X4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f509,plain,
( ~ spl21_37
| spl21_1
| ~ spl21_58
| spl21_59
| ~ spl21_4
| ~ spl21_46 ),
inference(avatar_split_clause,[],[f427,f405,f208,f506,f502,f193,f358]) ).
fof(f193,plain,
( spl21_1
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).
fof(f208,plain,
( spl21_4
<=> ilf_type(sK8,member_type(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_4])]) ).
fof(f427,plain,
( member(sK8,sK4)
| ~ ilf_type(sK4,set_type)
| empty(sK4)
| ~ ilf_type(sK8,set_type)
| ~ spl21_4
| ~ spl21_46 ),
inference(resolution,[],[f406,f210]) ).
fof(f210,plain,
( ilf_type(sK8,member_type(sK4))
| ~ spl21_4 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f500,plain,
spl21_57,
inference(avatar_split_clause,[],[f177,f498]) ).
fof(f177,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f496,plain,
spl21_56,
inference(avatar_split_clause,[],[f176,f494]) ).
fof(f176,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f492,plain,
spl21_55,
inference(avatar_split_clause,[],[f173,f490]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( member(X1,image(X2,X0))
| ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ( member(sK16(X0,X1,X2),X0)
& member(ordered_pair(sK16(X0,X1,X2),X1),X2)
& ilf_type(sK16(X0,X1,X2),set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f105,f106]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X4,X1),X2)
& ilf_type(X4,set_type) )
=> ( member(sK16(X0,X1,X2),X0)
& member(ordered_pair(sK16(X0,X1,X2),X1),X2)
& ilf_type(sK16(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X4] :
( member(X4,X0)
& member(ordered_pair(X4,X1),X2)
& ilf_type(X4,set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X1,image(X2,X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) )
| ~ member(X1,image(X2,X0)) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X1,image(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,binary_relation_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,image(X2,X0))
<=> ? [X3] :
( member(X3,X0)
& member(ordered_pair(X3,X1),X2)
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f485,plain,
spl21_54,
inference(avatar_split_clause,[],[f179,f483]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( image4(X0,X1,X2,X3) = image(X2,X3)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> image4(X0,X1,X2,X3) = image(X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p25) ).
fof(f475,plain,
spl21_53,
inference(avatar_split_clause,[],[f178,f473]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( ilf_type(image4(X0,X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(image4(X0,X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ! [X3] :
( ilf_type(X3,set_type)
=> ilf_type(image4(X0,X1,X2,X3),subset_type(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f471,plain,
spl21_52,
inference(avatar_split_clause,[],[f171,f469]) ).
fof(f171,plain,
! [X2,X0,X1] :
( member(ordered_pair(sK16(X0,X1,X2),X1),X2)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f463,plain,
( ~ spl21_9
| spl21_35 ),
inference(avatar_contradiction_clause,[],[f462]) ).
fof(f462,plain,
( $false
| ~ spl21_9
| spl21_35 ),
inference(resolution,[],[f352,f233]) ).
fof(f352,plain,
( ~ ilf_type(image4(sK6,sK4,sK7,sK5),set_type)
| spl21_35 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f350,plain,
( spl21_35
<=> ilf_type(image4(sK6,sK4,sK7,sK5),set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_35])]) ).
fof(f461,plain,
spl21_51,
inference(avatar_split_clause,[],[f172,f459]) ).
fof(f172,plain,
! [X2,X0,X1] :
( member(sK16(X0,X1,X2),X0)
| ~ member(X1,image(X2,X0))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f107]) ).
fof(f452,plain,
spl21_50,
inference(avatar_split_clause,[],[f164,f450]) ).
fof(f164,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK15(X0,X1),X1)
& member(sK15(X0,X1),X0)
& ilf_type(sK15(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK15(X0,X1),X1)
& member(sK15(X0,X1),X0)
& ilf_type(sK15(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f443,plain,
spl21_49,
inference(avatar_split_clause,[],[f155,f441]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f439,plain,
spl21_48,
inference(avatar_split_clause,[],[f154,f437]) ).
fof(f154,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f411,plain,
spl21_47,
inference(avatar_split_clause,[],[f183,f409]) ).
fof(f183,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f407,plain,
spl21_46,
inference(avatar_split_clause,[],[f182,f405]) ).
fof(f182,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f111]) ).
fof(f403,plain,
spl21_45,
inference(avatar_split_clause,[],[f169,f401]) ).
fof(f169,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(f399,plain,
spl21_44,
inference(avatar_split_clause,[],[f168,f397]) ).
fof(f168,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f103]) ).
fof(f395,plain,
spl21_43,
inference(avatar_split_clause,[],[f167,f393]) ).
fof(f167,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK15(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
fof(f391,plain,
spl21_42,
inference(avatar_split_clause,[],[f166,f389]) ).
fof(f166,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK15(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
fof(f387,plain,
( ~ spl21_9
| spl21_37 ),
inference(avatar_contradiction_clause,[],[f386]) ).
fof(f386,plain,
( $false
| ~ spl21_9
| spl21_37 ),
inference(resolution,[],[f360,f233]) ).
fof(f360,plain,
( ~ ilf_type(sK8,set_type)
| spl21_37 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f385,plain,
spl21_41,
inference(avatar_split_clause,[],[f139,f383]) ).
fof(f139,plain,
! [X0,X4] :
( ordered_pair(sK11(X4),sK12(X4)) = X4
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK10(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK10(X0),X0)
& ilf_type(sK10(X0),set_type) ) )
& ( ! [X4] :
( ( ordered_pair(sK11(X4),sK12(X4)) = X4
& ilf_type(sK12(X4),set_type)
& ilf_type(sK11(X4),set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f82,f85,f84,f83]) ).
fof(f83,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) )
=> ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK10(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK10(X0),X0)
& ilf_type(sK10(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
=> ( ? [X6] :
( ordered_pair(sK11(X4),X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(sK11(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X4] :
( ? [X6] :
( ordered_pair(sK11(X4),X6) = X4
& ilf_type(X6,set_type) )
=> ( ordered_pair(sK11(X4),sK12(X4)) = X4
& ilf_type(sK12(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( sP0(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f380,plain,
spl21_40,
inference(avatar_split_clause,[],[f180,f378]) ).
fof(f180,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f376,plain,
spl21_39,
inference(avatar_split_clause,[],[f142,f374]) ).
fof(f142,plain,
! [X2,X3,X0] :
( sP0(X0)
| ordered_pair(X2,X3) != sK10(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f86]) ).
fof(f365,plain,
spl21_38,
inference(avatar_split_clause,[],[f181,f363]) ).
fof(f181,plain,
! [X0,X1] :
( ilf_type(sK17(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( ilf_type(sK17(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f56,f109]) ).
fof(f109,plain,
! [X0,X1] :
( ? [X2] : ilf_type(X2,relation_type(X1,X0))
=> ilf_type(sK17(X0,X1),relation_type(X1,X0)) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ? [X2] : ilf_type(X2,relation_type(X1,X0))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ? [X2] : ilf_type(X2,relation_type(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f361,plain,
( ~ spl21_35
| ~ spl21_36
| ~ spl21_37
| ~ spl21_6
| ~ spl21_29 ),
inference(avatar_split_clause,[],[f324,f321,f218,f358,f354,f350]) ).
fof(f324,plain,
( ~ ilf_type(sK8,set_type)
| ~ empty(image4(sK6,sK4,sK7,sK5))
| ~ ilf_type(image4(sK6,sK4,sK7,sK5),set_type)
| ~ spl21_6
| ~ spl21_29 ),
inference(resolution,[],[f322,f220]) ).
fof(f348,plain,
spl21_34,
inference(avatar_split_clause,[],[f162,f346]) ).
fof(f162,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ member(sK14(X0,X1),X0)
| ~ member(sK14(X0,X1),X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ member(sK14(X0,X1),X0)
| ~ member(sK14(X0,X1),X1) )
& ( member(sK14(X0,X1),X0)
| member(sK14(X0,X1),X1) )
& ilf_type(sK14(X0,X1),set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| ~ ilf_type(X3,set_type) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f96,f97]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) )
& ilf_type(X2,set_type) )
=> ( ( ~ member(sK14(X0,X1),X0)
| ~ member(sK14(X0,X1),X1) )
& ( member(sK14(X0,X1),X0)
| member(sK14(X0,X1),X1) )
& ilf_type(sK14(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) )
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| ~ ilf_type(X3,set_type) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) )
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ! [X2] :
( ( member(X2,X0)
<=> member(X2,X1) )
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f344,plain,
spl21_33,
inference(avatar_split_clause,[],[f161,f342]) ).
fof(f161,plain,
! [X0,X1] :
( sP2(X0,X1)
| member(sK14(X0,X1),X0)
| member(sK14(X0,X1),X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f340,plain,
spl21_32,
inference(avatar_split_clause,[],[f153,f338]) ).
fof(f153,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ! [X1] :
( unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> unordered_pair(X0,X1) = unordered_pair(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f336,plain,
spl21_31,
inference(avatar_split_clause,[],[f159,f334]) ).
fof(f334,plain,
( spl21_31
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_31])]) ).
fof(f159,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f332,plain,
spl21_30,
inference(avatar_split_clause,[],[f158,f330]) ).
fof(f330,plain,
( spl21_30
<=> ! [X0,X1,X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_30])]) ).
fof(f158,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f323,plain,
spl21_29,
inference(avatar_split_clause,[],[f144,f321]) ).
fof(f144,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK13(X0),X0)
& ilf_type(sK13(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f88,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK13(X0),X0)
& ilf_type(sK13(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f319,plain,
( spl21_28
| ~ spl21_9
| ~ spl21_20 ),
inference(avatar_split_clause,[],[f282,f279,f232,f317]) ).
fof(f317,plain,
( spl21_28
<=> ! [X0] :
( relation_like(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_28])]) ).
fof(f279,plain,
( spl21_20
<=> ! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_20])]) ).
fof(f282,plain,
( ! [X0] :
( relation_like(X0)
| ~ empty(X0) )
| ~ spl21_9
| ~ spl21_20 ),
inference(resolution,[],[f280,f233]) ).
fof(f280,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| relation_like(X0)
| ~ empty(X0) )
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f315,plain,
spl21_27,
inference(avatar_split_clause,[],[f185,f313]) ).
fof(f185,plain,
! [X0] :
( ilf_type(sK19(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ilf_type(sK19(X0),member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f61,f114]) ).
fof(f114,plain,
! [X0] :
( ? [X1] : ilf_type(X1,member_type(X0))
=> ilf_type(sK19(X0),member_type(X0)) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0] :
( ? [X1] : ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ? [X1] : ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ? [X1] : ilf_type(X1,member_type(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(f310,plain,
spl21_26,
inference(avatar_split_clause,[],[f163,f308]) ).
fof(f163,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f45,f68,f67]) ).
fof(f68,plain,
! [X0,X1] :
( ( X0 = X1
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2] :
( ( member(X2,X0)
<=> member(X2,X1) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
<=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f306,plain,
spl21_25,
inference(avatar_split_clause,[],[f157,f304]) ).
fof(f157,plain,
! [X0,X1] :
( X0 = X1
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( X0 = X1
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| X0 != X1 ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f68]) ).
fof(f302,plain,
spl21_24,
inference(avatar_split_clause,[],[f146,f300]) ).
fof(f146,plain,
! [X0] :
( empty(X0)
| member(sK13(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
fof(f294,plain,
spl21_23,
inference(avatar_split_clause,[],[f191,f292]) ).
fof(f191,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f290,plain,
spl21_22,
inference(avatar_split_clause,[],[f184,f288]) ).
fof(f184,plain,
! [X0] :
( ilf_type(sK18(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ilf_type(sK18(X0),subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f59,f112]) ).
fof(f112,plain,
! [X0] :
( ? [X1] : ilf_type(X1,subset_type(X0))
=> ilf_type(sK18(X0),subset_type(X0)) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0] :
( ? [X1] : ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ? [X1] : ilf_type(X1,subset_type(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
fof(f286,plain,
spl21_21,
inference(avatar_split_clause,[],[f147,f284]) ).
fof(f147,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f281,plain,
spl21_20,
inference(avatar_split_clause,[],[f186,f279]) ).
fof(f186,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ( ilf_type(X0,set_type)
& empty(X0) )
=> relation_like(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p23) ).
fof(f277,plain,
( spl21_19
| ~ spl21_9
| ~ spl21_13 ),
inference(avatar_split_clause,[],[f253,f250,f232,f275]) ).
fof(f250,plain,
( spl21_13
<=> ! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_13])]) ).
fof(f253,plain,
( ! [X0] : sP1(X0)
| ~ spl21_9
| ~ spl21_13 ),
inference(resolution,[],[f251,f233]) ).
fof(f251,plain,
( ! [X0] :
( ~ ilf_type(X0,set_type)
| sP1(X0) )
| ~ spl21_13 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f273,plain,
spl21_18,
inference(avatar_split_clause,[],[f188,f271]) ).
fof(f188,plain,
! [X1] :
( sP2(X1,X1)
| ~ sP3(X1,X1) ),
inference(equality_resolution,[],[f156]) ).
fof(f156,plain,
! [X0,X1] :
( sP2(X1,X0)
| X0 != X1
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f269,plain,
spl21_17,
inference(avatar_split_clause,[],[f141,f267]) ).
fof(f141,plain,
! [X0] :
( sP0(X0)
| member(sK10(X0),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f265,plain,
spl21_16,
inference(avatar_split_clause,[],[f136,f263]) ).
fof(f136,plain,
! [X0] :
( relation_like(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ( ( relation_like(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ relation_like(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( relation_like(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f261,plain,
spl21_15,
inference(avatar_split_clause,[],[f135,f259]) ).
fof(f135,plain,
! [X0] :
( sP0(X0)
| ~ relation_like(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f257,plain,
spl21_14,
inference(avatar_split_clause,[],[f133,f255]) ).
fof(f133,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f252,plain,
spl21_13,
inference(avatar_split_clause,[],[f143,f250]) ).
fof(f143,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f37,f65,f64]) ).
fof(f37,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( relation_like(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
=> ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f248,plain,
( spl21_6
| spl21_12 ),
inference(avatar_split_clause,[],[f127,f245,f218]) ).
fof(f127,plain,
( member(ordered_pair(sK9,sK8),sK7)
| member(sK8,image4(sK6,sK4,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,sK8),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(sK8,image4(sK6,sK4,sK7,sK5)) )
& ( ( member(sK9,sK5)
& member(ordered_pair(sK9,sK8),sK7)
& ilf_type(sK9,member_type(sK6)) )
| member(sK8,image4(sK6,sK4,sK7,sK5)) )
& ilf_type(sK8,member_type(sK4))
& ilf_type(sK7,relation_type(sK6,sK4))
& ilf_type(sK6,set_type)
& ~ empty(sK6)
& ilf_type(sK5,set_type)
& ~ empty(sK5)
& ilf_type(sK4,set_type)
& ~ empty(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9])],[f72,f78,f77,f76,f75,f74,f73]) ).
fof(f73,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,X0,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,image4(X2,X0,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,sK4,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,image4(X2,sK4,X3,X1)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(X2,sK4)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(sK4,set_type)
& ~ empty(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,sK4,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,image4(X2,sK4,X3,X1)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(X2,sK4)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,sK4,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,image4(X2,sK4,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(X2,sK4)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(sK5,set_type)
& ~ empty(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,sK4,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,image4(X2,sK4,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(X2,sK4)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
=> ( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,image4(sK6,sK4,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(sK6)) )
| member(X4,image4(sK6,sK4,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK6,sK4)) )
& ilf_type(sK6,set_type)
& ~ empty(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,image4(sK6,sK4,X3,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(sK6)) )
| member(X4,image4(sK6,sK4,X3,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(X3,relation_type(sK6,sK4)) )
=> ( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,X4),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,image4(sK6,sK4,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,X4),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(X4,image4(sK6,sK4,sK7,sK5)) )
& ilf_type(X4,member_type(sK4)) )
& ilf_type(sK7,relation_type(sK6,sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,X4),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(X4,image4(sK6,sK4,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,X4),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(X4,image4(sK6,sK4,sK7,sK5)) )
& ilf_type(X4,member_type(sK4)) )
=> ( ( ! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,sK8),sK7)
| ~ ilf_type(X5,member_type(sK6)) )
| ~ member(sK8,image4(sK6,sK4,sK7,sK5)) )
& ( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,sK8),sK7)
& ilf_type(X6,member_type(sK6)) )
| member(sK8,image4(sK6,sK4,sK7,sK5)) )
& ilf_type(sK8,member_type(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ? [X6] :
( member(X6,sK5)
& member(ordered_pair(X6,sK8),sK7)
& ilf_type(X6,member_type(sK6)) )
=> ( member(sK9,sK5)
& member(ordered_pair(sK9,sK8),sK7)
& ilf_type(sK9,member_type(sK6)) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,X0,X3,X1)) )
& ( ? [X6] :
( member(X6,X1)
& member(ordered_pair(X6,X4),X3)
& ilf_type(X6,member_type(X2)) )
| member(X4,image4(X2,X0,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,X0,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,image4(X2,X0,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ! [X5] :
( ~ member(X5,X1)
| ~ member(ordered_pair(X5,X4),X3)
| ~ ilf_type(X5,member_type(X2)) )
| ~ member(X4,image4(X2,X0,X3,X1)) )
& ( ? [X5] :
( member(X5,X1)
& member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) )
| member(X4,image4(X2,X0,X3,X1)) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,image4(X2,X0,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( member(X4,image4(X2,X0,X3,X1))
<~> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) ) )
& ilf_type(X4,member_type(X0)) )
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type)
& ~ empty(X2) )
& ilf_type(X1,set_type)
& ~ empty(X1) )
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,image4(X2,X0,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ! [X2] :
( ( ilf_type(X2,set_type)
& ~ empty(X2) )
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ! [X4] :
( ilf_type(X4,member_type(X0))
=> ( member(X4,image4(X2,X0,X3,X1))
<=> ? [X5] :
( member(X5,X1)
& member(ordered_pair(X5,X4),X3)
& ilf_type(X5,member_type(X2)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_52) ).
fof(f243,plain,
( ~ spl21_6
| spl21_11 ),
inference(avatar_split_clause,[],[f129,f241,f218]) ).
fof(f129,plain,
! [X5] :
( ~ member(X5,sK5)
| ~ member(ordered_pair(X5,sK8),sK7)
| ~ ilf_type(X5,member_type(sK6))
| ~ member(sK8,image4(sK6,sK4,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f239,plain,
spl21_10,
inference(avatar_split_clause,[],[f187,f236]) ).
fof(f187,plain,
ilf_type(sK20,binary_relation_type),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
ilf_type(sK20,binary_relation_type),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f16,f116]) ).
fof(f116,plain,
( ? [X0] : ilf_type(X0,binary_relation_type)
=> ilf_type(sK20,binary_relation_type) ),
introduced(choice_axiom,[]) ).
fof(f16,axiom,
? [X0] : ilf_type(X0,binary_relation_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p16) ).
fof(f234,plain,
spl21_9,
inference(avatar_split_clause,[],[f130,f232]) ).
fof(f130,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f230,plain,
( spl21_6
| spl21_8 ),
inference(avatar_split_clause,[],[f126,f227,f218]) ).
fof(f126,plain,
( ilf_type(sK9,member_type(sK6))
| member(sK8,image4(sK6,sK4,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f225,plain,
( spl21_6
| spl21_7 ),
inference(avatar_split_clause,[],[f128,f222,f218]) ).
fof(f128,plain,
( member(sK9,sK5)
| member(sK8,image4(sK6,sK4,sK7,sK5)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f216,plain,
spl21_5,
inference(avatar_split_clause,[],[f124,f213]) ).
fof(f124,plain,
ilf_type(sK7,relation_type(sK6,sK4)),
inference(cnf_transformation,[],[f79]) ).
fof(f211,plain,
spl21_4,
inference(avatar_split_clause,[],[f125,f208]) ).
fof(f125,plain,
ilf_type(sK8,member_type(sK4)),
inference(cnf_transformation,[],[f79]) ).
fof(f206,plain,
~ spl21_3,
inference(avatar_split_clause,[],[f122,f203]) ).
fof(f122,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f79]) ).
fof(f201,plain,
~ spl21_2,
inference(avatar_split_clause,[],[f120,f198]) ).
fof(f198,plain,
( spl21_2
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).
fof(f120,plain,
~ empty(sK5),
inference(cnf_transformation,[],[f79]) ).
fof(f196,plain,
~ spl21_1,
inference(avatar_split_clause,[],[f118,f193]) ).
fof(f118,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET685+3 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 01:03:49 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (30854)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (30857)WARNING: value z3 for option sas not known
% 0.21/0.38 % (30858)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (30855)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (30856)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (30861)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 % (30859)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)
% 0.21/0.38 % (30860)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)
% 0.21/0.38 % (30857)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)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [1]
% 0.21/0.41 TRYING [2]
% 0.21/0.44 TRYING [4]
% 0.21/0.45 TRYING [3]
% 1.36/0.55 % (30859)First to succeed.
% 1.51/0.57 % (30859)Refutation found. Thanks to Tanya!
% 1.51/0.57 % SZS status Theorem for theBenchmark
% 1.51/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.51/0.59 % (30859)------------------------------
% 1.51/0.59 % (30859)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.51/0.59 % (30859)Termination reason: Refutation
% 1.51/0.59
% 1.51/0.59 % (30859)Memory used [KB]: 2851
% 1.51/0.59 % (30859)Time elapsed: 0.191 s
% 1.51/0.59 % (30859)Instructions burned: 274 (million)
% 1.51/0.59 % (30859)------------------------------
% 1.51/0.59 % (30859)------------------------------
% 1.51/0.59 % (30854)Success in time 0.219 s
%------------------------------------------------------------------------------